Meteoritics amp Planetary Science 38 Nr 7 989ndash1003 (2003)Abstract available online at httpmeteoriticsorg

989 copy Meteoritical Society 2003 Printed in USA

The Moraacutevka meteorite fall 2 Interpretation of infrasonic and seismic data

P G BROWN1 P KALENDA2 D O REVELLE3 and J BOROVI Egrave KA4

1Department of Physics and Astronomy University of Western Ontario London Ontario N6A 3K7 Canada2CoalExp Kosmonautu 2 70030 Ostrava 3 The Czech Republic

3Los Alamos National Laboratory PO Box 1663 MS J557 Los Alamos New Mexico 87545 USA4Astronomical Institute of the Academy of Sciences 25165 Ondrejov The Czech Republic

Corresponding author E-mail pbrownuwoca

(Received 06 September 2002 revision accepted 19 June 2003)

AbstractndashThe sound production from the Moraacutevka fireball has been examined in detail making useof infrasound and seismic data A detailed analysis of the production and propagation of sonic wavesduring the atmospheric entry of the Moraacutevka meteoroid demonstrates that the acoustic energy wasproduced both by the hypersonic flight of the meteoroid (producing a cylindrical blast wave) and byindividual fragmentation events of the meteoroid which acted as small explosions (producing quasi-spherical shock waves) The deviation of the ray normals for the fragmentation events was found tobe as much as 30deg beyond that expected from a purely cylindrical line source blast The mainfragmentation of the bolide was confined to heights above 30 km with a possible maximum inacoustic energy production near 38 km Seismic stations recorded both the direct arrival of theairwaves (the strongest signal) as well as air-coupled P-waves and Rayleigh waves (earlier signals)In addition deep underground stations detected the seismic signature of the fireball The seismic dataalone permit reconstruction of the fireball trajectory to a precision on the order of a few degrees Thevelocity of the meteoroid is much less well-determined by these seismic data The more distantinfrasonic station detected 3 distinct signals from the fireball identified as a thermospheric return astratospheric return and an unusual mode propagating through the stratosphere horizontally and thenleaking to the receiver

INTRODUCTION

The Moraacutevka meteorite fall is undoubtedly the mostdocumented in history This ordinary chondrite fell on May 62000 in the Czech Republic while the passage of the fireballthrough the atmosphere was recorded by videographersvisual observers infrasonic microphones seismographs onthe ground and by satellites in orbit Reconstruction of thefireball trajectory and initial velocity upon entry (Boroviegrave kaet al 2003a) has permitted accurate determination of the pre-fall orbit only the seventh meteorite orbit to date Analysis ofthese fireball data together with laboratory analysis of therecovered meteorites (see Boroviegrave ka et al 2003b) hasfacilitated analysis of the orbital evolution of the Moraacutevkameteoroid while measurement of the initial mass of the pre-atmospheric body by 4 independent methods has enabledcross-calibrations of these various techniques Analysis ofvideo recordings in combination with seismic data has alsoprovided for the first time observational measurements of

high spatial and temporal resolution relating to thefragmentation behavior of a large body entering the Earthrsquosatmosphere (Boroviegrave ka and Kalenda 2003)

As part of the broad interdisciplinary study of theMoraacutevka meteorite fall this work focuses on the soundproduction accompanying the fireball By understanding theacoustic processes present in Moraacutevka we hope to establishthe observational baseline for the interpretation of otherfireball acoustic data where much less information may beavailable The acoustic energy budget is part of the broaderenergy balance associated with the entry of large meteoroids(cf Ceplecha et al 1998) and insight into its behavior is akey component to understanding the overall entry behavior ofbodies into planetary atmospheres

In particular we examine infrasonic recordings (acousticfrequencies from 001ndash20 Hz) of the Moraacutevka fireball andseismic data These include infrasonic data from FreyungGermany and seismic data from a large number of stationsthat recorded both direct acoustic arrivals and sound energy

990 Brown et al

converted to seismic waves The amount of data incombination with such a well-known fireball trajectory hasenabled analyses not done previously for any fireball Ofparticular interest is establishment of the exact nature of theacoustic source production at the fireball The prevailingtheoretical models (cf ReVelle 1976) suggest that if thesound is generated primarily by the ballistic shockaccompanying the fireballrsquos ablation the behavior of thesource should be that of a cylindrical line source In contrastif fragmentation is significant one might expect the soundproduced to be more similar to that of a moving point sourceThe primary difference between these 2 cases is that acousticrays at the source propagate normal to the fireball trajectoryfor a cylindrical line source In the case of a moving pointsource rays may deviate significantly from thisperpendicular condition though the magnitude of thisdeviation has not yet been measured and likely depends onthe nature and geometry of the associated fragmentationHowever the nature of such fragmentation events andconstraints on the sources (height deviation of rays fromnormal propagation etc) has not before been observationallydetermined with the precision possible for the Moraacutevka fallAdditionally a detailed understanding of the nature of thesound propagation the atmospheric ducts involved and theinterpretation of the associated seismic records provide aunique opportunity to study effects caused by atmosphericpropagation and to clearly separate these from source effects

SEISMIC DATA DESCRIPTION AND INTERPRETATION

In addition to the acoustic energy generated by theMoraacutevka fireball and detected directly in the atmosphere bymicrobarographs significant signal energy was transferredinto seismic vibrations and registered by a large number ofseismographs proximal to the fireball trajectory Seismic

detections of bright fireballs are not exceptional (see egCumming 1989 Cevolani 1994 Brown et al 2002b) Inparticular Qamar (1995) showed using the re-entry of theSpace Shuttle as an example that sonic waves can be used forthe determination of the height and velocity for moderatelysupersonic objects

From examination of the records of several seismicstations Brown et al (2002b) concluded that the Tagish Lakefireball produced some cylindrical shock waves in addition topossible quasi-spherical shocks produced from fragmentationevents while Anglin and Haddon (1987) were able to interpretthe seismic signature of the airwave from a bright fireball nearYellowknife Canada as due entirely to a cylindrical line-source shock In contrast the fireball associated with the Vilnameteorite fall detected by Folinsbee et al (1969) producedmost of its acoustic energy at the detonation near the end pointof its trajectory as seen from one particular seismic stationAnglin and Haddon (1987) also demonstrated the generationof individual types of waves genetically related to the primarysonic blast wave from the Yellowknife fireball Brown et al(2002b) have shown that in some cases the first waves toarrive at a distant station are the P-waves generated byacoustic coupling near the subterminal point of the trajectorywhere sound first reaches the earthrsquos surface

The above analyses were limited by either a low numberor suboptimal distribution of seismic stations andorincomplete knowledge of the fireball trajectory The Moraacutevkafireball on the other hand was registered at 16 seismicstations ranging from the immediate vicinity of the trajectoryground projection up to a distance of 180 km The stations arelisted in Table 1 and their positions are plotted in Fig 1together with the path of the fireball

The fireball flew over the core of the Seismic PolygonOKD (Ostrava-Karvina mining district) operated by the DPBPaskov firm (J Hole egrave ko personal communication) Thepolygon is formed by 7 surface or near-surface stations and 3

Table 1 List of the seismic stations that detected the Moraacutevka fireballCode Location Operator Longitude (deg E) Latitude (deg N) Altitude (m) Depth (m)

CSM Egrave SM mine DPB 185608 498004 278 0RAJ Karvinaacute-Raacutej DPB 185817 498514 272 30LUT Orlovaacute-Lutyne DPB 184150 498832 217 30PRS Prstnaacute DPB 185528 499143 205 30BMZ Ostrava-Kraacutesneacute Pole DPB 181411 498344 250 17HAV Haviacute oslash ov DPB 184763 497619 301 30CHO Chotebuz DPB 185594 497682 301 30MAJ Maacutej mine DPB 184713 498237 -365 575CSA Egrave SA mine DPB 184925 498531 -497 717KVE Kv igrave ten mine DPB 185007 498003 -141 350RAC Raciboacuterz PAN 181905 500829 214 2OJC Ojcoacutew PAN 197972 502187 300 0VRAC Vranov MU 165888 493092 470 5MORC Moravskyacute Beroun MU 175458 497752 742 5KRUC Moravskyacute Krumlov MU 163939 490611 341 0JAVC Velkaacute Javorina MU 176695 488749 827 0

The Moraacutevka meteorite fall Infrasonic and seismic data 991

deep underground stations Each station is equipped with a 3-component seismometer with a sampling frequency of 125Hz The digital recording is triggered after a seismic event isdetected at a minimum of 5 stations An 8-sec record is thenwritten For Moraacutevka the record starts at 115318744 UT(the station clocks are radio controlled) This time was too latefor stations HAV and CHO where the onset of the main signalis missing A rough analogue record shows that the onsetoccurred here a few tenths of a second earlier The digitalrecord lasts for 1 min

The fireball signal was also detected at 2 stations inPoland operated by the Polish Academy of Science (PAN PWiejacz and W Wojtak personal communication) One ofthese stations (RAC) was only 20 km from the trajectoryground projection Four stations operated by MasarykUniversity in Brno (MU J Pazdiacuterkovaacute personalcommunication) also detected the fireball The samplingfrequency at these stations was between 20 and 80 Hz

By analyzing the seismic records we were able toidentify several types of waves most visible at those stationslying some distance from the fireball trajectory where arrivaltimes are widely separated At all stations the first arrivals areair-coupled P-waves originating in the vicinity of trajectoryterminal point (ie the point where most of the meteoroidmass became subsonic) This is the lowest point of thesupersonic trajectory and the waves from this point reach theground first At the point where their surface trace velocity iscomparable to the surface P-wave velocity they aretransmitted into the ground (or alternatively they arerefracted under the critical angle according to Snellrsquos law(about 5deg) and continue to the station as near-surface groundP-waves) Subsequently P-waves from other more distantpoints along the trajectory arrive

The seismic records from stations BMZ and MORC areshown in Figs 2 and 3 respectively Both contain P-waves

The strongest signal however is associated with the directarrival of airwaves later on These first airwaves come fromthe point along the trajectory nearest the station Theypropagate as a cylindrical blast wave from the trajectory witha very small Mach cone angle given by the ratio of fireballvelocity to the speed of sound (see the section on cylindricalline source blast below) Near the end of the trajectory wherethe velocity of the meteoroid becomes very low the airwavesalso propagate as a quasi-spherical wave to the stations lyingdownrange of the trajectory terminal point (VRAC KRUCJAVC) Of course the actual shape of the wave is deformedby the varying speed of sound at various altitudes The onsetof the direct airwaves is always quite sharp in the seismicrecords and the waves have high frequencies correspondingto acoustic frequencies (50ndash2000 Hz) Although the directairwaves are under sampled on all stations they are easilyvisible in the filtered signal (Fig 3)

These direct airwaves are preceded by genetically relatedair-coupled Rayleigh waves which are formed by thetransformation of direct airwaves on the ground and movingalong the surface The amplitude of the Rayleigh wavesgradually increases until the arrival of the airwaves (Fig 2)Both types of waves can be distinguished clearly by the muchlower frequencies of the Rayleigh waves

In addition to the strong arrival of the blast wave thedirect airwave signal also contains numerous individualdisturbances (sub-maxima) We interpret these as having beengenerated by various point sources along the trajectory Thesesources are presumably connected with individual meteoroidfragmentation events The acoustic waves propagate asspherical waves from the source and the arrival time thendepends on the distance to the station We were able tolocalize a number of fragmentation events using their seismicsignatures as described in more detail in Boroviegrave ka andKalenda (2003)

Fig 1 Positions of seismic stations relative to the fireball trajectory as derived from the video records The right panel represents a detailedview of the central part Fireball altitudes in km are given in this part Deep underground stations are plotted as filled triangles

992 Brown et al

Fig 2 Seismic record from station BMZ and the description of individual wave groups The time is given in seconds after 115300 UT Thefirst P-waves arrived before the start of the record

Fig 3 Seismic record from station MORC and the description of individual wave groups The original waveform is given in the upper plotThe filtered signal with low frequencies (lt25 Hz) removed is in the lower plot

The Moraacutevka meteorite fall Infrasonic and seismic data 993

Particular emphasis has been devoted to analysis of theseismic signals recorded in the deep underground stationsHere P-waves are registered having been generated by therefraction of the airwaves on the surface A given ray comingto the underground station traverses smaller distances in theair than would be the case for detection at a station at thesurface having the same coordinates However the ray stillhas to travel through the rock down to the station Given thatthe P-wave signal velocity is typically 2ndash4 kms in near-surface rock we found that in our case (with relativelyshallow stations) these corrections are negligible and thetiming at the underground stations was therefore usedwithout change with the station depths being ignored

Table 2 provides the arrival times of different types ofwaves at each station The signal at the distant stations wasweak Acoustic ray tracing showed that stations KRUC andJAVC lie almost in the acoustic shadow with most of theairwaves reflected above the surface The identification of theP-type wave at station RAC is uncertainmdashthe given time mayin fact correspond to a seismic event not connected with thefireball

To check our identifications of the direct airwaves and todemonstrate the internal consistency of the seismic data andour interpretations of it we use the timings of the arrivals ofdirect airwaves to compute the fireball trajectory independentof the video data (cf Boroviegrave ka et al 2003a) A similarapproach was recently used independently by Ishihara et al(2001) who also studied the correlation of shock waveamplitude with meteoroid mass We used stations CSM RAJLUT PRS BMZ RAC OJC and MORC for trajectorycomputation Stations VRAC KRUC and JAVC could not beused because they lie in the region where the cylindrical wavedoes not propagate For a chosen initial latitude of 4990deg wecomputed the following 7 free parameters of the trajectorythe remaining 2 coordinates of the initial point (longitude andaltitude) the azimuth and slope of the trajectory the time offireball passage through the initial point (t0) the velocity anddeceleration of the fireball at that point The procedure wasiterative Because the speed of sound changes with

temperature ie altitude we computed the average speed ofsound from a particular altitude to each station When thefireball altitude was improved in the next iterative step theaverage sound speed was also recomputed The real measuredtemperature profile (see next section) was used to computesound speeds and in these computations the wind wasignored

The azimuth and slope of the trajectory comparefavorably to the values found from video reductions Thealtitude however is closely related to the time (t0) and bothparameters could not be determined simultaneously withgood precision We therefore used the observed satellite timeof the fireball (cf Boroviegrave ka et al 2003a) 1151525 as t0The other resulting parameters were as follows 18482deglongitude 317 km high 1720deg azimuth of the ground path198deg slope in the atmosphere (from horizontal) and 83 kmsvelocity The deceleration could not be reliably determinedthe beginning point lies only 15 km west and 300 m belowthe video trajectory the slope is within 1deg of the video dataand the azimuth differs by 35deg The velocity differssignificantly from the video value of 18 kms at 32 kmaltitude Except for the velocity we obtained reasonableresults even ignoring wind corrections We also ignored thefact that the fireball consisted of a number of laterallyseparated fragments Our good agreement with the video-determined trajectory demonstrates that the cylindrical blastwave was clearly present while the recording of numeroussub-maxima in the seismic amplitude (cf Boroviegrave ka andKalenda [2003] for details) establishes the presence ofacoustic energy from several fragmentation events producingquasi-spherical shocks

THE INFRASONIC DATA

The detection of infrasonic waves from fireballs has beenreported extensively in the past (eg ReVelle 1976 1997Evers and Haak 2001 Brown et al 2002a) However in veryfew cases have details of the trajectory velocity andfragmentation behavior of the associated fireball been

Table 2 Seismic waves first arrival times at different stationsa

CSM RAJ LUT PRS BMZ HAV CHO MAJ CSA KVE

P term ND ND ND ND ND ND ND ND ND NDRayleigh (R reg P) ND 936 962 981 124 ND ND 90 ND NDDirect-air (DA reg P) 901 964 1009 1028 1291 ND ND 9295 9526 904

RAC OJC MORC VRAC KRUC JAVC

P term 564b NS 753 815c NS NSRayleigh 1284 NS 245 182c NS 248Direct-air 1377 3389 2455 NA NA NADirect-air term NA NA NA NS 503 3079

aThe time is given in seconds after 115150 UT ND = no data at the time of expected first arrival NS = wave not seen in the data NA = not applicable Forthe underground stations (MAJ CSA KVE) the first arrival of Rayleigh and direct-air waves transformed to P-waves is given The waves designated asldquotermrdquo originate in the terminal point of the trajectory

bUncertain identificationcWeak signal near to the noise level

994 Brown et al

available comparable to the Moraacutevka fall All these detailsoffer potential insight into the source generation mechanismof the infrasound and permit us to estimate the source energyof the fireball from infrasonic records for comparison withother techniques

Infrasonic signals associated with the Moraacutevka eventwere recorded in Freyung Germany by station FREYUNG(137131deg E 488516deg N h = 1111 m) which is part of theInternational Monitoring System (IMS) of theComprehensive Test Ban Treaty (CTBT) at a distance of360 km from the fireball endpoint (see Borovi egrave ka et al2003a) The signals are shown in Fig 4 The station recordedthe airwave arrival from the fireball beginning 1182 sec afterthe fireball (121132 UT) and ceasing approximately 308 seclater at 121638 UT To define the signal characteristics weexamine the frequency spectrum of the original signal Thisspectrogram is shown in Fig 5 Here we see that the signal isvisible between 03 and 3 Hz below 03 Hz interference frommicrobaroms overwhelms the bolide signal (cf Evers andHaak [2001] for a description of microbaroms) Some signalenergy in the most energetic portions of the wave trainextends up to the Nyquist cutoff for the sensors near 9 Hz To

define the portion of the record having clear signal energyfrom the event we band pass the signals over the frequencyrange of 03ndash9 Hz and then perform a cross-correlationbetween the 4 microphones over 30 sec windows to define thedirection (azimuth) to the signal maximum cross-correlationwithin each window bin The cross-correlation result isshown in Fig 6 together with the associated directions inFig 7 This beam-forming technique is described in detail inEvers and Haak (2001)

Phenomenologically the signal consists of 3 majorportions The most obvious are the 2 signal wave trainswhich are clearly visible in the filtered amplitudes (Fig 4)The first of these major wave trains (train 1) coincides withthe onset of the signal at 121132 UT (1182 sec) andcontinues for approximately 43 sec ending near 121215 UT(1225 sec) when the amplitude decreases almost to theambient noise levels We note however that the signal cross-correlation remains well above background levels during thisamplitude minimum (Fig 6) indicating the presence ofcontinuing coherent acoustic energy from the fireball Thisongoing signal is also noticeable in the frequency spectra

The main body of the signal begins near 121237 UT(1247 sec) (train 2) Here the peak amplitude of the entiresignal occurs near 121257 UT (1267 sec) The amplitude oftrain 2 returns to near noise levels beginning at 121330 UT(1300 sec) However the cross correlation remains at least onestandard deviation above background for almost another 3minutes after this time period as can be seen in Fig 6 Indeedthe azimuth directions to maximum cross-correlation shownin Fig 7 indicate continued arrivals as seen at Freyung from65ndash67deg azimuth (azimuth is counted from north) during thisinterval beginning near 121400 UT (1330 sec) which wedesignate as train 3 This arrival is visible almost exclusivelyin cross-correlation and in the azimuth records little or noamplitude fluctuations above background are in evidence

In addition to these data Fig 8 shows the trace velocityof the signal at maximum cross-correlation in each of the

Fig 4 The recorded infrasound signal on all 4 channels at Freyungfor the Moraacutevka fireball Note that these waveforms have been bandpassed from 03ndash9 Hz to most clearly define the fireball signal

Fig 5 Frequency spectrogram of all 4 channels (channel one at topchannel four at the bottom) of the infrasound array The spectrogramgrey-scale shows gradations in dB

The Moraacutevka meteorite fall Infrasonic and seismic data 995

30 sec window bins over the course of the entire fireballairwave The trace velocity is a measure of the apparentvelocity of travel of the signal from one microphone to thenext the steeper the arrivals the higher the trace velocitiesHere we see that very little variation occurs in the tracevelocities over trains 1 and 2 with a slight possible increaseapparent over the duration of train 3 These wave train

signals are summarized in Table 3 along with times ofmaximum peak amplitudes and corresponding periods atmaximum amplitude

In the following sections we will use 2 approaches tostudy the propagation of acoustic waves from the fireballtrajectory to the station at Freyung to interpret these signalsFirst we employ a purely analytical method for a line source

Fig 6 The maximum correlation coefficient during the time centered around the Moraacutevka fireball signal at Freyung Windows of 30 sec (with50 overlap per window) are used to define individual measurements of cross-correlation The background cross-correlation in this frequencybandpass (03ndash9 Hz) calculated for the interval 3 minutes before the onset of the signal is 031 plusmn 002 and is shown by a thick solid horizontalline (mean) and thin lines representing the range of the standard deviation

Fig 7 Observed azimuths of infrasound arrival (north = 0) for each maximum in cross-correlation per bin

996 Brown et al

producing a cylindrical blast wave in a range-independentatmosphere Next a detailed numerical ray tracing approachis examined using moving point sources along the trajectoryin a range-dependent model atmosphere

INFRASONIC ANALYSIS FOR A CYLINDRICAL LINE SOURCE IN A

RANGE-INDEPENDENT ATMOSPHERE

As a means of examining the infrasound propagation in arange-independent atmosphere we can make use of thegeometrical acoustics approximation (wavelengths that aresmall compared to the pressure scale height the vertical scaleover which significant atmospheric pressure gradients canoccur) for which there are 2 constants of the motion in ahorizontally stratified steady state atmosphere that is anatmosphere with perfect stratification These constants are theheading of the wave normal (not the acoustic ray) from thesource and the characteristic velocity (Vk) generated at thesource In this approximation the arriving trace velocities atthe array are the same as the Vk values at the initial source

heights at which they were generated The characteristicvelocity can be thought of as the horizontal propagationvelocity modified for the effects of horizontal wind and entrygeometry (see ReVelle [1976] for a complete discussion)

Here we have reproduced the cylindrical line source blastwave approach developed by ReVelle (1976) In this methodthe characteristic velocity of the acoustic signal from the linesource is calculated as a function of altitude throughout theknown trajectory Due to non-steady effects or imperfectstratification (range dependent atmosphere effects etc) thevalue of the characteristic velocity is expected to be modifiedduring propagation In Figs 9 and 10 we have indicated theatmospheric structure parameters the so-called effectiveacoustic velocity (the signal propagation velocity includingwinds) and the calculated characteristic velocity (Vk) for therange of observed back azimuths from the infrasonicdetection at Freyung These parameters are all discussedfurther by Ceplecha et al (1998 p 380)

To model these acoustic arrivals we made use of theradiosonde data from Poprad Slovakia (~150 km ESE fromthe fireball) at 12 UT on May 6 2000 to define the

Fig 8 Observed trace velocities of the infrasound for each maximum in cross-correlation per bin

Table 3 Observed signal characteristics of the Moraacutevka fireball as seen from Freyung Germany on 6 May 2000 The start and end times are referenced to 115150 UT

Wave-train Start End DurationTime of max Azimuth

Peak amplitude

Trace velocity Period

Meansignal speed

(sec) (sec) (sec) (UT) (mPa) (kms) (s) (kms)

1 1180 1226 43 121142 685 638 0344 32 0302-0312plusmn07 plusmn72 plusmn0003 plusmn03

2 1247 1300 53 121257 667 2333 0355 41 0285-0297plusmn28 plusmn328 plusmn0013 plusmn08

3 1325 1490 165 ndash ndash 6 0353 ndash 0248-0279plusmn3 plusmn0026

The Moraacutevka meteorite fall Infrasonic and seismic data 997

temperature and wind field up to 30 km in altitude Above 30km we merged these radiosonde data with the MSIS-E (MassSpectrometer and Incoherent Scatter model) to produce thetemperature profile (cf Picone et al 1997) to a height of 140km inputting the appropriate geomagnetic indices for

May 6 2000 These indices significantly affect theatmospheric temperature and thus sound speed at heightsabove ~100 km The wind field above 30 km uses the HWM(Horizontal Wind Model) (Hedin et al 1996)

The propagation criterion within the geometricalacoustics approximation can be stated simply Whenever thecharacteristic velocity at the source exceeds the maximumeffective horizontal sound velocity over a given heightinterval ldquoraysrdquo will refract in such a way that they will reachthe ground (with sound waves bending away from regions ofincreasing temperatureincreasing sound speed gradients)

As indicated in Fig 10 for the altitude region from theground to ~118 km the maximum effective horizontal soundspeed is equal to 347 ms for our atmospheric conditions Forthose ldquoraysrdquo that have a Vk value greater than this valueldquorayrdquo paths exist between the line source sound generationaltitudes and points on the ground though in general only asmall subset will reach any given location (ie Freyung inour case)

Since the line source is a complicated acoustic raygeneration source we will first describe briefly the acousticradiation pattern In all cases where the velocity of themeteoroid is much higher than the local sound speed theradiation is perpendicular to the trajectory The only regionwhere this is not quite correct is near the bolide end heightwhere the Mach cone opens up substantially as the meteoroidis heavily decelerated shortly before the onset of dark flightand the fall of meteorites toward Earth Within the entryplane the vertical plane containing the trajectory that has anormal that is tangent to the earthrsquos surface immediatelybelow the mid-point of the fireball path the rays travel inexactly opposite azimuth to the heading of the bolide ietoward 3555deg (from the north) and have a downwardcomponent At the same time rays exist at all heights with anupward motion the heading of which is the same as the bolideie 1755deg but these do not generally reach the ground nearthe region of the fall ellipse and have not been examined hereAs the downward rays outside of the entry plane are examinedand we consider additional propagation directions we findthat the ray headings turn progressively toward less northerlydirections as the ray launch angle becomes less steepEventually as seen in Fig 11 the ray launch angle goes tozero (horizontally launched rays) at right angles to thetrajectory

Beyond this angle the rays have no initial downwardcomponent As further angular deviations from the entryplane are considered rays are launched at progressively largerhorizontal launch angles with an initial upward component totheir motion At horizontal launch angles of ~15ndash30deg andangular deviations from the entry plane of 110ndash115deg ie 20ndash25deg degrees above the horizontal the proper initial launchdirections are reached to enable rays to propagate to Freyung(arrival azimuths to Freyung of ~75ndash60deg where the arrivalazimuth is equal to the bolide heading (1755deg) minus theangular entry plane deviation) Note that these rays travel

Fig 9 Characteristic velocity as a function of height for the Moraacutevkabolide modeled as a line source explosion along with the effectivehorizontal sound speed as a function of height (far left hand curve asindicated)

Fig 10 Effective horizontal sound velocity versus height for ldquorayrdquopaths from the Moraacutevka trajectory over a range of azimuths (627deg to771deg) towards Freyung

998 Brown et al

upward first and are refracted downward by the zone of verylarge sound speed in the lower thermosphere These are theonly rays predicted to arrive at Freyung by the cylindrical linesource model

We summarize the predicted cylindrical line sourcebehavior by taking the vertical line from the ground effectivesound speed value until it crosses each of the respective Vk

contour lines for each direction with the minimum Vk valueequal to ~347 ms in Table 4

Having established that the only possible returns from aline source for Moraacutevka are rays launched upward initiallyand subsequently arriving after refraction from the lowerthermosphere below ~118 km (see also Fig 14 path 4) wemay estimate the region along the fireball trajectory fromwhich rays might be generated Our predicted lowest sourceheights for signal azimuths from 63ndash70deg for Moraacutevka as seenat Freyung are largely ~28 km in reasonable agreement withthe moving point source (see next section) and seismicresults We emphasize that the cylindrical line source modeldoes not show any downward stratospheric-type returns eventhough that such rays are observed in the infrasound seemsindisputable (see below)

Based on these calculations we plot the Vk value as afunction of the horizontal launch direction and of the entryplane deviations as shown in Fig 11 The computed line

source Vk values in Figs 10 and 11 vary from ~350ndash366 msfor source heights from ~28ndash36 km or 347ndash420 ms overazimuths at Freyung from ~63ndash77deg for all allowed sourceheights given in Table 4 The measured infrasonic tracespeeds (=Vk in a steady state horizontally stratifiedatmosphere assuming perfect stratification) are ~347ndash372 ms for azimuths at Freyung from ~62ndash702deg (see Figs 7 and 8)These calculations indicate the possible degree of errorinherent in infrasonic trace speeds at certain times effects dueto atmospheric range dependence non-steady effects localplanetary boundary influences or all of the above

INFRASONIC ANALYSIS OF A MOVING POINT SOURCE IN A RANGE-DEPENDENT ATMOSPHERE

If a significant fragmentation along the fireball trajectoryexists we expect that some rays will be launched at anglesother than purely normal to the trajectory To investigate thisscenario we shot rays from each point along the trajectorybelow 40 km in the direction of Freyung but with a widerange of elevation angles The rays were allowed to propagatethrough a steady state model atmosphere that allows forrange-dependence of atmospheric properties ie imperfectstratification effects including refraction in both thehorizontal and vertical planes The range dependence ispresent as a small change in the temperature (and thus thesound speed) at each height within the MSIS model Over therelatively short distance between the fireball and Freyunghowever this temperature change is on the order of 1deg or lessat most heights Clearly most of the differences between theresults from this model and from the cylindrical line sourcemodel arise primarily from differing initial launch geometriesfor the rays involved

We followed the complete acoustic path for each ray todetermine the delay time and arrival direction at the receiverof those rays passing within 10 km horizontally or verticallyand of the receiver array The wind field and temperatureprofiles used are shown in Fig 12 and the same atmosphericprofiles were used as in the range-independent analysisearlier

Fig 11 Contoured line source characteristic velocities (Vk) (ms) fora source height of 35 km for Moraacutevka as a function of the horizontalldquorayrdquo launch angle and the angular deviation from the entry plane Adeviation of 90deg is the dividing line between possible initial ldquorayrdquolaunch angles with upward (downward) paths for deviations gt90deg(lt90deg) Possible ldquorayrdquo paths to Freyung are indicated by the arrow forangular deviations from ~110ndash115deg and corresponding upward ldquorayrdquolaunch angles ~25ndash32deg The triangles represent computed Vk valuesand the labeled (connected) lines are the resulting contour values forVk The horizontal arrow shows the range of launch deviations andangular deviations for arrivals that could be observed at Freyung

Table 4 Possible infrasonic arrivals to Freyung from analytical solutions in the line source geometry and range-independent atmosphere

Azimuth arrival angle at Freyung (deg)

Angular entry plane deviation (deg)

Possible source altitudes (km)

627 1128 100andash695 651 1104 00andash690675 1080 280ndash650699 1056 280ndash640723 1032 345ndash595747 1008 345ndash590771 984 375ndash560

aThe Moraacutevka bolide did not maintain the necessary characteristics to be aline source explosion at such low heights

The Moraacutevka meteorite fall Infrasonic and seismic data 999

In this numerical model for a given elevation angle foreach launched ray the algorithm searches for ray pathsbeginning near the nominal great-circle azimuth between thepoint source along the fireball path and Freyung At eachiteration the closest approach distance between a test ray atsome launch azimuth and the receiver (Freyung) isdetermined and another ray at a slightly different azimuth ischosen in an attempt to decrease this distance and so forthThis iterative process continues until a ray launch azimuth isfound that meets the arrival criteria at Freyung or somespecified number of iterations made without success(typically on the order of several hundred at each launchelevation) This technique is used to find the full range ofpossible acoustic paths between each point along the fireballtrajectory and Freyung without any predetermination of thesource characteristics

The results of these acoustic runs are shown in Fig 13From the figure the modeled delay times clearly produceseveral sets of distinct arrivals at Freyung First an early setof model arrivals near 1180 sec corresponds well to the firstobserved maxima (train 1) in the amplitude record Second

2 major sets of acoustic arrivals starting at 1200 sec and 1330sec at low heights along the fireball trajectory and crossingnear 1280 sec at a source altitude of 42 km represent thesecond and largest maxima train 2 Finally 3 distinct sets ofarrival pathways beginning just before 1400 sec andcontinuing until 1550 sec correspond to the weaker train 3We will examine each of these arrival paths and label themchronologically from 1ndash6

The first of these paths (path 1) arrives with mean signalspeeds near 031 kms intermediate between the speedsexpected of tropospheric and stratospheric returns (cfCeplecha et al 1998 p 384) From Fig 13 these modeledarrivals are perhaps 10ndash20 sec earlier than the main signal fortrain 1 though they correspond with the beginning of thesignal at Freyung For the given travel times of ~1200 secthese errors amount to 1ndash2 which is a remarkableagreement given our approximations in the modeledatmosphere Figure 14 shows a typical arrival ray for thisacoustic path

Clearly this is an unusual ray path that resembles raysthat ldquoleakrdquo from the stratospheric waveguide and in so doing

Fig 12 Model atmospheric temperature profile (top) and wind field(bottom) used for numerical ray tracing and line source modelling

Fig 13 Modeled arrival times as a function of source height alongthe fireball trajectory (lower plot) compared to the observed signalamplitude at Freyung (top) The acoustic branch identifications givenin the lower plot follow the convention used in Figs 14 and 16 with(A) representing the anomalous ldquoleaky-ductrdquo path (S) stratosphericpaths and (T) thermospheric returns

1000 Brown et al

have shorter paths and thus higher average signal velocitiesthan normal stratospheric returns (cf Arase [1959] for anexample of this effect in the ocean) These waves propagateparallel to the Earthrsquos surface at the top of the stratosphericduct and ldquoleakrdquo back to the surface In previous work theinclusion of explicit range dependence of temperaturetypically results in these types of acoustic arrivals From oursimulation results the source heights responsible for thisinfrasound return are restricted to the interval from 34ndash40 kmaltitude along the fireball trajectory

We have found that removing the range dependence ofthe atmosphere does not remove this acoustic path Insteadwe were able to find this arrival only by searching with veryfine steps (01deg) in our numerical ray launch elevationsmodeled within the framework of a moving point source Fora given height only a very small range of launch anglesproduces this anomalous arrival path between the fireball andFreyung as shown in Fig 15 We find that for precisely theproper launch angle the ray paths appear to travel along thetop interface of the stratospheric duct where the turning pointat the local maximum in sound velocity is reached near 45 kmaltitude We also observe that generation of acoustic energyover this height interval is independently confirmed by themeasured arrival azimuth of 685deg which compares veryfavorably with our modeled range of ray arrival azimuths atFreyung for train 1 (67degndash69deg)

For train 2 the mean signal speed near 029 kms is

characteristic of stratospheric returns Typical raysassociated with these acoustic paths are shown in Fig 14 asa group of paths labeled 2 Clearly these paths arestratospheric arrivals corresponding to rays launched atslightly different downward angles along the flighttrajectory The timing of the arrivals relative to the sourceheights suggests sound generation primarily in the intervalabove 30 km The time of maximum for train 2 suggests apossible maximum in sound production near ~38 km thoughdifferences between the true atmosphere and our modelatmosphere make this number uncertain by at least severalkm The thermospheric path 3 also has an arrival timeconsistent with contribution to train 2 but this return islikely very weak (see below)

The final signal train (3) has a mean signal velocity near025 kms which is representative of thermospheric returnsFigure 14 shows the thermospheric ray arrivals typical ofpaths 4ndash6 Clearly all these paths represent thermosphericreturns For thermospheric returns to be the weakest of allinfrasonic signals is not uncommon due to the high signalabsorption at the top of the thermospheric waveguide (cfBeer [1974] for a detailed discussion) One of these arrivals(path 5) is an extremely high thermospheric arrival withconcomitantly high attenuation Thus path 5 probablycontributes little or not at all to the thermospheric signals Forthe same reason path 3 probably does not contributesignificantly to train 2

Fig 14 Examples of acoustic ray propagation from the fireball trajectory (here a point at 35 km altitude) to the station Freyung Path 1 isconfined to the top of the stratospheric channel (near 45 km altitude) and then leaks to the receiver This is the mode of propagation for thesignals associated with the observed train 1 The paths labeled 2 are confined to the stratospheric channel (between 5 km and 45 km) andform the train 2 Paths 3ndash6 are confined to the thermospheric channel (between ground level and 120ndash160 km) Path 3 may contribute totrain 2 while paths 4ndash6 form train 3

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

The Moraacutevka meteorite fall Infrasonic and seismic data 991

deep underground stations Each station is equipped with a 3-component seismometer with a sampling frequency of 125Hz The digital recording is triggered after a seismic event isdetected at a minimum of 5 stations An 8-sec record is thenwritten For Moraacutevka the record starts at 115318744 UT(the station clocks are radio controlled) This time was too latefor stations HAV and CHO where the onset of the main signalis missing A rough analogue record shows that the onsetoccurred here a few tenths of a second earlier The digitalrecord lasts for 1 min

The fireball signal was also detected at 2 stations inPoland operated by the Polish Academy of Science (PAN PWiejacz and W Wojtak personal communication) One ofthese stations (RAC) was only 20 km from the trajectoryground projection Four stations operated by MasarykUniversity in Brno (MU J Pazdiacuterkovaacute personalcommunication) also detected the fireball The samplingfrequency at these stations was between 20 and 80 Hz

By analyzing the seismic records we were able toidentify several types of waves most visible at those stationslying some distance from the fireball trajectory where arrivaltimes are widely separated At all stations the first arrivals areair-coupled P-waves originating in the vicinity of trajectoryterminal point (ie the point where most of the meteoroidmass became subsonic) This is the lowest point of thesupersonic trajectory and the waves from this point reach theground first At the point where their surface trace velocity iscomparable to the surface P-wave velocity they aretransmitted into the ground (or alternatively they arerefracted under the critical angle according to Snellrsquos law(about 5deg) and continue to the station as near-surface groundP-waves) Subsequently P-waves from other more distantpoints along the trajectory arrive

The seismic records from stations BMZ and MORC areshown in Figs 2 and 3 respectively Both contain P-waves

The strongest signal however is associated with the directarrival of airwaves later on These first airwaves come fromthe point along the trajectory nearest the station Theypropagate as a cylindrical blast wave from the trajectory witha very small Mach cone angle given by the ratio of fireballvelocity to the speed of sound (see the section on cylindricalline source blast below) Near the end of the trajectory wherethe velocity of the meteoroid becomes very low the airwavesalso propagate as a quasi-spherical wave to the stations lyingdownrange of the trajectory terminal point (VRAC KRUCJAVC) Of course the actual shape of the wave is deformedby the varying speed of sound at various altitudes The onsetof the direct airwaves is always quite sharp in the seismicrecords and the waves have high frequencies correspondingto acoustic frequencies (50ndash2000 Hz) Although the directairwaves are under sampled on all stations they are easilyvisible in the filtered signal (Fig 3)

These direct airwaves are preceded by genetically relatedair-coupled Rayleigh waves which are formed by thetransformation of direct airwaves on the ground and movingalong the surface The amplitude of the Rayleigh wavesgradually increases until the arrival of the airwaves (Fig 2)Both types of waves can be distinguished clearly by the muchlower frequencies of the Rayleigh waves

In addition to the strong arrival of the blast wave thedirect airwave signal also contains numerous individualdisturbances (sub-maxima) We interpret these as having beengenerated by various point sources along the trajectory Thesesources are presumably connected with individual meteoroidfragmentation events The acoustic waves propagate asspherical waves from the source and the arrival time thendepends on the distance to the station We were able tolocalize a number of fragmentation events using their seismicsignatures as described in more detail in Boroviegrave ka andKalenda (2003)

Fig 1 Positions of seismic stations relative to the fireball trajectory as derived from the video records The right panel represents a detailedview of the central part Fireball altitudes in km are given in this part Deep underground stations are plotted as filled triangles

992 Brown et al

Fig 2 Seismic record from station BMZ and the description of individual wave groups The time is given in seconds after 115300 UT Thefirst P-waves arrived before the start of the record

Fig 3 Seismic record from station MORC and the description of individual wave groups The original waveform is given in the upper plotThe filtered signal with low frequencies (lt25 Hz) removed is in the lower plot

The Moraacutevka meteorite fall Infrasonic and seismic data 993

Particular emphasis has been devoted to analysis of theseismic signals recorded in the deep underground stationsHere P-waves are registered having been generated by therefraction of the airwaves on the surface A given ray comingto the underground station traverses smaller distances in theair than would be the case for detection at a station at thesurface having the same coordinates However the ray stillhas to travel through the rock down to the station Given thatthe P-wave signal velocity is typically 2ndash4 kms in near-surface rock we found that in our case (with relativelyshallow stations) these corrections are negligible and thetiming at the underground stations was therefore usedwithout change with the station depths being ignored

Table 2 provides the arrival times of different types ofwaves at each station The signal at the distant stations wasweak Acoustic ray tracing showed that stations KRUC andJAVC lie almost in the acoustic shadow with most of theairwaves reflected above the surface The identification of theP-type wave at station RAC is uncertainmdashthe given time mayin fact correspond to a seismic event not connected with thefireball

To check our identifications of the direct airwaves and todemonstrate the internal consistency of the seismic data andour interpretations of it we use the timings of the arrivals ofdirect airwaves to compute the fireball trajectory independentof the video data (cf Boroviegrave ka et al 2003a) A similarapproach was recently used independently by Ishihara et al(2001) who also studied the correlation of shock waveamplitude with meteoroid mass We used stations CSM RAJLUT PRS BMZ RAC OJC and MORC for trajectorycomputation Stations VRAC KRUC and JAVC could not beused because they lie in the region where the cylindrical wavedoes not propagate For a chosen initial latitude of 4990deg wecomputed the following 7 free parameters of the trajectorythe remaining 2 coordinates of the initial point (longitude andaltitude) the azimuth and slope of the trajectory the time offireball passage through the initial point (t0) the velocity anddeceleration of the fireball at that point The procedure wasiterative Because the speed of sound changes with

temperature ie altitude we computed the average speed ofsound from a particular altitude to each station When thefireball altitude was improved in the next iterative step theaverage sound speed was also recomputed The real measuredtemperature profile (see next section) was used to computesound speeds and in these computations the wind wasignored

The azimuth and slope of the trajectory comparefavorably to the values found from video reductions Thealtitude however is closely related to the time (t0) and bothparameters could not be determined simultaneously withgood precision We therefore used the observed satellite timeof the fireball (cf Boroviegrave ka et al 2003a) 1151525 as t0The other resulting parameters were as follows 18482deglongitude 317 km high 1720deg azimuth of the ground path198deg slope in the atmosphere (from horizontal) and 83 kmsvelocity The deceleration could not be reliably determinedthe beginning point lies only 15 km west and 300 m belowthe video trajectory the slope is within 1deg of the video dataand the azimuth differs by 35deg The velocity differssignificantly from the video value of 18 kms at 32 kmaltitude Except for the velocity we obtained reasonableresults even ignoring wind corrections We also ignored thefact that the fireball consisted of a number of laterallyseparated fragments Our good agreement with the video-determined trajectory demonstrates that the cylindrical blastwave was clearly present while the recording of numeroussub-maxima in the seismic amplitude (cf Boroviegrave ka andKalenda [2003] for details) establishes the presence ofacoustic energy from several fragmentation events producingquasi-spherical shocks

THE INFRASONIC DATA

The detection of infrasonic waves from fireballs has beenreported extensively in the past (eg ReVelle 1976 1997Evers and Haak 2001 Brown et al 2002a) However in veryfew cases have details of the trajectory velocity andfragmentation behavior of the associated fireball been

Table 2 Seismic waves first arrival times at different stationsa

CSM RAJ LUT PRS BMZ HAV CHO MAJ CSA KVE

P term ND ND ND ND ND ND ND ND ND NDRayleigh (R reg P) ND 936 962 981 124 ND ND 90 ND NDDirect-air (DA reg P) 901 964 1009 1028 1291 ND ND 9295 9526 904

RAC OJC MORC VRAC KRUC JAVC

P term 564b NS 753 815c NS NSRayleigh 1284 NS 245 182c NS 248Direct-air 1377 3389 2455 NA NA NADirect-air term NA NA NA NS 503 3079

aThe time is given in seconds after 115150 UT ND = no data at the time of expected first arrival NS = wave not seen in the data NA = not applicable Forthe underground stations (MAJ CSA KVE) the first arrival of Rayleigh and direct-air waves transformed to P-waves is given The waves designated asldquotermrdquo originate in the terminal point of the trajectory

bUncertain identificationcWeak signal near to the noise level

994 Brown et al

available comparable to the Moraacutevka fall All these detailsoffer potential insight into the source generation mechanismof the infrasound and permit us to estimate the source energyof the fireball from infrasonic records for comparison withother techniques

Infrasonic signals associated with the Moraacutevka eventwere recorded in Freyung Germany by station FREYUNG(137131deg E 488516deg N h = 1111 m) which is part of theInternational Monitoring System (IMS) of theComprehensive Test Ban Treaty (CTBT) at a distance of360 km from the fireball endpoint (see Borovi egrave ka et al2003a) The signals are shown in Fig 4 The station recordedthe airwave arrival from the fireball beginning 1182 sec afterthe fireball (121132 UT) and ceasing approximately 308 seclater at 121638 UT To define the signal characteristics weexamine the frequency spectrum of the original signal Thisspectrogram is shown in Fig 5 Here we see that the signal isvisible between 03 and 3 Hz below 03 Hz interference frommicrobaroms overwhelms the bolide signal (cf Evers andHaak [2001] for a description of microbaroms) Some signalenergy in the most energetic portions of the wave trainextends up to the Nyquist cutoff for the sensors near 9 Hz To

define the portion of the record having clear signal energyfrom the event we band pass the signals over the frequencyrange of 03ndash9 Hz and then perform a cross-correlationbetween the 4 microphones over 30 sec windows to define thedirection (azimuth) to the signal maximum cross-correlationwithin each window bin The cross-correlation result isshown in Fig 6 together with the associated directions inFig 7 This beam-forming technique is described in detail inEvers and Haak (2001)

Phenomenologically the signal consists of 3 majorportions The most obvious are the 2 signal wave trainswhich are clearly visible in the filtered amplitudes (Fig 4)The first of these major wave trains (train 1) coincides withthe onset of the signal at 121132 UT (1182 sec) andcontinues for approximately 43 sec ending near 121215 UT(1225 sec) when the amplitude decreases almost to theambient noise levels We note however that the signal cross-correlation remains well above background levels during thisamplitude minimum (Fig 6) indicating the presence ofcontinuing coherent acoustic energy from the fireball Thisongoing signal is also noticeable in the frequency spectra

The main body of the signal begins near 121237 UT(1247 sec) (train 2) Here the peak amplitude of the entiresignal occurs near 121257 UT (1267 sec) The amplitude oftrain 2 returns to near noise levels beginning at 121330 UT(1300 sec) However the cross correlation remains at least onestandard deviation above background for almost another 3minutes after this time period as can be seen in Fig 6 Indeedthe azimuth directions to maximum cross-correlation shownin Fig 7 indicate continued arrivals as seen at Freyung from65ndash67deg azimuth (azimuth is counted from north) during thisinterval beginning near 121400 UT (1330 sec) which wedesignate as train 3 This arrival is visible almost exclusivelyin cross-correlation and in the azimuth records little or noamplitude fluctuations above background are in evidence

In addition to these data Fig 8 shows the trace velocityof the signal at maximum cross-correlation in each of the

Fig 4 The recorded infrasound signal on all 4 channels at Freyungfor the Moraacutevka fireball Note that these waveforms have been bandpassed from 03ndash9 Hz to most clearly define the fireball signal

Fig 5 Frequency spectrogram of all 4 channels (channel one at topchannel four at the bottom) of the infrasound array The spectrogramgrey-scale shows gradations in dB

The Moraacutevka meteorite fall Infrasonic and seismic data 995

30 sec window bins over the course of the entire fireballairwave The trace velocity is a measure of the apparentvelocity of travel of the signal from one microphone to thenext the steeper the arrivals the higher the trace velocitiesHere we see that very little variation occurs in the tracevelocities over trains 1 and 2 with a slight possible increaseapparent over the duration of train 3 These wave train

signals are summarized in Table 3 along with times ofmaximum peak amplitudes and corresponding periods atmaximum amplitude

In the following sections we will use 2 approaches tostudy the propagation of acoustic waves from the fireballtrajectory to the station at Freyung to interpret these signalsFirst we employ a purely analytical method for a line source

Fig 6 The maximum correlation coefficient during the time centered around the Moraacutevka fireball signal at Freyung Windows of 30 sec (with50 overlap per window) are used to define individual measurements of cross-correlation The background cross-correlation in this frequencybandpass (03ndash9 Hz) calculated for the interval 3 minutes before the onset of the signal is 031 plusmn 002 and is shown by a thick solid horizontalline (mean) and thin lines representing the range of the standard deviation

Fig 7 Observed azimuths of infrasound arrival (north = 0) for each maximum in cross-correlation per bin

996 Brown et al

producing a cylindrical blast wave in a range-independentatmosphere Next a detailed numerical ray tracing approachis examined using moving point sources along the trajectoryin a range-dependent model atmosphere

INFRASONIC ANALYSIS FOR A CYLINDRICAL LINE SOURCE IN A

RANGE-INDEPENDENT ATMOSPHERE

As a means of examining the infrasound propagation in arange-independent atmosphere we can make use of thegeometrical acoustics approximation (wavelengths that aresmall compared to the pressure scale height the vertical scaleover which significant atmospheric pressure gradients canoccur) for which there are 2 constants of the motion in ahorizontally stratified steady state atmosphere that is anatmosphere with perfect stratification These constants are theheading of the wave normal (not the acoustic ray) from thesource and the characteristic velocity (Vk) generated at thesource In this approximation the arriving trace velocities atthe array are the same as the Vk values at the initial source

heights at which they were generated The characteristicvelocity can be thought of as the horizontal propagationvelocity modified for the effects of horizontal wind and entrygeometry (see ReVelle [1976] for a complete discussion)

Here we have reproduced the cylindrical line source blastwave approach developed by ReVelle (1976) In this methodthe characteristic velocity of the acoustic signal from the linesource is calculated as a function of altitude throughout theknown trajectory Due to non-steady effects or imperfectstratification (range dependent atmosphere effects etc) thevalue of the characteristic velocity is expected to be modifiedduring propagation In Figs 9 and 10 we have indicated theatmospheric structure parameters the so-called effectiveacoustic velocity (the signal propagation velocity includingwinds) and the calculated characteristic velocity (Vk) for therange of observed back azimuths from the infrasonicdetection at Freyung These parameters are all discussedfurther by Ceplecha et al (1998 p 380)

To model these acoustic arrivals we made use of theradiosonde data from Poprad Slovakia (~150 km ESE fromthe fireball) at 12 UT on May 6 2000 to define the

Fig 8 Observed trace velocities of the infrasound for each maximum in cross-correlation per bin

Table 3 Observed signal characteristics of the Moraacutevka fireball as seen from Freyung Germany on 6 May 2000 The start and end times are referenced to 115150 UT

Wave-train Start End DurationTime of max Azimuth

Peak amplitude

Trace velocity Period

Meansignal speed

(sec) (sec) (sec) (UT) (mPa) (kms) (s) (kms)

1 1180 1226 43 121142 685 638 0344 32 0302-0312plusmn07 plusmn72 plusmn0003 plusmn03

2 1247 1300 53 121257 667 2333 0355 41 0285-0297plusmn28 plusmn328 plusmn0013 plusmn08

3 1325 1490 165 ndash ndash 6 0353 ndash 0248-0279plusmn3 plusmn0026

The Moraacutevka meteorite fall Infrasonic and seismic data 997

temperature and wind field up to 30 km in altitude Above 30km we merged these radiosonde data with the MSIS-E (MassSpectrometer and Incoherent Scatter model) to produce thetemperature profile (cf Picone et al 1997) to a height of 140km inputting the appropriate geomagnetic indices for

May 6 2000 These indices significantly affect theatmospheric temperature and thus sound speed at heightsabove ~100 km The wind field above 30 km uses the HWM(Horizontal Wind Model) (Hedin et al 1996)

The propagation criterion within the geometricalacoustics approximation can be stated simply Whenever thecharacteristic velocity at the source exceeds the maximumeffective horizontal sound velocity over a given heightinterval ldquoraysrdquo will refract in such a way that they will reachthe ground (with sound waves bending away from regions ofincreasing temperatureincreasing sound speed gradients)

As indicated in Fig 10 for the altitude region from theground to ~118 km the maximum effective horizontal soundspeed is equal to 347 ms for our atmospheric conditions Forthose ldquoraysrdquo that have a Vk value greater than this valueldquorayrdquo paths exist between the line source sound generationaltitudes and points on the ground though in general only asmall subset will reach any given location (ie Freyung inour case)

Since the line source is a complicated acoustic raygeneration source we will first describe briefly the acousticradiation pattern In all cases where the velocity of themeteoroid is much higher than the local sound speed theradiation is perpendicular to the trajectory The only regionwhere this is not quite correct is near the bolide end heightwhere the Mach cone opens up substantially as the meteoroidis heavily decelerated shortly before the onset of dark flightand the fall of meteorites toward Earth Within the entryplane the vertical plane containing the trajectory that has anormal that is tangent to the earthrsquos surface immediatelybelow the mid-point of the fireball path the rays travel inexactly opposite azimuth to the heading of the bolide ietoward 3555deg (from the north) and have a downwardcomponent At the same time rays exist at all heights with anupward motion the heading of which is the same as the bolideie 1755deg but these do not generally reach the ground nearthe region of the fall ellipse and have not been examined hereAs the downward rays outside of the entry plane are examinedand we consider additional propagation directions we findthat the ray headings turn progressively toward less northerlydirections as the ray launch angle becomes less steepEventually as seen in Fig 11 the ray launch angle goes tozero (horizontally launched rays) at right angles to thetrajectory

Beyond this angle the rays have no initial downwardcomponent As further angular deviations from the entryplane are considered rays are launched at progressively largerhorizontal launch angles with an initial upward component totheir motion At horizontal launch angles of ~15ndash30deg andangular deviations from the entry plane of 110ndash115deg ie 20ndash25deg degrees above the horizontal the proper initial launchdirections are reached to enable rays to propagate to Freyung(arrival azimuths to Freyung of ~75ndash60deg where the arrivalazimuth is equal to the bolide heading (1755deg) minus theangular entry plane deviation) Note that these rays travel

Fig 9 Characteristic velocity as a function of height for the Moraacutevkabolide modeled as a line source explosion along with the effectivehorizontal sound speed as a function of height (far left hand curve asindicated)

Fig 10 Effective horizontal sound velocity versus height for ldquorayrdquopaths from the Moraacutevka trajectory over a range of azimuths (627deg to771deg) towards Freyung

998 Brown et al

upward first and are refracted downward by the zone of verylarge sound speed in the lower thermosphere These are theonly rays predicted to arrive at Freyung by the cylindrical linesource model

We summarize the predicted cylindrical line sourcebehavior by taking the vertical line from the ground effectivesound speed value until it crosses each of the respective Vk

contour lines for each direction with the minimum Vk valueequal to ~347 ms in Table 4

Having established that the only possible returns from aline source for Moraacutevka are rays launched upward initiallyand subsequently arriving after refraction from the lowerthermosphere below ~118 km (see also Fig 14 path 4) wemay estimate the region along the fireball trajectory fromwhich rays might be generated Our predicted lowest sourceheights for signal azimuths from 63ndash70deg for Moraacutevka as seenat Freyung are largely ~28 km in reasonable agreement withthe moving point source (see next section) and seismicresults We emphasize that the cylindrical line source modeldoes not show any downward stratospheric-type returns eventhough that such rays are observed in the infrasound seemsindisputable (see below)

Based on these calculations we plot the Vk value as afunction of the horizontal launch direction and of the entryplane deviations as shown in Fig 11 The computed line

source Vk values in Figs 10 and 11 vary from ~350ndash366 msfor source heights from ~28ndash36 km or 347ndash420 ms overazimuths at Freyung from ~63ndash77deg for all allowed sourceheights given in Table 4 The measured infrasonic tracespeeds (=Vk in a steady state horizontally stratifiedatmosphere assuming perfect stratification) are ~347ndash372 ms for azimuths at Freyung from ~62ndash702deg (see Figs 7 and 8)These calculations indicate the possible degree of errorinherent in infrasonic trace speeds at certain times effects dueto atmospheric range dependence non-steady effects localplanetary boundary influences or all of the above

INFRASONIC ANALYSIS OF A MOVING POINT SOURCE IN A RANGE-DEPENDENT ATMOSPHERE

If a significant fragmentation along the fireball trajectoryexists we expect that some rays will be launched at anglesother than purely normal to the trajectory To investigate thisscenario we shot rays from each point along the trajectorybelow 40 km in the direction of Freyung but with a widerange of elevation angles The rays were allowed to propagatethrough a steady state model atmosphere that allows forrange-dependence of atmospheric properties ie imperfectstratification effects including refraction in both thehorizontal and vertical planes The range dependence ispresent as a small change in the temperature (and thus thesound speed) at each height within the MSIS model Over therelatively short distance between the fireball and Freyunghowever this temperature change is on the order of 1deg or lessat most heights Clearly most of the differences between theresults from this model and from the cylindrical line sourcemodel arise primarily from differing initial launch geometriesfor the rays involved

We followed the complete acoustic path for each ray todetermine the delay time and arrival direction at the receiverof those rays passing within 10 km horizontally or verticallyand of the receiver array The wind field and temperatureprofiles used are shown in Fig 12 and the same atmosphericprofiles were used as in the range-independent analysisearlier

Fig 11 Contoured line source characteristic velocities (Vk) (ms) fora source height of 35 km for Moraacutevka as a function of the horizontalldquorayrdquo launch angle and the angular deviation from the entry plane Adeviation of 90deg is the dividing line between possible initial ldquorayrdquolaunch angles with upward (downward) paths for deviations gt90deg(lt90deg) Possible ldquorayrdquo paths to Freyung are indicated by the arrow forangular deviations from ~110ndash115deg and corresponding upward ldquorayrdquolaunch angles ~25ndash32deg The triangles represent computed Vk valuesand the labeled (connected) lines are the resulting contour values forVk The horizontal arrow shows the range of launch deviations andangular deviations for arrivals that could be observed at Freyung

Table 4 Possible infrasonic arrivals to Freyung from analytical solutions in the line source geometry and range-independent atmosphere

Azimuth arrival angle at Freyung (deg)

Angular entry plane deviation (deg)

Possible source altitudes (km)

627 1128 100andash695 651 1104 00andash690675 1080 280ndash650699 1056 280ndash640723 1032 345ndash595747 1008 345ndash590771 984 375ndash560

aThe Moraacutevka bolide did not maintain the necessary characteristics to be aline source explosion at such low heights

The Moraacutevka meteorite fall Infrasonic and seismic data 999

In this numerical model for a given elevation angle foreach launched ray the algorithm searches for ray pathsbeginning near the nominal great-circle azimuth between thepoint source along the fireball path and Freyung At eachiteration the closest approach distance between a test ray atsome launch azimuth and the receiver (Freyung) isdetermined and another ray at a slightly different azimuth ischosen in an attempt to decrease this distance and so forthThis iterative process continues until a ray launch azimuth isfound that meets the arrival criteria at Freyung or somespecified number of iterations made without success(typically on the order of several hundred at each launchelevation) This technique is used to find the full range ofpossible acoustic paths between each point along the fireballtrajectory and Freyung without any predetermination of thesource characteristics

The results of these acoustic runs are shown in Fig 13From the figure the modeled delay times clearly produceseveral sets of distinct arrivals at Freyung First an early setof model arrivals near 1180 sec corresponds well to the firstobserved maxima (train 1) in the amplitude record Second

2 major sets of acoustic arrivals starting at 1200 sec and 1330sec at low heights along the fireball trajectory and crossingnear 1280 sec at a source altitude of 42 km represent thesecond and largest maxima train 2 Finally 3 distinct sets ofarrival pathways beginning just before 1400 sec andcontinuing until 1550 sec correspond to the weaker train 3We will examine each of these arrival paths and label themchronologically from 1ndash6

The first of these paths (path 1) arrives with mean signalspeeds near 031 kms intermediate between the speedsexpected of tropospheric and stratospheric returns (cfCeplecha et al 1998 p 384) From Fig 13 these modeledarrivals are perhaps 10ndash20 sec earlier than the main signal fortrain 1 though they correspond with the beginning of thesignal at Freyung For the given travel times of ~1200 secthese errors amount to 1ndash2 which is a remarkableagreement given our approximations in the modeledatmosphere Figure 14 shows a typical arrival ray for thisacoustic path

Clearly this is an unusual ray path that resembles raysthat ldquoleakrdquo from the stratospheric waveguide and in so doing

Fig 12 Model atmospheric temperature profile (top) and wind field(bottom) used for numerical ray tracing and line source modelling

Fig 13 Modeled arrival times as a function of source height alongthe fireball trajectory (lower plot) compared to the observed signalamplitude at Freyung (top) The acoustic branch identifications givenin the lower plot follow the convention used in Figs 14 and 16 with(A) representing the anomalous ldquoleaky-ductrdquo path (S) stratosphericpaths and (T) thermospheric returns

1000 Brown et al

have shorter paths and thus higher average signal velocitiesthan normal stratospheric returns (cf Arase [1959] for anexample of this effect in the ocean) These waves propagateparallel to the Earthrsquos surface at the top of the stratosphericduct and ldquoleakrdquo back to the surface In previous work theinclusion of explicit range dependence of temperaturetypically results in these types of acoustic arrivals From oursimulation results the source heights responsible for thisinfrasound return are restricted to the interval from 34ndash40 kmaltitude along the fireball trajectory

We have found that removing the range dependence ofthe atmosphere does not remove this acoustic path Insteadwe were able to find this arrival only by searching with veryfine steps (01deg) in our numerical ray launch elevationsmodeled within the framework of a moving point source Fora given height only a very small range of launch anglesproduces this anomalous arrival path between the fireball andFreyung as shown in Fig 15 We find that for precisely theproper launch angle the ray paths appear to travel along thetop interface of the stratospheric duct where the turning pointat the local maximum in sound velocity is reached near 45 kmaltitude We also observe that generation of acoustic energyover this height interval is independently confirmed by themeasured arrival azimuth of 685deg which compares veryfavorably with our modeled range of ray arrival azimuths atFreyung for train 1 (67degndash69deg)

For train 2 the mean signal speed near 029 kms is

characteristic of stratospheric returns Typical raysassociated with these acoustic paths are shown in Fig 14 asa group of paths labeled 2 Clearly these paths arestratospheric arrivals corresponding to rays launched atslightly different downward angles along the flighttrajectory The timing of the arrivals relative to the sourceheights suggests sound generation primarily in the intervalabove 30 km The time of maximum for train 2 suggests apossible maximum in sound production near ~38 km thoughdifferences between the true atmosphere and our modelatmosphere make this number uncertain by at least severalkm The thermospheric path 3 also has an arrival timeconsistent with contribution to train 2 but this return islikely very weak (see below)

The final signal train (3) has a mean signal velocity near025 kms which is representative of thermospheric returnsFigure 14 shows the thermospheric ray arrivals typical ofpaths 4ndash6 Clearly all these paths represent thermosphericreturns For thermospheric returns to be the weakest of allinfrasonic signals is not uncommon due to the high signalabsorption at the top of the thermospheric waveguide (cfBeer [1974] for a detailed discussion) One of these arrivals(path 5) is an extremely high thermospheric arrival withconcomitantly high attenuation Thus path 5 probablycontributes little or not at all to the thermospheric signals Forthe same reason path 3 probably does not contributesignificantly to train 2

Fig 14 Examples of acoustic ray propagation from the fireball trajectory (here a point at 35 km altitude) to the station Freyung Path 1 isconfined to the top of the stratospheric channel (near 45 km altitude) and then leaks to the receiver This is the mode of propagation for thesignals associated with the observed train 1 The paths labeled 2 are confined to the stratospheric channel (between 5 km and 45 km) andform the train 2 Paths 3ndash6 are confined to the thermospheric channel (between ground level and 120ndash160 km) Path 3 may contribute totrain 2 while paths 4ndash6 form train 3

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

992 Brown et al

Fig 2 Seismic record from station BMZ and the description of individual wave groups The time is given in seconds after 115300 UT Thefirst P-waves arrived before the start of the record

Fig 3 Seismic record from station MORC and the description of individual wave groups The original waveform is given in the upper plotThe filtered signal with low frequencies (lt25 Hz) removed is in the lower plot

The Moraacutevka meteorite fall Infrasonic and seismic data 993

Particular emphasis has been devoted to analysis of theseismic signals recorded in the deep underground stationsHere P-waves are registered having been generated by therefraction of the airwaves on the surface A given ray comingto the underground station traverses smaller distances in theair than would be the case for detection at a station at thesurface having the same coordinates However the ray stillhas to travel through the rock down to the station Given thatthe P-wave signal velocity is typically 2ndash4 kms in near-surface rock we found that in our case (with relativelyshallow stations) these corrections are negligible and thetiming at the underground stations was therefore usedwithout change with the station depths being ignored

Table 2 provides the arrival times of different types ofwaves at each station The signal at the distant stations wasweak Acoustic ray tracing showed that stations KRUC andJAVC lie almost in the acoustic shadow with most of theairwaves reflected above the surface The identification of theP-type wave at station RAC is uncertainmdashthe given time mayin fact correspond to a seismic event not connected with thefireball

To check our identifications of the direct airwaves and todemonstrate the internal consistency of the seismic data andour interpretations of it we use the timings of the arrivals ofdirect airwaves to compute the fireball trajectory independentof the video data (cf Boroviegrave ka et al 2003a) A similarapproach was recently used independently by Ishihara et al(2001) who also studied the correlation of shock waveamplitude with meteoroid mass We used stations CSM RAJLUT PRS BMZ RAC OJC and MORC for trajectorycomputation Stations VRAC KRUC and JAVC could not beused because they lie in the region where the cylindrical wavedoes not propagate For a chosen initial latitude of 4990deg wecomputed the following 7 free parameters of the trajectorythe remaining 2 coordinates of the initial point (longitude andaltitude) the azimuth and slope of the trajectory the time offireball passage through the initial point (t0) the velocity anddeceleration of the fireball at that point The procedure wasiterative Because the speed of sound changes with

temperature ie altitude we computed the average speed ofsound from a particular altitude to each station When thefireball altitude was improved in the next iterative step theaverage sound speed was also recomputed The real measuredtemperature profile (see next section) was used to computesound speeds and in these computations the wind wasignored

The azimuth and slope of the trajectory comparefavorably to the values found from video reductions Thealtitude however is closely related to the time (t0) and bothparameters could not be determined simultaneously withgood precision We therefore used the observed satellite timeof the fireball (cf Boroviegrave ka et al 2003a) 1151525 as t0The other resulting parameters were as follows 18482deglongitude 317 km high 1720deg azimuth of the ground path198deg slope in the atmosphere (from horizontal) and 83 kmsvelocity The deceleration could not be reliably determinedthe beginning point lies only 15 km west and 300 m belowthe video trajectory the slope is within 1deg of the video dataand the azimuth differs by 35deg The velocity differssignificantly from the video value of 18 kms at 32 kmaltitude Except for the velocity we obtained reasonableresults even ignoring wind corrections We also ignored thefact that the fireball consisted of a number of laterallyseparated fragments Our good agreement with the video-determined trajectory demonstrates that the cylindrical blastwave was clearly present while the recording of numeroussub-maxima in the seismic amplitude (cf Boroviegrave ka andKalenda [2003] for details) establishes the presence ofacoustic energy from several fragmentation events producingquasi-spherical shocks

THE INFRASONIC DATA

The detection of infrasonic waves from fireballs has beenreported extensively in the past (eg ReVelle 1976 1997Evers and Haak 2001 Brown et al 2002a) However in veryfew cases have details of the trajectory velocity andfragmentation behavior of the associated fireball been

Table 2 Seismic waves first arrival times at different stationsa

CSM RAJ LUT PRS BMZ HAV CHO MAJ CSA KVE

P term ND ND ND ND ND ND ND ND ND NDRayleigh (R reg P) ND 936 962 981 124 ND ND 90 ND NDDirect-air (DA reg P) 901 964 1009 1028 1291 ND ND 9295 9526 904

RAC OJC MORC VRAC KRUC JAVC

P term 564b NS 753 815c NS NSRayleigh 1284 NS 245 182c NS 248Direct-air 1377 3389 2455 NA NA NADirect-air term NA NA NA NS 503 3079

aThe time is given in seconds after 115150 UT ND = no data at the time of expected first arrival NS = wave not seen in the data NA = not applicable Forthe underground stations (MAJ CSA KVE) the first arrival of Rayleigh and direct-air waves transformed to P-waves is given The waves designated asldquotermrdquo originate in the terminal point of the trajectory

bUncertain identificationcWeak signal near to the noise level

994 Brown et al

available comparable to the Moraacutevka fall All these detailsoffer potential insight into the source generation mechanismof the infrasound and permit us to estimate the source energyof the fireball from infrasonic records for comparison withother techniques

Infrasonic signals associated with the Moraacutevka eventwere recorded in Freyung Germany by station FREYUNG(137131deg E 488516deg N h = 1111 m) which is part of theInternational Monitoring System (IMS) of theComprehensive Test Ban Treaty (CTBT) at a distance of360 km from the fireball endpoint (see Borovi egrave ka et al2003a) The signals are shown in Fig 4 The station recordedthe airwave arrival from the fireball beginning 1182 sec afterthe fireball (121132 UT) and ceasing approximately 308 seclater at 121638 UT To define the signal characteristics weexamine the frequency spectrum of the original signal Thisspectrogram is shown in Fig 5 Here we see that the signal isvisible between 03 and 3 Hz below 03 Hz interference frommicrobaroms overwhelms the bolide signal (cf Evers andHaak [2001] for a description of microbaroms) Some signalenergy in the most energetic portions of the wave trainextends up to the Nyquist cutoff for the sensors near 9 Hz To

define the portion of the record having clear signal energyfrom the event we band pass the signals over the frequencyrange of 03ndash9 Hz and then perform a cross-correlationbetween the 4 microphones over 30 sec windows to define thedirection (azimuth) to the signal maximum cross-correlationwithin each window bin The cross-correlation result isshown in Fig 6 together with the associated directions inFig 7 This beam-forming technique is described in detail inEvers and Haak (2001)

Phenomenologically the signal consists of 3 majorportions The most obvious are the 2 signal wave trainswhich are clearly visible in the filtered amplitudes (Fig 4)The first of these major wave trains (train 1) coincides withthe onset of the signal at 121132 UT (1182 sec) andcontinues for approximately 43 sec ending near 121215 UT(1225 sec) when the amplitude decreases almost to theambient noise levels We note however that the signal cross-correlation remains well above background levels during thisamplitude minimum (Fig 6) indicating the presence ofcontinuing coherent acoustic energy from the fireball Thisongoing signal is also noticeable in the frequency spectra

The main body of the signal begins near 121237 UT(1247 sec) (train 2) Here the peak amplitude of the entiresignal occurs near 121257 UT (1267 sec) The amplitude oftrain 2 returns to near noise levels beginning at 121330 UT(1300 sec) However the cross correlation remains at least onestandard deviation above background for almost another 3minutes after this time period as can be seen in Fig 6 Indeedthe azimuth directions to maximum cross-correlation shownin Fig 7 indicate continued arrivals as seen at Freyung from65ndash67deg azimuth (azimuth is counted from north) during thisinterval beginning near 121400 UT (1330 sec) which wedesignate as train 3 This arrival is visible almost exclusivelyin cross-correlation and in the azimuth records little or noamplitude fluctuations above background are in evidence

In addition to these data Fig 8 shows the trace velocityof the signal at maximum cross-correlation in each of the

Fig 4 The recorded infrasound signal on all 4 channels at Freyungfor the Moraacutevka fireball Note that these waveforms have been bandpassed from 03ndash9 Hz to most clearly define the fireball signal

Fig 5 Frequency spectrogram of all 4 channels (channel one at topchannel four at the bottom) of the infrasound array The spectrogramgrey-scale shows gradations in dB

The Moraacutevka meteorite fall Infrasonic and seismic data 995

30 sec window bins over the course of the entire fireballairwave The trace velocity is a measure of the apparentvelocity of travel of the signal from one microphone to thenext the steeper the arrivals the higher the trace velocitiesHere we see that very little variation occurs in the tracevelocities over trains 1 and 2 with a slight possible increaseapparent over the duration of train 3 These wave train

signals are summarized in Table 3 along with times ofmaximum peak amplitudes and corresponding periods atmaximum amplitude

In the following sections we will use 2 approaches tostudy the propagation of acoustic waves from the fireballtrajectory to the station at Freyung to interpret these signalsFirst we employ a purely analytical method for a line source

Fig 6 The maximum correlation coefficient during the time centered around the Moraacutevka fireball signal at Freyung Windows of 30 sec (with50 overlap per window) are used to define individual measurements of cross-correlation The background cross-correlation in this frequencybandpass (03ndash9 Hz) calculated for the interval 3 minutes before the onset of the signal is 031 plusmn 002 and is shown by a thick solid horizontalline (mean) and thin lines representing the range of the standard deviation

Fig 7 Observed azimuths of infrasound arrival (north = 0) for each maximum in cross-correlation per bin

996 Brown et al

producing a cylindrical blast wave in a range-independentatmosphere Next a detailed numerical ray tracing approachis examined using moving point sources along the trajectoryin a range-dependent model atmosphere

INFRASONIC ANALYSIS FOR A CYLINDRICAL LINE SOURCE IN A

RANGE-INDEPENDENT ATMOSPHERE

As a means of examining the infrasound propagation in arange-independent atmosphere we can make use of thegeometrical acoustics approximation (wavelengths that aresmall compared to the pressure scale height the vertical scaleover which significant atmospheric pressure gradients canoccur) for which there are 2 constants of the motion in ahorizontally stratified steady state atmosphere that is anatmosphere with perfect stratification These constants are theheading of the wave normal (not the acoustic ray) from thesource and the characteristic velocity (Vk) generated at thesource In this approximation the arriving trace velocities atthe array are the same as the Vk values at the initial source

heights at which they were generated The characteristicvelocity can be thought of as the horizontal propagationvelocity modified for the effects of horizontal wind and entrygeometry (see ReVelle [1976] for a complete discussion)

Here we have reproduced the cylindrical line source blastwave approach developed by ReVelle (1976) In this methodthe characteristic velocity of the acoustic signal from the linesource is calculated as a function of altitude throughout theknown trajectory Due to non-steady effects or imperfectstratification (range dependent atmosphere effects etc) thevalue of the characteristic velocity is expected to be modifiedduring propagation In Figs 9 and 10 we have indicated theatmospheric structure parameters the so-called effectiveacoustic velocity (the signal propagation velocity includingwinds) and the calculated characteristic velocity (Vk) for therange of observed back azimuths from the infrasonicdetection at Freyung These parameters are all discussedfurther by Ceplecha et al (1998 p 380)

To model these acoustic arrivals we made use of theradiosonde data from Poprad Slovakia (~150 km ESE fromthe fireball) at 12 UT on May 6 2000 to define the

Fig 8 Observed trace velocities of the infrasound for each maximum in cross-correlation per bin

Table 3 Observed signal characteristics of the Moraacutevka fireball as seen from Freyung Germany on 6 May 2000 The start and end times are referenced to 115150 UT

Wave-train Start End DurationTime of max Azimuth

Peak amplitude

Trace velocity Period

Meansignal speed

(sec) (sec) (sec) (UT) (mPa) (kms) (s) (kms)

1 1180 1226 43 121142 685 638 0344 32 0302-0312plusmn07 plusmn72 plusmn0003 plusmn03

2 1247 1300 53 121257 667 2333 0355 41 0285-0297plusmn28 plusmn328 plusmn0013 plusmn08

3 1325 1490 165 ndash ndash 6 0353 ndash 0248-0279plusmn3 plusmn0026

The Moraacutevka meteorite fall Infrasonic and seismic data 997

temperature and wind field up to 30 km in altitude Above 30km we merged these radiosonde data with the MSIS-E (MassSpectrometer and Incoherent Scatter model) to produce thetemperature profile (cf Picone et al 1997) to a height of 140km inputting the appropriate geomagnetic indices for

May 6 2000 These indices significantly affect theatmospheric temperature and thus sound speed at heightsabove ~100 km The wind field above 30 km uses the HWM(Horizontal Wind Model) (Hedin et al 1996)

The propagation criterion within the geometricalacoustics approximation can be stated simply Whenever thecharacteristic velocity at the source exceeds the maximumeffective horizontal sound velocity over a given heightinterval ldquoraysrdquo will refract in such a way that they will reachthe ground (with sound waves bending away from regions ofincreasing temperatureincreasing sound speed gradients)

As indicated in Fig 10 for the altitude region from theground to ~118 km the maximum effective horizontal soundspeed is equal to 347 ms for our atmospheric conditions Forthose ldquoraysrdquo that have a Vk value greater than this valueldquorayrdquo paths exist between the line source sound generationaltitudes and points on the ground though in general only asmall subset will reach any given location (ie Freyung inour case)

Since the line source is a complicated acoustic raygeneration source we will first describe briefly the acousticradiation pattern In all cases where the velocity of themeteoroid is much higher than the local sound speed theradiation is perpendicular to the trajectory The only regionwhere this is not quite correct is near the bolide end heightwhere the Mach cone opens up substantially as the meteoroidis heavily decelerated shortly before the onset of dark flightand the fall of meteorites toward Earth Within the entryplane the vertical plane containing the trajectory that has anormal that is tangent to the earthrsquos surface immediatelybelow the mid-point of the fireball path the rays travel inexactly opposite azimuth to the heading of the bolide ietoward 3555deg (from the north) and have a downwardcomponent At the same time rays exist at all heights with anupward motion the heading of which is the same as the bolideie 1755deg but these do not generally reach the ground nearthe region of the fall ellipse and have not been examined hereAs the downward rays outside of the entry plane are examinedand we consider additional propagation directions we findthat the ray headings turn progressively toward less northerlydirections as the ray launch angle becomes less steepEventually as seen in Fig 11 the ray launch angle goes tozero (horizontally launched rays) at right angles to thetrajectory

Beyond this angle the rays have no initial downwardcomponent As further angular deviations from the entryplane are considered rays are launched at progressively largerhorizontal launch angles with an initial upward component totheir motion At horizontal launch angles of ~15ndash30deg andangular deviations from the entry plane of 110ndash115deg ie 20ndash25deg degrees above the horizontal the proper initial launchdirections are reached to enable rays to propagate to Freyung(arrival azimuths to Freyung of ~75ndash60deg where the arrivalazimuth is equal to the bolide heading (1755deg) minus theangular entry plane deviation) Note that these rays travel

Fig 9 Characteristic velocity as a function of height for the Moraacutevkabolide modeled as a line source explosion along with the effectivehorizontal sound speed as a function of height (far left hand curve asindicated)

Fig 10 Effective horizontal sound velocity versus height for ldquorayrdquopaths from the Moraacutevka trajectory over a range of azimuths (627deg to771deg) towards Freyung

998 Brown et al

upward first and are refracted downward by the zone of verylarge sound speed in the lower thermosphere These are theonly rays predicted to arrive at Freyung by the cylindrical linesource model

We summarize the predicted cylindrical line sourcebehavior by taking the vertical line from the ground effectivesound speed value until it crosses each of the respective Vk

contour lines for each direction with the minimum Vk valueequal to ~347 ms in Table 4

Having established that the only possible returns from aline source for Moraacutevka are rays launched upward initiallyand subsequently arriving after refraction from the lowerthermosphere below ~118 km (see also Fig 14 path 4) wemay estimate the region along the fireball trajectory fromwhich rays might be generated Our predicted lowest sourceheights for signal azimuths from 63ndash70deg for Moraacutevka as seenat Freyung are largely ~28 km in reasonable agreement withthe moving point source (see next section) and seismicresults We emphasize that the cylindrical line source modeldoes not show any downward stratospheric-type returns eventhough that such rays are observed in the infrasound seemsindisputable (see below)

Based on these calculations we plot the Vk value as afunction of the horizontal launch direction and of the entryplane deviations as shown in Fig 11 The computed line

source Vk values in Figs 10 and 11 vary from ~350ndash366 msfor source heights from ~28ndash36 km or 347ndash420 ms overazimuths at Freyung from ~63ndash77deg for all allowed sourceheights given in Table 4 The measured infrasonic tracespeeds (=Vk in a steady state horizontally stratifiedatmosphere assuming perfect stratification) are ~347ndash372 ms for azimuths at Freyung from ~62ndash702deg (see Figs 7 and 8)These calculations indicate the possible degree of errorinherent in infrasonic trace speeds at certain times effects dueto atmospheric range dependence non-steady effects localplanetary boundary influences or all of the above

INFRASONIC ANALYSIS OF A MOVING POINT SOURCE IN A RANGE-DEPENDENT ATMOSPHERE

If a significant fragmentation along the fireball trajectoryexists we expect that some rays will be launched at anglesother than purely normal to the trajectory To investigate thisscenario we shot rays from each point along the trajectorybelow 40 km in the direction of Freyung but with a widerange of elevation angles The rays were allowed to propagatethrough a steady state model atmosphere that allows forrange-dependence of atmospheric properties ie imperfectstratification effects including refraction in both thehorizontal and vertical planes The range dependence ispresent as a small change in the temperature (and thus thesound speed) at each height within the MSIS model Over therelatively short distance between the fireball and Freyunghowever this temperature change is on the order of 1deg or lessat most heights Clearly most of the differences between theresults from this model and from the cylindrical line sourcemodel arise primarily from differing initial launch geometriesfor the rays involved

We followed the complete acoustic path for each ray todetermine the delay time and arrival direction at the receiverof those rays passing within 10 km horizontally or verticallyand of the receiver array The wind field and temperatureprofiles used are shown in Fig 12 and the same atmosphericprofiles were used as in the range-independent analysisearlier

Fig 11 Contoured line source characteristic velocities (Vk) (ms) fora source height of 35 km for Moraacutevka as a function of the horizontalldquorayrdquo launch angle and the angular deviation from the entry plane Adeviation of 90deg is the dividing line between possible initial ldquorayrdquolaunch angles with upward (downward) paths for deviations gt90deg(lt90deg) Possible ldquorayrdquo paths to Freyung are indicated by the arrow forangular deviations from ~110ndash115deg and corresponding upward ldquorayrdquolaunch angles ~25ndash32deg The triangles represent computed Vk valuesand the labeled (connected) lines are the resulting contour values forVk The horizontal arrow shows the range of launch deviations andangular deviations for arrivals that could be observed at Freyung

Table 4 Possible infrasonic arrivals to Freyung from analytical solutions in the line source geometry and range-independent atmosphere

Azimuth arrival angle at Freyung (deg)

Angular entry plane deviation (deg)

Possible source altitudes (km)

627 1128 100andash695 651 1104 00andash690675 1080 280ndash650699 1056 280ndash640723 1032 345ndash595747 1008 345ndash590771 984 375ndash560

aThe Moraacutevka bolide did not maintain the necessary characteristics to be aline source explosion at such low heights

The Moraacutevka meteorite fall Infrasonic and seismic data 999

In this numerical model for a given elevation angle foreach launched ray the algorithm searches for ray pathsbeginning near the nominal great-circle azimuth between thepoint source along the fireball path and Freyung At eachiteration the closest approach distance between a test ray atsome launch azimuth and the receiver (Freyung) isdetermined and another ray at a slightly different azimuth ischosen in an attempt to decrease this distance and so forthThis iterative process continues until a ray launch azimuth isfound that meets the arrival criteria at Freyung or somespecified number of iterations made without success(typically on the order of several hundred at each launchelevation) This technique is used to find the full range ofpossible acoustic paths between each point along the fireballtrajectory and Freyung without any predetermination of thesource characteristics

The results of these acoustic runs are shown in Fig 13From the figure the modeled delay times clearly produceseveral sets of distinct arrivals at Freyung First an early setof model arrivals near 1180 sec corresponds well to the firstobserved maxima (train 1) in the amplitude record Second

2 major sets of acoustic arrivals starting at 1200 sec and 1330sec at low heights along the fireball trajectory and crossingnear 1280 sec at a source altitude of 42 km represent thesecond and largest maxima train 2 Finally 3 distinct sets ofarrival pathways beginning just before 1400 sec andcontinuing until 1550 sec correspond to the weaker train 3We will examine each of these arrival paths and label themchronologically from 1ndash6

The first of these paths (path 1) arrives with mean signalspeeds near 031 kms intermediate between the speedsexpected of tropospheric and stratospheric returns (cfCeplecha et al 1998 p 384) From Fig 13 these modeledarrivals are perhaps 10ndash20 sec earlier than the main signal fortrain 1 though they correspond with the beginning of thesignal at Freyung For the given travel times of ~1200 secthese errors amount to 1ndash2 which is a remarkableagreement given our approximations in the modeledatmosphere Figure 14 shows a typical arrival ray for thisacoustic path

Clearly this is an unusual ray path that resembles raysthat ldquoleakrdquo from the stratospheric waveguide and in so doing

Fig 12 Model atmospheric temperature profile (top) and wind field(bottom) used for numerical ray tracing and line source modelling

Fig 13 Modeled arrival times as a function of source height alongthe fireball trajectory (lower plot) compared to the observed signalamplitude at Freyung (top) The acoustic branch identifications givenin the lower plot follow the convention used in Figs 14 and 16 with(A) representing the anomalous ldquoleaky-ductrdquo path (S) stratosphericpaths and (T) thermospheric returns

1000 Brown et al

have shorter paths and thus higher average signal velocitiesthan normal stratospheric returns (cf Arase [1959] for anexample of this effect in the ocean) These waves propagateparallel to the Earthrsquos surface at the top of the stratosphericduct and ldquoleakrdquo back to the surface In previous work theinclusion of explicit range dependence of temperaturetypically results in these types of acoustic arrivals From oursimulation results the source heights responsible for thisinfrasound return are restricted to the interval from 34ndash40 kmaltitude along the fireball trajectory

We have found that removing the range dependence ofthe atmosphere does not remove this acoustic path Insteadwe were able to find this arrival only by searching with veryfine steps (01deg) in our numerical ray launch elevationsmodeled within the framework of a moving point source Fora given height only a very small range of launch anglesproduces this anomalous arrival path between the fireball andFreyung as shown in Fig 15 We find that for precisely theproper launch angle the ray paths appear to travel along thetop interface of the stratospheric duct where the turning pointat the local maximum in sound velocity is reached near 45 kmaltitude We also observe that generation of acoustic energyover this height interval is independently confirmed by themeasured arrival azimuth of 685deg which compares veryfavorably with our modeled range of ray arrival azimuths atFreyung for train 1 (67degndash69deg)

For train 2 the mean signal speed near 029 kms is

characteristic of stratospheric returns Typical raysassociated with these acoustic paths are shown in Fig 14 asa group of paths labeled 2 Clearly these paths arestratospheric arrivals corresponding to rays launched atslightly different downward angles along the flighttrajectory The timing of the arrivals relative to the sourceheights suggests sound generation primarily in the intervalabove 30 km The time of maximum for train 2 suggests apossible maximum in sound production near ~38 km thoughdifferences between the true atmosphere and our modelatmosphere make this number uncertain by at least severalkm The thermospheric path 3 also has an arrival timeconsistent with contribution to train 2 but this return islikely very weak (see below)

The final signal train (3) has a mean signal velocity near025 kms which is representative of thermospheric returnsFigure 14 shows the thermospheric ray arrivals typical ofpaths 4ndash6 Clearly all these paths represent thermosphericreturns For thermospheric returns to be the weakest of allinfrasonic signals is not uncommon due to the high signalabsorption at the top of the thermospheric waveguide (cfBeer [1974] for a detailed discussion) One of these arrivals(path 5) is an extremely high thermospheric arrival withconcomitantly high attenuation Thus path 5 probablycontributes little or not at all to the thermospheric signals Forthe same reason path 3 probably does not contributesignificantly to train 2

Fig 14 Examples of acoustic ray propagation from the fireball trajectory (here a point at 35 km altitude) to the station Freyung Path 1 isconfined to the top of the stratospheric channel (near 45 km altitude) and then leaks to the receiver This is the mode of propagation for thesignals associated with the observed train 1 The paths labeled 2 are confined to the stratospheric channel (between 5 km and 45 km) andform the train 2 Paths 3ndash6 are confined to the thermospheric channel (between ground level and 120ndash160 km) Path 3 may contribute totrain 2 while paths 4ndash6 form train 3

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

The Moraacutevka meteorite fall Infrasonic and seismic data 993

Particular emphasis has been devoted to analysis of theseismic signals recorded in the deep underground stationsHere P-waves are registered having been generated by therefraction of the airwaves on the surface A given ray comingto the underground station traverses smaller distances in theair than would be the case for detection at a station at thesurface having the same coordinates However the ray stillhas to travel through the rock down to the station Given thatthe P-wave signal velocity is typically 2ndash4 kms in near-surface rock we found that in our case (with relativelyshallow stations) these corrections are negligible and thetiming at the underground stations was therefore usedwithout change with the station depths being ignored

Table 2 provides the arrival times of different types ofwaves at each station The signal at the distant stations wasweak Acoustic ray tracing showed that stations KRUC andJAVC lie almost in the acoustic shadow with most of theairwaves reflected above the surface The identification of theP-type wave at station RAC is uncertainmdashthe given time mayin fact correspond to a seismic event not connected with thefireball

To check our identifications of the direct airwaves and todemonstrate the internal consistency of the seismic data andour interpretations of it we use the timings of the arrivals ofdirect airwaves to compute the fireball trajectory independentof the video data (cf Boroviegrave ka et al 2003a) A similarapproach was recently used independently by Ishihara et al(2001) who also studied the correlation of shock waveamplitude with meteoroid mass We used stations CSM RAJLUT PRS BMZ RAC OJC and MORC for trajectorycomputation Stations VRAC KRUC and JAVC could not beused because they lie in the region where the cylindrical wavedoes not propagate For a chosen initial latitude of 4990deg wecomputed the following 7 free parameters of the trajectorythe remaining 2 coordinates of the initial point (longitude andaltitude) the azimuth and slope of the trajectory the time offireball passage through the initial point (t0) the velocity anddeceleration of the fireball at that point The procedure wasiterative Because the speed of sound changes with

temperature ie altitude we computed the average speed ofsound from a particular altitude to each station When thefireball altitude was improved in the next iterative step theaverage sound speed was also recomputed The real measuredtemperature profile (see next section) was used to computesound speeds and in these computations the wind wasignored

The azimuth and slope of the trajectory comparefavorably to the values found from video reductions Thealtitude however is closely related to the time (t0) and bothparameters could not be determined simultaneously withgood precision We therefore used the observed satellite timeof the fireball (cf Boroviegrave ka et al 2003a) 1151525 as t0The other resulting parameters were as follows 18482deglongitude 317 km high 1720deg azimuth of the ground path198deg slope in the atmosphere (from horizontal) and 83 kmsvelocity The deceleration could not be reliably determinedthe beginning point lies only 15 km west and 300 m belowthe video trajectory the slope is within 1deg of the video dataand the azimuth differs by 35deg The velocity differssignificantly from the video value of 18 kms at 32 kmaltitude Except for the velocity we obtained reasonableresults even ignoring wind corrections We also ignored thefact that the fireball consisted of a number of laterallyseparated fragments Our good agreement with the video-determined trajectory demonstrates that the cylindrical blastwave was clearly present while the recording of numeroussub-maxima in the seismic amplitude (cf Boroviegrave ka andKalenda [2003] for details) establishes the presence ofacoustic energy from several fragmentation events producingquasi-spherical shocks

THE INFRASONIC DATA

The detection of infrasonic waves from fireballs has beenreported extensively in the past (eg ReVelle 1976 1997Evers and Haak 2001 Brown et al 2002a) However in veryfew cases have details of the trajectory velocity andfragmentation behavior of the associated fireball been

Table 2 Seismic waves first arrival times at different stationsa

CSM RAJ LUT PRS BMZ HAV CHO MAJ CSA KVE

P term ND ND ND ND ND ND ND ND ND NDRayleigh (R reg P) ND 936 962 981 124 ND ND 90 ND NDDirect-air (DA reg P) 901 964 1009 1028 1291 ND ND 9295 9526 904

RAC OJC MORC VRAC KRUC JAVC

P term 564b NS 753 815c NS NSRayleigh 1284 NS 245 182c NS 248Direct-air 1377 3389 2455 NA NA NADirect-air term NA NA NA NS 503 3079

aThe time is given in seconds after 115150 UT ND = no data at the time of expected first arrival NS = wave not seen in the data NA = not applicable Forthe underground stations (MAJ CSA KVE) the first arrival of Rayleigh and direct-air waves transformed to P-waves is given The waves designated asldquotermrdquo originate in the terminal point of the trajectory

bUncertain identificationcWeak signal near to the noise level

994 Brown et al

available comparable to the Moraacutevka fall All these detailsoffer potential insight into the source generation mechanismof the infrasound and permit us to estimate the source energyof the fireball from infrasonic records for comparison withother techniques

Infrasonic signals associated with the Moraacutevka eventwere recorded in Freyung Germany by station FREYUNG(137131deg E 488516deg N h = 1111 m) which is part of theInternational Monitoring System (IMS) of theComprehensive Test Ban Treaty (CTBT) at a distance of360 km from the fireball endpoint (see Borovi egrave ka et al2003a) The signals are shown in Fig 4 The station recordedthe airwave arrival from the fireball beginning 1182 sec afterthe fireball (121132 UT) and ceasing approximately 308 seclater at 121638 UT To define the signal characteristics weexamine the frequency spectrum of the original signal Thisspectrogram is shown in Fig 5 Here we see that the signal isvisible between 03 and 3 Hz below 03 Hz interference frommicrobaroms overwhelms the bolide signal (cf Evers andHaak [2001] for a description of microbaroms) Some signalenergy in the most energetic portions of the wave trainextends up to the Nyquist cutoff for the sensors near 9 Hz To

define the portion of the record having clear signal energyfrom the event we band pass the signals over the frequencyrange of 03ndash9 Hz and then perform a cross-correlationbetween the 4 microphones over 30 sec windows to define thedirection (azimuth) to the signal maximum cross-correlationwithin each window bin The cross-correlation result isshown in Fig 6 together with the associated directions inFig 7 This beam-forming technique is described in detail inEvers and Haak (2001)

Phenomenologically the signal consists of 3 majorportions The most obvious are the 2 signal wave trainswhich are clearly visible in the filtered amplitudes (Fig 4)The first of these major wave trains (train 1) coincides withthe onset of the signal at 121132 UT (1182 sec) andcontinues for approximately 43 sec ending near 121215 UT(1225 sec) when the amplitude decreases almost to theambient noise levels We note however that the signal cross-correlation remains well above background levels during thisamplitude minimum (Fig 6) indicating the presence ofcontinuing coherent acoustic energy from the fireball Thisongoing signal is also noticeable in the frequency spectra

The main body of the signal begins near 121237 UT(1247 sec) (train 2) Here the peak amplitude of the entiresignal occurs near 121257 UT (1267 sec) The amplitude oftrain 2 returns to near noise levels beginning at 121330 UT(1300 sec) However the cross correlation remains at least onestandard deviation above background for almost another 3minutes after this time period as can be seen in Fig 6 Indeedthe azimuth directions to maximum cross-correlation shownin Fig 7 indicate continued arrivals as seen at Freyung from65ndash67deg azimuth (azimuth is counted from north) during thisinterval beginning near 121400 UT (1330 sec) which wedesignate as train 3 This arrival is visible almost exclusivelyin cross-correlation and in the azimuth records little or noamplitude fluctuations above background are in evidence

In addition to these data Fig 8 shows the trace velocityof the signal at maximum cross-correlation in each of the

Fig 4 The recorded infrasound signal on all 4 channels at Freyungfor the Moraacutevka fireball Note that these waveforms have been bandpassed from 03ndash9 Hz to most clearly define the fireball signal

Fig 5 Frequency spectrogram of all 4 channels (channel one at topchannel four at the bottom) of the infrasound array The spectrogramgrey-scale shows gradations in dB

The Moraacutevka meteorite fall Infrasonic and seismic data 995

30 sec window bins over the course of the entire fireballairwave The trace velocity is a measure of the apparentvelocity of travel of the signal from one microphone to thenext the steeper the arrivals the higher the trace velocitiesHere we see that very little variation occurs in the tracevelocities over trains 1 and 2 with a slight possible increaseapparent over the duration of train 3 These wave train

signals are summarized in Table 3 along with times ofmaximum peak amplitudes and corresponding periods atmaximum amplitude

In the following sections we will use 2 approaches tostudy the propagation of acoustic waves from the fireballtrajectory to the station at Freyung to interpret these signalsFirst we employ a purely analytical method for a line source

Fig 6 The maximum correlation coefficient during the time centered around the Moraacutevka fireball signal at Freyung Windows of 30 sec (with50 overlap per window) are used to define individual measurements of cross-correlation The background cross-correlation in this frequencybandpass (03ndash9 Hz) calculated for the interval 3 minutes before the onset of the signal is 031 plusmn 002 and is shown by a thick solid horizontalline (mean) and thin lines representing the range of the standard deviation

Fig 7 Observed azimuths of infrasound arrival (north = 0) for each maximum in cross-correlation per bin

996 Brown et al

producing a cylindrical blast wave in a range-independentatmosphere Next a detailed numerical ray tracing approachis examined using moving point sources along the trajectoryin a range-dependent model atmosphere

INFRASONIC ANALYSIS FOR A CYLINDRICAL LINE SOURCE IN A

RANGE-INDEPENDENT ATMOSPHERE

As a means of examining the infrasound propagation in arange-independent atmosphere we can make use of thegeometrical acoustics approximation (wavelengths that aresmall compared to the pressure scale height the vertical scaleover which significant atmospheric pressure gradients canoccur) for which there are 2 constants of the motion in ahorizontally stratified steady state atmosphere that is anatmosphere with perfect stratification These constants are theheading of the wave normal (not the acoustic ray) from thesource and the characteristic velocity (Vk) generated at thesource In this approximation the arriving trace velocities atthe array are the same as the Vk values at the initial source

heights at which they were generated The characteristicvelocity can be thought of as the horizontal propagationvelocity modified for the effects of horizontal wind and entrygeometry (see ReVelle [1976] for a complete discussion)

Here we have reproduced the cylindrical line source blastwave approach developed by ReVelle (1976) In this methodthe characteristic velocity of the acoustic signal from the linesource is calculated as a function of altitude throughout theknown trajectory Due to non-steady effects or imperfectstratification (range dependent atmosphere effects etc) thevalue of the characteristic velocity is expected to be modifiedduring propagation In Figs 9 and 10 we have indicated theatmospheric structure parameters the so-called effectiveacoustic velocity (the signal propagation velocity includingwinds) and the calculated characteristic velocity (Vk) for therange of observed back azimuths from the infrasonicdetection at Freyung These parameters are all discussedfurther by Ceplecha et al (1998 p 380)

To model these acoustic arrivals we made use of theradiosonde data from Poprad Slovakia (~150 km ESE fromthe fireball) at 12 UT on May 6 2000 to define the

Fig 8 Observed trace velocities of the infrasound for each maximum in cross-correlation per bin

Table 3 Observed signal characteristics of the Moraacutevka fireball as seen from Freyung Germany on 6 May 2000 The start and end times are referenced to 115150 UT

Wave-train Start End DurationTime of max Azimuth

Peak amplitude

Trace velocity Period

Meansignal speed

(sec) (sec) (sec) (UT) (mPa) (kms) (s) (kms)

1 1180 1226 43 121142 685 638 0344 32 0302-0312plusmn07 plusmn72 plusmn0003 plusmn03

2 1247 1300 53 121257 667 2333 0355 41 0285-0297plusmn28 plusmn328 plusmn0013 plusmn08

3 1325 1490 165 ndash ndash 6 0353 ndash 0248-0279plusmn3 plusmn0026

The Moraacutevka meteorite fall Infrasonic and seismic data 997

temperature and wind field up to 30 km in altitude Above 30km we merged these radiosonde data with the MSIS-E (MassSpectrometer and Incoherent Scatter model) to produce thetemperature profile (cf Picone et al 1997) to a height of 140km inputting the appropriate geomagnetic indices for

May 6 2000 These indices significantly affect theatmospheric temperature and thus sound speed at heightsabove ~100 km The wind field above 30 km uses the HWM(Horizontal Wind Model) (Hedin et al 1996)

The propagation criterion within the geometricalacoustics approximation can be stated simply Whenever thecharacteristic velocity at the source exceeds the maximumeffective horizontal sound velocity over a given heightinterval ldquoraysrdquo will refract in such a way that they will reachthe ground (with sound waves bending away from regions ofincreasing temperatureincreasing sound speed gradients)

As indicated in Fig 10 for the altitude region from theground to ~118 km the maximum effective horizontal soundspeed is equal to 347 ms for our atmospheric conditions Forthose ldquoraysrdquo that have a Vk value greater than this valueldquorayrdquo paths exist between the line source sound generationaltitudes and points on the ground though in general only asmall subset will reach any given location (ie Freyung inour case)

Since the line source is a complicated acoustic raygeneration source we will first describe briefly the acousticradiation pattern In all cases where the velocity of themeteoroid is much higher than the local sound speed theradiation is perpendicular to the trajectory The only regionwhere this is not quite correct is near the bolide end heightwhere the Mach cone opens up substantially as the meteoroidis heavily decelerated shortly before the onset of dark flightand the fall of meteorites toward Earth Within the entryplane the vertical plane containing the trajectory that has anormal that is tangent to the earthrsquos surface immediatelybelow the mid-point of the fireball path the rays travel inexactly opposite azimuth to the heading of the bolide ietoward 3555deg (from the north) and have a downwardcomponent At the same time rays exist at all heights with anupward motion the heading of which is the same as the bolideie 1755deg but these do not generally reach the ground nearthe region of the fall ellipse and have not been examined hereAs the downward rays outside of the entry plane are examinedand we consider additional propagation directions we findthat the ray headings turn progressively toward less northerlydirections as the ray launch angle becomes less steepEventually as seen in Fig 11 the ray launch angle goes tozero (horizontally launched rays) at right angles to thetrajectory

Beyond this angle the rays have no initial downwardcomponent As further angular deviations from the entryplane are considered rays are launched at progressively largerhorizontal launch angles with an initial upward component totheir motion At horizontal launch angles of ~15ndash30deg andangular deviations from the entry plane of 110ndash115deg ie 20ndash25deg degrees above the horizontal the proper initial launchdirections are reached to enable rays to propagate to Freyung(arrival azimuths to Freyung of ~75ndash60deg where the arrivalazimuth is equal to the bolide heading (1755deg) minus theangular entry plane deviation) Note that these rays travel

Fig 9 Characteristic velocity as a function of height for the Moraacutevkabolide modeled as a line source explosion along with the effectivehorizontal sound speed as a function of height (far left hand curve asindicated)

Fig 10 Effective horizontal sound velocity versus height for ldquorayrdquopaths from the Moraacutevka trajectory over a range of azimuths (627deg to771deg) towards Freyung

998 Brown et al

upward first and are refracted downward by the zone of verylarge sound speed in the lower thermosphere These are theonly rays predicted to arrive at Freyung by the cylindrical linesource model

We summarize the predicted cylindrical line sourcebehavior by taking the vertical line from the ground effectivesound speed value until it crosses each of the respective Vk

contour lines for each direction with the minimum Vk valueequal to ~347 ms in Table 4

Having established that the only possible returns from aline source for Moraacutevka are rays launched upward initiallyand subsequently arriving after refraction from the lowerthermosphere below ~118 km (see also Fig 14 path 4) wemay estimate the region along the fireball trajectory fromwhich rays might be generated Our predicted lowest sourceheights for signal azimuths from 63ndash70deg for Moraacutevka as seenat Freyung are largely ~28 km in reasonable agreement withthe moving point source (see next section) and seismicresults We emphasize that the cylindrical line source modeldoes not show any downward stratospheric-type returns eventhough that such rays are observed in the infrasound seemsindisputable (see below)

Based on these calculations we plot the Vk value as afunction of the horizontal launch direction and of the entryplane deviations as shown in Fig 11 The computed line

source Vk values in Figs 10 and 11 vary from ~350ndash366 msfor source heights from ~28ndash36 km or 347ndash420 ms overazimuths at Freyung from ~63ndash77deg for all allowed sourceheights given in Table 4 The measured infrasonic tracespeeds (=Vk in a steady state horizontally stratifiedatmosphere assuming perfect stratification) are ~347ndash372 ms for azimuths at Freyung from ~62ndash702deg (see Figs 7 and 8)These calculations indicate the possible degree of errorinherent in infrasonic trace speeds at certain times effects dueto atmospheric range dependence non-steady effects localplanetary boundary influences or all of the above

INFRASONIC ANALYSIS OF A MOVING POINT SOURCE IN A RANGE-DEPENDENT ATMOSPHERE

If a significant fragmentation along the fireball trajectoryexists we expect that some rays will be launched at anglesother than purely normal to the trajectory To investigate thisscenario we shot rays from each point along the trajectorybelow 40 km in the direction of Freyung but with a widerange of elevation angles The rays were allowed to propagatethrough a steady state model atmosphere that allows forrange-dependence of atmospheric properties ie imperfectstratification effects including refraction in both thehorizontal and vertical planes The range dependence ispresent as a small change in the temperature (and thus thesound speed) at each height within the MSIS model Over therelatively short distance between the fireball and Freyunghowever this temperature change is on the order of 1deg or lessat most heights Clearly most of the differences between theresults from this model and from the cylindrical line sourcemodel arise primarily from differing initial launch geometriesfor the rays involved

We followed the complete acoustic path for each ray todetermine the delay time and arrival direction at the receiverof those rays passing within 10 km horizontally or verticallyand of the receiver array The wind field and temperatureprofiles used are shown in Fig 12 and the same atmosphericprofiles were used as in the range-independent analysisearlier

Fig 11 Contoured line source characteristic velocities (Vk) (ms) fora source height of 35 km for Moraacutevka as a function of the horizontalldquorayrdquo launch angle and the angular deviation from the entry plane Adeviation of 90deg is the dividing line between possible initial ldquorayrdquolaunch angles with upward (downward) paths for deviations gt90deg(lt90deg) Possible ldquorayrdquo paths to Freyung are indicated by the arrow forangular deviations from ~110ndash115deg and corresponding upward ldquorayrdquolaunch angles ~25ndash32deg The triangles represent computed Vk valuesand the labeled (connected) lines are the resulting contour values forVk The horizontal arrow shows the range of launch deviations andangular deviations for arrivals that could be observed at Freyung

Table 4 Possible infrasonic arrivals to Freyung from analytical solutions in the line source geometry and range-independent atmosphere

Azimuth arrival angle at Freyung (deg)

Angular entry plane deviation (deg)

Possible source altitudes (km)

627 1128 100andash695 651 1104 00andash690675 1080 280ndash650699 1056 280ndash640723 1032 345ndash595747 1008 345ndash590771 984 375ndash560

aThe Moraacutevka bolide did not maintain the necessary characteristics to be aline source explosion at such low heights

The Moraacutevka meteorite fall Infrasonic and seismic data 999

In this numerical model for a given elevation angle foreach launched ray the algorithm searches for ray pathsbeginning near the nominal great-circle azimuth between thepoint source along the fireball path and Freyung At eachiteration the closest approach distance between a test ray atsome launch azimuth and the receiver (Freyung) isdetermined and another ray at a slightly different azimuth ischosen in an attempt to decrease this distance and so forthThis iterative process continues until a ray launch azimuth isfound that meets the arrival criteria at Freyung or somespecified number of iterations made without success(typically on the order of several hundred at each launchelevation) This technique is used to find the full range ofpossible acoustic paths between each point along the fireballtrajectory and Freyung without any predetermination of thesource characteristics

The results of these acoustic runs are shown in Fig 13From the figure the modeled delay times clearly produceseveral sets of distinct arrivals at Freyung First an early setof model arrivals near 1180 sec corresponds well to the firstobserved maxima (train 1) in the amplitude record Second

2 major sets of acoustic arrivals starting at 1200 sec and 1330sec at low heights along the fireball trajectory and crossingnear 1280 sec at a source altitude of 42 km represent thesecond and largest maxima train 2 Finally 3 distinct sets ofarrival pathways beginning just before 1400 sec andcontinuing until 1550 sec correspond to the weaker train 3We will examine each of these arrival paths and label themchronologically from 1ndash6

The first of these paths (path 1) arrives with mean signalspeeds near 031 kms intermediate between the speedsexpected of tropospheric and stratospheric returns (cfCeplecha et al 1998 p 384) From Fig 13 these modeledarrivals are perhaps 10ndash20 sec earlier than the main signal fortrain 1 though they correspond with the beginning of thesignal at Freyung For the given travel times of ~1200 secthese errors amount to 1ndash2 which is a remarkableagreement given our approximations in the modeledatmosphere Figure 14 shows a typical arrival ray for thisacoustic path

Clearly this is an unusual ray path that resembles raysthat ldquoleakrdquo from the stratospheric waveguide and in so doing

Fig 12 Model atmospheric temperature profile (top) and wind field(bottom) used for numerical ray tracing and line source modelling

Fig 13 Modeled arrival times as a function of source height alongthe fireball trajectory (lower plot) compared to the observed signalamplitude at Freyung (top) The acoustic branch identifications givenin the lower plot follow the convention used in Figs 14 and 16 with(A) representing the anomalous ldquoleaky-ductrdquo path (S) stratosphericpaths and (T) thermospheric returns

1000 Brown et al

have shorter paths and thus higher average signal velocitiesthan normal stratospheric returns (cf Arase [1959] for anexample of this effect in the ocean) These waves propagateparallel to the Earthrsquos surface at the top of the stratosphericduct and ldquoleakrdquo back to the surface In previous work theinclusion of explicit range dependence of temperaturetypically results in these types of acoustic arrivals From oursimulation results the source heights responsible for thisinfrasound return are restricted to the interval from 34ndash40 kmaltitude along the fireball trajectory

We have found that removing the range dependence ofthe atmosphere does not remove this acoustic path Insteadwe were able to find this arrival only by searching with veryfine steps (01deg) in our numerical ray launch elevationsmodeled within the framework of a moving point source Fora given height only a very small range of launch anglesproduces this anomalous arrival path between the fireball andFreyung as shown in Fig 15 We find that for precisely theproper launch angle the ray paths appear to travel along thetop interface of the stratospheric duct where the turning pointat the local maximum in sound velocity is reached near 45 kmaltitude We also observe that generation of acoustic energyover this height interval is independently confirmed by themeasured arrival azimuth of 685deg which compares veryfavorably with our modeled range of ray arrival azimuths atFreyung for train 1 (67degndash69deg)

For train 2 the mean signal speed near 029 kms is

characteristic of stratospheric returns Typical raysassociated with these acoustic paths are shown in Fig 14 asa group of paths labeled 2 Clearly these paths arestratospheric arrivals corresponding to rays launched atslightly different downward angles along the flighttrajectory The timing of the arrivals relative to the sourceheights suggests sound generation primarily in the intervalabove 30 km The time of maximum for train 2 suggests apossible maximum in sound production near ~38 km thoughdifferences between the true atmosphere and our modelatmosphere make this number uncertain by at least severalkm The thermospheric path 3 also has an arrival timeconsistent with contribution to train 2 but this return islikely very weak (see below)

The final signal train (3) has a mean signal velocity near025 kms which is representative of thermospheric returnsFigure 14 shows the thermospheric ray arrivals typical ofpaths 4ndash6 Clearly all these paths represent thermosphericreturns For thermospheric returns to be the weakest of allinfrasonic signals is not uncommon due to the high signalabsorption at the top of the thermospheric waveguide (cfBeer [1974] for a detailed discussion) One of these arrivals(path 5) is an extremely high thermospheric arrival withconcomitantly high attenuation Thus path 5 probablycontributes little or not at all to the thermospheric signals Forthe same reason path 3 probably does not contributesignificantly to train 2

Fig 14 Examples of acoustic ray propagation from the fireball trajectory (here a point at 35 km altitude) to the station Freyung Path 1 isconfined to the top of the stratospheric channel (near 45 km altitude) and then leaks to the receiver This is the mode of propagation for thesignals associated with the observed train 1 The paths labeled 2 are confined to the stratospheric channel (between 5 km and 45 km) andform the train 2 Paths 3ndash6 are confined to the thermospheric channel (between ground level and 120ndash160 km) Path 3 may contribute totrain 2 while paths 4ndash6 form train 3

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

994 Brown et al

available comparable to the Moraacutevka fall All these detailsoffer potential insight into the source generation mechanismof the infrasound and permit us to estimate the source energyof the fireball from infrasonic records for comparison withother techniques

Infrasonic signals associated with the Moraacutevka eventwere recorded in Freyung Germany by station FREYUNG(137131deg E 488516deg N h = 1111 m) which is part of theInternational Monitoring System (IMS) of theComprehensive Test Ban Treaty (CTBT) at a distance of360 km from the fireball endpoint (see Borovi egrave ka et al2003a) The signals are shown in Fig 4 The station recordedthe airwave arrival from the fireball beginning 1182 sec afterthe fireball (121132 UT) and ceasing approximately 308 seclater at 121638 UT To define the signal characteristics weexamine the frequency spectrum of the original signal Thisspectrogram is shown in Fig 5 Here we see that the signal isvisible between 03 and 3 Hz below 03 Hz interference frommicrobaroms overwhelms the bolide signal (cf Evers andHaak [2001] for a description of microbaroms) Some signalenergy in the most energetic portions of the wave trainextends up to the Nyquist cutoff for the sensors near 9 Hz To

define the portion of the record having clear signal energyfrom the event we band pass the signals over the frequencyrange of 03ndash9 Hz and then perform a cross-correlationbetween the 4 microphones over 30 sec windows to define thedirection (azimuth) to the signal maximum cross-correlationwithin each window bin The cross-correlation result isshown in Fig 6 together with the associated directions inFig 7 This beam-forming technique is described in detail inEvers and Haak (2001)

Phenomenologically the signal consists of 3 majorportions The most obvious are the 2 signal wave trainswhich are clearly visible in the filtered amplitudes (Fig 4)The first of these major wave trains (train 1) coincides withthe onset of the signal at 121132 UT (1182 sec) andcontinues for approximately 43 sec ending near 121215 UT(1225 sec) when the amplitude decreases almost to theambient noise levels We note however that the signal cross-correlation remains well above background levels during thisamplitude minimum (Fig 6) indicating the presence ofcontinuing coherent acoustic energy from the fireball Thisongoing signal is also noticeable in the frequency spectra

The main body of the signal begins near 121237 UT(1247 sec) (train 2) Here the peak amplitude of the entiresignal occurs near 121257 UT (1267 sec) The amplitude oftrain 2 returns to near noise levels beginning at 121330 UT(1300 sec) However the cross correlation remains at least onestandard deviation above background for almost another 3minutes after this time period as can be seen in Fig 6 Indeedthe azimuth directions to maximum cross-correlation shownin Fig 7 indicate continued arrivals as seen at Freyung from65ndash67deg azimuth (azimuth is counted from north) during thisinterval beginning near 121400 UT (1330 sec) which wedesignate as train 3 This arrival is visible almost exclusivelyin cross-correlation and in the azimuth records little or noamplitude fluctuations above background are in evidence

In addition to these data Fig 8 shows the trace velocityof the signal at maximum cross-correlation in each of the

Fig 4 The recorded infrasound signal on all 4 channels at Freyungfor the Moraacutevka fireball Note that these waveforms have been bandpassed from 03ndash9 Hz to most clearly define the fireball signal

Fig 5 Frequency spectrogram of all 4 channels (channel one at topchannel four at the bottom) of the infrasound array The spectrogramgrey-scale shows gradations in dB

The Moraacutevka meteorite fall Infrasonic and seismic data 995

30 sec window bins over the course of the entire fireballairwave The trace velocity is a measure of the apparentvelocity of travel of the signal from one microphone to thenext the steeper the arrivals the higher the trace velocitiesHere we see that very little variation occurs in the tracevelocities over trains 1 and 2 with a slight possible increaseapparent over the duration of train 3 These wave train

signals are summarized in Table 3 along with times ofmaximum peak amplitudes and corresponding periods atmaximum amplitude

In the following sections we will use 2 approaches tostudy the propagation of acoustic waves from the fireballtrajectory to the station at Freyung to interpret these signalsFirst we employ a purely analytical method for a line source

Fig 6 The maximum correlation coefficient during the time centered around the Moraacutevka fireball signal at Freyung Windows of 30 sec (with50 overlap per window) are used to define individual measurements of cross-correlation The background cross-correlation in this frequencybandpass (03ndash9 Hz) calculated for the interval 3 minutes before the onset of the signal is 031 plusmn 002 and is shown by a thick solid horizontalline (mean) and thin lines representing the range of the standard deviation

Fig 7 Observed azimuths of infrasound arrival (north = 0) for each maximum in cross-correlation per bin

996 Brown et al

producing a cylindrical blast wave in a range-independentatmosphere Next a detailed numerical ray tracing approachis examined using moving point sources along the trajectoryin a range-dependent model atmosphere

INFRASONIC ANALYSIS FOR A CYLINDRICAL LINE SOURCE IN A

RANGE-INDEPENDENT ATMOSPHERE

As a means of examining the infrasound propagation in arange-independent atmosphere we can make use of thegeometrical acoustics approximation (wavelengths that aresmall compared to the pressure scale height the vertical scaleover which significant atmospheric pressure gradients canoccur) for which there are 2 constants of the motion in ahorizontally stratified steady state atmosphere that is anatmosphere with perfect stratification These constants are theheading of the wave normal (not the acoustic ray) from thesource and the characteristic velocity (Vk) generated at thesource In this approximation the arriving trace velocities atthe array are the same as the Vk values at the initial source

heights at which they were generated The characteristicvelocity can be thought of as the horizontal propagationvelocity modified for the effects of horizontal wind and entrygeometry (see ReVelle [1976] for a complete discussion)

Here we have reproduced the cylindrical line source blastwave approach developed by ReVelle (1976) In this methodthe characteristic velocity of the acoustic signal from the linesource is calculated as a function of altitude throughout theknown trajectory Due to non-steady effects or imperfectstratification (range dependent atmosphere effects etc) thevalue of the characteristic velocity is expected to be modifiedduring propagation In Figs 9 and 10 we have indicated theatmospheric structure parameters the so-called effectiveacoustic velocity (the signal propagation velocity includingwinds) and the calculated characteristic velocity (Vk) for therange of observed back azimuths from the infrasonicdetection at Freyung These parameters are all discussedfurther by Ceplecha et al (1998 p 380)

To model these acoustic arrivals we made use of theradiosonde data from Poprad Slovakia (~150 km ESE fromthe fireball) at 12 UT on May 6 2000 to define the

Fig 8 Observed trace velocities of the infrasound for each maximum in cross-correlation per bin

Table 3 Observed signal characteristics of the Moraacutevka fireball as seen from Freyung Germany on 6 May 2000 The start and end times are referenced to 115150 UT

Wave-train Start End DurationTime of max Azimuth

Peak amplitude

Trace velocity Period

Meansignal speed

(sec) (sec) (sec) (UT) (mPa) (kms) (s) (kms)

1 1180 1226 43 121142 685 638 0344 32 0302-0312plusmn07 plusmn72 plusmn0003 plusmn03

2 1247 1300 53 121257 667 2333 0355 41 0285-0297plusmn28 plusmn328 plusmn0013 plusmn08

3 1325 1490 165 ndash ndash 6 0353 ndash 0248-0279plusmn3 plusmn0026

The Moraacutevka meteorite fall Infrasonic and seismic data 997

temperature and wind field up to 30 km in altitude Above 30km we merged these radiosonde data with the MSIS-E (MassSpectrometer and Incoherent Scatter model) to produce thetemperature profile (cf Picone et al 1997) to a height of 140km inputting the appropriate geomagnetic indices for

May 6 2000 These indices significantly affect theatmospheric temperature and thus sound speed at heightsabove ~100 km The wind field above 30 km uses the HWM(Horizontal Wind Model) (Hedin et al 1996)

The propagation criterion within the geometricalacoustics approximation can be stated simply Whenever thecharacteristic velocity at the source exceeds the maximumeffective horizontal sound velocity over a given heightinterval ldquoraysrdquo will refract in such a way that they will reachthe ground (with sound waves bending away from regions ofincreasing temperatureincreasing sound speed gradients)

As indicated in Fig 10 for the altitude region from theground to ~118 km the maximum effective horizontal soundspeed is equal to 347 ms for our atmospheric conditions Forthose ldquoraysrdquo that have a Vk value greater than this valueldquorayrdquo paths exist between the line source sound generationaltitudes and points on the ground though in general only asmall subset will reach any given location (ie Freyung inour case)

Since the line source is a complicated acoustic raygeneration source we will first describe briefly the acousticradiation pattern In all cases where the velocity of themeteoroid is much higher than the local sound speed theradiation is perpendicular to the trajectory The only regionwhere this is not quite correct is near the bolide end heightwhere the Mach cone opens up substantially as the meteoroidis heavily decelerated shortly before the onset of dark flightand the fall of meteorites toward Earth Within the entryplane the vertical plane containing the trajectory that has anormal that is tangent to the earthrsquos surface immediatelybelow the mid-point of the fireball path the rays travel inexactly opposite azimuth to the heading of the bolide ietoward 3555deg (from the north) and have a downwardcomponent At the same time rays exist at all heights with anupward motion the heading of which is the same as the bolideie 1755deg but these do not generally reach the ground nearthe region of the fall ellipse and have not been examined hereAs the downward rays outside of the entry plane are examinedand we consider additional propagation directions we findthat the ray headings turn progressively toward less northerlydirections as the ray launch angle becomes less steepEventually as seen in Fig 11 the ray launch angle goes tozero (horizontally launched rays) at right angles to thetrajectory

Beyond this angle the rays have no initial downwardcomponent As further angular deviations from the entryplane are considered rays are launched at progressively largerhorizontal launch angles with an initial upward component totheir motion At horizontal launch angles of ~15ndash30deg andangular deviations from the entry plane of 110ndash115deg ie 20ndash25deg degrees above the horizontal the proper initial launchdirections are reached to enable rays to propagate to Freyung(arrival azimuths to Freyung of ~75ndash60deg where the arrivalazimuth is equal to the bolide heading (1755deg) minus theangular entry plane deviation) Note that these rays travel

Fig 9 Characteristic velocity as a function of height for the Moraacutevkabolide modeled as a line source explosion along with the effectivehorizontal sound speed as a function of height (far left hand curve asindicated)

Fig 10 Effective horizontal sound velocity versus height for ldquorayrdquopaths from the Moraacutevka trajectory over a range of azimuths (627deg to771deg) towards Freyung

998 Brown et al

upward first and are refracted downward by the zone of verylarge sound speed in the lower thermosphere These are theonly rays predicted to arrive at Freyung by the cylindrical linesource model

We summarize the predicted cylindrical line sourcebehavior by taking the vertical line from the ground effectivesound speed value until it crosses each of the respective Vk

contour lines for each direction with the minimum Vk valueequal to ~347 ms in Table 4

Having established that the only possible returns from aline source for Moraacutevka are rays launched upward initiallyand subsequently arriving after refraction from the lowerthermosphere below ~118 km (see also Fig 14 path 4) wemay estimate the region along the fireball trajectory fromwhich rays might be generated Our predicted lowest sourceheights for signal azimuths from 63ndash70deg for Moraacutevka as seenat Freyung are largely ~28 km in reasonable agreement withthe moving point source (see next section) and seismicresults We emphasize that the cylindrical line source modeldoes not show any downward stratospheric-type returns eventhough that such rays are observed in the infrasound seemsindisputable (see below)

Based on these calculations we plot the Vk value as afunction of the horizontal launch direction and of the entryplane deviations as shown in Fig 11 The computed line

source Vk values in Figs 10 and 11 vary from ~350ndash366 msfor source heights from ~28ndash36 km or 347ndash420 ms overazimuths at Freyung from ~63ndash77deg for all allowed sourceheights given in Table 4 The measured infrasonic tracespeeds (=Vk in a steady state horizontally stratifiedatmosphere assuming perfect stratification) are ~347ndash372 ms for azimuths at Freyung from ~62ndash702deg (see Figs 7 and 8)These calculations indicate the possible degree of errorinherent in infrasonic trace speeds at certain times effects dueto atmospheric range dependence non-steady effects localplanetary boundary influences or all of the above

INFRASONIC ANALYSIS OF A MOVING POINT SOURCE IN A RANGE-DEPENDENT ATMOSPHERE

If a significant fragmentation along the fireball trajectoryexists we expect that some rays will be launched at anglesother than purely normal to the trajectory To investigate thisscenario we shot rays from each point along the trajectorybelow 40 km in the direction of Freyung but with a widerange of elevation angles The rays were allowed to propagatethrough a steady state model atmosphere that allows forrange-dependence of atmospheric properties ie imperfectstratification effects including refraction in both thehorizontal and vertical planes The range dependence ispresent as a small change in the temperature (and thus thesound speed) at each height within the MSIS model Over therelatively short distance between the fireball and Freyunghowever this temperature change is on the order of 1deg or lessat most heights Clearly most of the differences between theresults from this model and from the cylindrical line sourcemodel arise primarily from differing initial launch geometriesfor the rays involved

We followed the complete acoustic path for each ray todetermine the delay time and arrival direction at the receiverof those rays passing within 10 km horizontally or verticallyand of the receiver array The wind field and temperatureprofiles used are shown in Fig 12 and the same atmosphericprofiles were used as in the range-independent analysisearlier

Fig 11 Contoured line source characteristic velocities (Vk) (ms) fora source height of 35 km for Moraacutevka as a function of the horizontalldquorayrdquo launch angle and the angular deviation from the entry plane Adeviation of 90deg is the dividing line between possible initial ldquorayrdquolaunch angles with upward (downward) paths for deviations gt90deg(lt90deg) Possible ldquorayrdquo paths to Freyung are indicated by the arrow forangular deviations from ~110ndash115deg and corresponding upward ldquorayrdquolaunch angles ~25ndash32deg The triangles represent computed Vk valuesand the labeled (connected) lines are the resulting contour values forVk The horizontal arrow shows the range of launch deviations andangular deviations for arrivals that could be observed at Freyung

Table 4 Possible infrasonic arrivals to Freyung from analytical solutions in the line source geometry and range-independent atmosphere

Azimuth arrival angle at Freyung (deg)

Angular entry plane deviation (deg)

Possible source altitudes (km)

627 1128 100andash695 651 1104 00andash690675 1080 280ndash650699 1056 280ndash640723 1032 345ndash595747 1008 345ndash590771 984 375ndash560

aThe Moraacutevka bolide did not maintain the necessary characteristics to be aline source explosion at such low heights

The Moraacutevka meteorite fall Infrasonic and seismic data 999

In this numerical model for a given elevation angle foreach launched ray the algorithm searches for ray pathsbeginning near the nominal great-circle azimuth between thepoint source along the fireball path and Freyung At eachiteration the closest approach distance between a test ray atsome launch azimuth and the receiver (Freyung) isdetermined and another ray at a slightly different azimuth ischosen in an attempt to decrease this distance and so forthThis iterative process continues until a ray launch azimuth isfound that meets the arrival criteria at Freyung or somespecified number of iterations made without success(typically on the order of several hundred at each launchelevation) This technique is used to find the full range ofpossible acoustic paths between each point along the fireballtrajectory and Freyung without any predetermination of thesource characteristics

The results of these acoustic runs are shown in Fig 13From the figure the modeled delay times clearly produceseveral sets of distinct arrivals at Freyung First an early setof model arrivals near 1180 sec corresponds well to the firstobserved maxima (train 1) in the amplitude record Second

2 major sets of acoustic arrivals starting at 1200 sec and 1330sec at low heights along the fireball trajectory and crossingnear 1280 sec at a source altitude of 42 km represent thesecond and largest maxima train 2 Finally 3 distinct sets ofarrival pathways beginning just before 1400 sec andcontinuing until 1550 sec correspond to the weaker train 3We will examine each of these arrival paths and label themchronologically from 1ndash6

The first of these paths (path 1) arrives with mean signalspeeds near 031 kms intermediate between the speedsexpected of tropospheric and stratospheric returns (cfCeplecha et al 1998 p 384) From Fig 13 these modeledarrivals are perhaps 10ndash20 sec earlier than the main signal fortrain 1 though they correspond with the beginning of thesignal at Freyung For the given travel times of ~1200 secthese errors amount to 1ndash2 which is a remarkableagreement given our approximations in the modeledatmosphere Figure 14 shows a typical arrival ray for thisacoustic path

Clearly this is an unusual ray path that resembles raysthat ldquoleakrdquo from the stratospheric waveguide and in so doing

Fig 12 Model atmospheric temperature profile (top) and wind field(bottom) used for numerical ray tracing and line source modelling

Fig 13 Modeled arrival times as a function of source height alongthe fireball trajectory (lower plot) compared to the observed signalamplitude at Freyung (top) The acoustic branch identifications givenin the lower plot follow the convention used in Figs 14 and 16 with(A) representing the anomalous ldquoleaky-ductrdquo path (S) stratosphericpaths and (T) thermospheric returns

1000 Brown et al

have shorter paths and thus higher average signal velocitiesthan normal stratospheric returns (cf Arase [1959] for anexample of this effect in the ocean) These waves propagateparallel to the Earthrsquos surface at the top of the stratosphericduct and ldquoleakrdquo back to the surface In previous work theinclusion of explicit range dependence of temperaturetypically results in these types of acoustic arrivals From oursimulation results the source heights responsible for thisinfrasound return are restricted to the interval from 34ndash40 kmaltitude along the fireball trajectory

We have found that removing the range dependence ofthe atmosphere does not remove this acoustic path Insteadwe were able to find this arrival only by searching with veryfine steps (01deg) in our numerical ray launch elevationsmodeled within the framework of a moving point source Fora given height only a very small range of launch anglesproduces this anomalous arrival path between the fireball andFreyung as shown in Fig 15 We find that for precisely theproper launch angle the ray paths appear to travel along thetop interface of the stratospheric duct where the turning pointat the local maximum in sound velocity is reached near 45 kmaltitude We also observe that generation of acoustic energyover this height interval is independently confirmed by themeasured arrival azimuth of 685deg which compares veryfavorably with our modeled range of ray arrival azimuths atFreyung for train 1 (67degndash69deg)

For train 2 the mean signal speed near 029 kms is

characteristic of stratospheric returns Typical raysassociated with these acoustic paths are shown in Fig 14 asa group of paths labeled 2 Clearly these paths arestratospheric arrivals corresponding to rays launched atslightly different downward angles along the flighttrajectory The timing of the arrivals relative to the sourceheights suggests sound generation primarily in the intervalabove 30 km The time of maximum for train 2 suggests apossible maximum in sound production near ~38 km thoughdifferences between the true atmosphere and our modelatmosphere make this number uncertain by at least severalkm The thermospheric path 3 also has an arrival timeconsistent with contribution to train 2 but this return islikely very weak (see below)

The final signal train (3) has a mean signal velocity near025 kms which is representative of thermospheric returnsFigure 14 shows the thermospheric ray arrivals typical ofpaths 4ndash6 Clearly all these paths represent thermosphericreturns For thermospheric returns to be the weakest of allinfrasonic signals is not uncommon due to the high signalabsorption at the top of the thermospheric waveguide (cfBeer [1974] for a detailed discussion) One of these arrivals(path 5) is an extremely high thermospheric arrival withconcomitantly high attenuation Thus path 5 probablycontributes little or not at all to the thermospheric signals Forthe same reason path 3 probably does not contributesignificantly to train 2

Fig 14 Examples of acoustic ray propagation from the fireball trajectory (here a point at 35 km altitude) to the station Freyung Path 1 isconfined to the top of the stratospheric channel (near 45 km altitude) and then leaks to the receiver This is the mode of propagation for thesignals associated with the observed train 1 The paths labeled 2 are confined to the stratospheric channel (between 5 km and 45 km) andform the train 2 Paths 3ndash6 are confined to the thermospheric channel (between ground level and 120ndash160 km) Path 3 may contribute totrain 2 while paths 4ndash6 form train 3

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

The Moraacutevka meteorite fall Infrasonic and seismic data 995

30 sec window bins over the course of the entire fireballairwave The trace velocity is a measure of the apparentvelocity of travel of the signal from one microphone to thenext the steeper the arrivals the higher the trace velocitiesHere we see that very little variation occurs in the tracevelocities over trains 1 and 2 with a slight possible increaseapparent over the duration of train 3 These wave train

signals are summarized in Table 3 along with times ofmaximum peak amplitudes and corresponding periods atmaximum amplitude

In the following sections we will use 2 approaches tostudy the propagation of acoustic waves from the fireballtrajectory to the station at Freyung to interpret these signalsFirst we employ a purely analytical method for a line source

Fig 6 The maximum correlation coefficient during the time centered around the Moraacutevka fireball signal at Freyung Windows of 30 sec (with50 overlap per window) are used to define individual measurements of cross-correlation The background cross-correlation in this frequencybandpass (03ndash9 Hz) calculated for the interval 3 minutes before the onset of the signal is 031 plusmn 002 and is shown by a thick solid horizontalline (mean) and thin lines representing the range of the standard deviation

Fig 7 Observed azimuths of infrasound arrival (north = 0) for each maximum in cross-correlation per bin

996 Brown et al

producing a cylindrical blast wave in a range-independentatmosphere Next a detailed numerical ray tracing approachis examined using moving point sources along the trajectoryin a range-dependent model atmosphere

INFRASONIC ANALYSIS FOR A CYLINDRICAL LINE SOURCE IN A

RANGE-INDEPENDENT ATMOSPHERE

As a means of examining the infrasound propagation in arange-independent atmosphere we can make use of thegeometrical acoustics approximation (wavelengths that aresmall compared to the pressure scale height the vertical scaleover which significant atmospheric pressure gradients canoccur) for which there are 2 constants of the motion in ahorizontally stratified steady state atmosphere that is anatmosphere with perfect stratification These constants are theheading of the wave normal (not the acoustic ray) from thesource and the characteristic velocity (Vk) generated at thesource In this approximation the arriving trace velocities atthe array are the same as the Vk values at the initial source

heights at which they were generated The characteristicvelocity can be thought of as the horizontal propagationvelocity modified for the effects of horizontal wind and entrygeometry (see ReVelle [1976] for a complete discussion)

Here we have reproduced the cylindrical line source blastwave approach developed by ReVelle (1976) In this methodthe characteristic velocity of the acoustic signal from the linesource is calculated as a function of altitude throughout theknown trajectory Due to non-steady effects or imperfectstratification (range dependent atmosphere effects etc) thevalue of the characteristic velocity is expected to be modifiedduring propagation In Figs 9 and 10 we have indicated theatmospheric structure parameters the so-called effectiveacoustic velocity (the signal propagation velocity includingwinds) and the calculated characteristic velocity (Vk) for therange of observed back azimuths from the infrasonicdetection at Freyung These parameters are all discussedfurther by Ceplecha et al (1998 p 380)

To model these acoustic arrivals we made use of theradiosonde data from Poprad Slovakia (~150 km ESE fromthe fireball) at 12 UT on May 6 2000 to define the

Fig 8 Observed trace velocities of the infrasound for each maximum in cross-correlation per bin

Table 3 Observed signal characteristics of the Moraacutevka fireball as seen from Freyung Germany on 6 May 2000 The start and end times are referenced to 115150 UT

Wave-train Start End DurationTime of max Azimuth

Peak amplitude

Trace velocity Period

Meansignal speed

(sec) (sec) (sec) (UT) (mPa) (kms) (s) (kms)

1 1180 1226 43 121142 685 638 0344 32 0302-0312plusmn07 plusmn72 plusmn0003 plusmn03

2 1247 1300 53 121257 667 2333 0355 41 0285-0297plusmn28 plusmn328 plusmn0013 plusmn08

3 1325 1490 165 ndash ndash 6 0353 ndash 0248-0279plusmn3 plusmn0026

The Moraacutevka meteorite fall Infrasonic and seismic data 997

temperature and wind field up to 30 km in altitude Above 30km we merged these radiosonde data with the MSIS-E (MassSpectrometer and Incoherent Scatter model) to produce thetemperature profile (cf Picone et al 1997) to a height of 140km inputting the appropriate geomagnetic indices for

May 6 2000 These indices significantly affect theatmospheric temperature and thus sound speed at heightsabove ~100 km The wind field above 30 km uses the HWM(Horizontal Wind Model) (Hedin et al 1996)

The propagation criterion within the geometricalacoustics approximation can be stated simply Whenever thecharacteristic velocity at the source exceeds the maximumeffective horizontal sound velocity over a given heightinterval ldquoraysrdquo will refract in such a way that they will reachthe ground (with sound waves bending away from regions ofincreasing temperatureincreasing sound speed gradients)

As indicated in Fig 10 for the altitude region from theground to ~118 km the maximum effective horizontal soundspeed is equal to 347 ms for our atmospheric conditions Forthose ldquoraysrdquo that have a Vk value greater than this valueldquorayrdquo paths exist between the line source sound generationaltitudes and points on the ground though in general only asmall subset will reach any given location (ie Freyung inour case)

Since the line source is a complicated acoustic raygeneration source we will first describe briefly the acousticradiation pattern In all cases where the velocity of themeteoroid is much higher than the local sound speed theradiation is perpendicular to the trajectory The only regionwhere this is not quite correct is near the bolide end heightwhere the Mach cone opens up substantially as the meteoroidis heavily decelerated shortly before the onset of dark flightand the fall of meteorites toward Earth Within the entryplane the vertical plane containing the trajectory that has anormal that is tangent to the earthrsquos surface immediatelybelow the mid-point of the fireball path the rays travel inexactly opposite azimuth to the heading of the bolide ietoward 3555deg (from the north) and have a downwardcomponent At the same time rays exist at all heights with anupward motion the heading of which is the same as the bolideie 1755deg but these do not generally reach the ground nearthe region of the fall ellipse and have not been examined hereAs the downward rays outside of the entry plane are examinedand we consider additional propagation directions we findthat the ray headings turn progressively toward less northerlydirections as the ray launch angle becomes less steepEventually as seen in Fig 11 the ray launch angle goes tozero (horizontally launched rays) at right angles to thetrajectory

Beyond this angle the rays have no initial downwardcomponent As further angular deviations from the entryplane are considered rays are launched at progressively largerhorizontal launch angles with an initial upward component totheir motion At horizontal launch angles of ~15ndash30deg andangular deviations from the entry plane of 110ndash115deg ie 20ndash25deg degrees above the horizontal the proper initial launchdirections are reached to enable rays to propagate to Freyung(arrival azimuths to Freyung of ~75ndash60deg where the arrivalazimuth is equal to the bolide heading (1755deg) minus theangular entry plane deviation) Note that these rays travel

Fig 9 Characteristic velocity as a function of height for the Moraacutevkabolide modeled as a line source explosion along with the effectivehorizontal sound speed as a function of height (far left hand curve asindicated)

Fig 10 Effective horizontal sound velocity versus height for ldquorayrdquopaths from the Moraacutevka trajectory over a range of azimuths (627deg to771deg) towards Freyung

998 Brown et al

upward first and are refracted downward by the zone of verylarge sound speed in the lower thermosphere These are theonly rays predicted to arrive at Freyung by the cylindrical linesource model

We summarize the predicted cylindrical line sourcebehavior by taking the vertical line from the ground effectivesound speed value until it crosses each of the respective Vk

contour lines for each direction with the minimum Vk valueequal to ~347 ms in Table 4

Having established that the only possible returns from aline source for Moraacutevka are rays launched upward initiallyand subsequently arriving after refraction from the lowerthermosphere below ~118 km (see also Fig 14 path 4) wemay estimate the region along the fireball trajectory fromwhich rays might be generated Our predicted lowest sourceheights for signal azimuths from 63ndash70deg for Moraacutevka as seenat Freyung are largely ~28 km in reasonable agreement withthe moving point source (see next section) and seismicresults We emphasize that the cylindrical line source modeldoes not show any downward stratospheric-type returns eventhough that such rays are observed in the infrasound seemsindisputable (see below)

Based on these calculations we plot the Vk value as afunction of the horizontal launch direction and of the entryplane deviations as shown in Fig 11 The computed line

source Vk values in Figs 10 and 11 vary from ~350ndash366 msfor source heights from ~28ndash36 km or 347ndash420 ms overazimuths at Freyung from ~63ndash77deg for all allowed sourceheights given in Table 4 The measured infrasonic tracespeeds (=Vk in a steady state horizontally stratifiedatmosphere assuming perfect stratification) are ~347ndash372 ms for azimuths at Freyung from ~62ndash702deg (see Figs 7 and 8)These calculations indicate the possible degree of errorinherent in infrasonic trace speeds at certain times effects dueto atmospheric range dependence non-steady effects localplanetary boundary influences or all of the above

INFRASONIC ANALYSIS OF A MOVING POINT SOURCE IN A RANGE-DEPENDENT ATMOSPHERE

If a significant fragmentation along the fireball trajectoryexists we expect that some rays will be launched at anglesother than purely normal to the trajectory To investigate thisscenario we shot rays from each point along the trajectorybelow 40 km in the direction of Freyung but with a widerange of elevation angles The rays were allowed to propagatethrough a steady state model atmosphere that allows forrange-dependence of atmospheric properties ie imperfectstratification effects including refraction in both thehorizontal and vertical planes The range dependence ispresent as a small change in the temperature (and thus thesound speed) at each height within the MSIS model Over therelatively short distance between the fireball and Freyunghowever this temperature change is on the order of 1deg or lessat most heights Clearly most of the differences between theresults from this model and from the cylindrical line sourcemodel arise primarily from differing initial launch geometriesfor the rays involved

We followed the complete acoustic path for each ray todetermine the delay time and arrival direction at the receiverof those rays passing within 10 km horizontally or verticallyand of the receiver array The wind field and temperatureprofiles used are shown in Fig 12 and the same atmosphericprofiles were used as in the range-independent analysisearlier

Fig 11 Contoured line source characteristic velocities (Vk) (ms) fora source height of 35 km for Moraacutevka as a function of the horizontalldquorayrdquo launch angle and the angular deviation from the entry plane Adeviation of 90deg is the dividing line between possible initial ldquorayrdquolaunch angles with upward (downward) paths for deviations gt90deg(lt90deg) Possible ldquorayrdquo paths to Freyung are indicated by the arrow forangular deviations from ~110ndash115deg and corresponding upward ldquorayrdquolaunch angles ~25ndash32deg The triangles represent computed Vk valuesand the labeled (connected) lines are the resulting contour values forVk The horizontal arrow shows the range of launch deviations andangular deviations for arrivals that could be observed at Freyung

Table 4 Possible infrasonic arrivals to Freyung from analytical solutions in the line source geometry and range-independent atmosphere

Azimuth arrival angle at Freyung (deg)

Angular entry plane deviation (deg)

Possible source altitudes (km)

627 1128 100andash695 651 1104 00andash690675 1080 280ndash650699 1056 280ndash640723 1032 345ndash595747 1008 345ndash590771 984 375ndash560

aThe Moraacutevka bolide did not maintain the necessary characteristics to be aline source explosion at such low heights

The Moraacutevka meteorite fall Infrasonic and seismic data 999

In this numerical model for a given elevation angle foreach launched ray the algorithm searches for ray pathsbeginning near the nominal great-circle azimuth between thepoint source along the fireball path and Freyung At eachiteration the closest approach distance between a test ray atsome launch azimuth and the receiver (Freyung) isdetermined and another ray at a slightly different azimuth ischosen in an attempt to decrease this distance and so forthThis iterative process continues until a ray launch azimuth isfound that meets the arrival criteria at Freyung or somespecified number of iterations made without success(typically on the order of several hundred at each launchelevation) This technique is used to find the full range ofpossible acoustic paths between each point along the fireballtrajectory and Freyung without any predetermination of thesource characteristics

The results of these acoustic runs are shown in Fig 13From the figure the modeled delay times clearly produceseveral sets of distinct arrivals at Freyung First an early setof model arrivals near 1180 sec corresponds well to the firstobserved maxima (train 1) in the amplitude record Second

2 major sets of acoustic arrivals starting at 1200 sec and 1330sec at low heights along the fireball trajectory and crossingnear 1280 sec at a source altitude of 42 km represent thesecond and largest maxima train 2 Finally 3 distinct sets ofarrival pathways beginning just before 1400 sec andcontinuing until 1550 sec correspond to the weaker train 3We will examine each of these arrival paths and label themchronologically from 1ndash6

The first of these paths (path 1) arrives with mean signalspeeds near 031 kms intermediate between the speedsexpected of tropospheric and stratospheric returns (cfCeplecha et al 1998 p 384) From Fig 13 these modeledarrivals are perhaps 10ndash20 sec earlier than the main signal fortrain 1 though they correspond with the beginning of thesignal at Freyung For the given travel times of ~1200 secthese errors amount to 1ndash2 which is a remarkableagreement given our approximations in the modeledatmosphere Figure 14 shows a typical arrival ray for thisacoustic path

Clearly this is an unusual ray path that resembles raysthat ldquoleakrdquo from the stratospheric waveguide and in so doing

Fig 12 Model atmospheric temperature profile (top) and wind field(bottom) used for numerical ray tracing and line source modelling

Fig 13 Modeled arrival times as a function of source height alongthe fireball trajectory (lower plot) compared to the observed signalamplitude at Freyung (top) The acoustic branch identifications givenin the lower plot follow the convention used in Figs 14 and 16 with(A) representing the anomalous ldquoleaky-ductrdquo path (S) stratosphericpaths and (T) thermospheric returns

1000 Brown et al

have shorter paths and thus higher average signal velocitiesthan normal stratospheric returns (cf Arase [1959] for anexample of this effect in the ocean) These waves propagateparallel to the Earthrsquos surface at the top of the stratosphericduct and ldquoleakrdquo back to the surface In previous work theinclusion of explicit range dependence of temperaturetypically results in these types of acoustic arrivals From oursimulation results the source heights responsible for thisinfrasound return are restricted to the interval from 34ndash40 kmaltitude along the fireball trajectory

We have found that removing the range dependence ofthe atmosphere does not remove this acoustic path Insteadwe were able to find this arrival only by searching with veryfine steps (01deg) in our numerical ray launch elevationsmodeled within the framework of a moving point source Fora given height only a very small range of launch anglesproduces this anomalous arrival path between the fireball andFreyung as shown in Fig 15 We find that for precisely theproper launch angle the ray paths appear to travel along thetop interface of the stratospheric duct where the turning pointat the local maximum in sound velocity is reached near 45 kmaltitude We also observe that generation of acoustic energyover this height interval is independently confirmed by themeasured arrival azimuth of 685deg which compares veryfavorably with our modeled range of ray arrival azimuths atFreyung for train 1 (67degndash69deg)

For train 2 the mean signal speed near 029 kms is

characteristic of stratospheric returns Typical raysassociated with these acoustic paths are shown in Fig 14 asa group of paths labeled 2 Clearly these paths arestratospheric arrivals corresponding to rays launched atslightly different downward angles along the flighttrajectory The timing of the arrivals relative to the sourceheights suggests sound generation primarily in the intervalabove 30 km The time of maximum for train 2 suggests apossible maximum in sound production near ~38 km thoughdifferences between the true atmosphere and our modelatmosphere make this number uncertain by at least severalkm The thermospheric path 3 also has an arrival timeconsistent with contribution to train 2 but this return islikely very weak (see below)

The final signal train (3) has a mean signal velocity near025 kms which is representative of thermospheric returnsFigure 14 shows the thermospheric ray arrivals typical ofpaths 4ndash6 Clearly all these paths represent thermosphericreturns For thermospheric returns to be the weakest of allinfrasonic signals is not uncommon due to the high signalabsorption at the top of the thermospheric waveguide (cfBeer [1974] for a detailed discussion) One of these arrivals(path 5) is an extremely high thermospheric arrival withconcomitantly high attenuation Thus path 5 probablycontributes little or not at all to the thermospheric signals Forthe same reason path 3 probably does not contributesignificantly to train 2

Fig 14 Examples of acoustic ray propagation from the fireball trajectory (here a point at 35 km altitude) to the station Freyung Path 1 isconfined to the top of the stratospheric channel (near 45 km altitude) and then leaks to the receiver This is the mode of propagation for thesignals associated with the observed train 1 The paths labeled 2 are confined to the stratospheric channel (between 5 km and 45 km) andform the train 2 Paths 3ndash6 are confined to the thermospheric channel (between ground level and 120ndash160 km) Path 3 may contribute totrain 2 while paths 4ndash6 form train 3

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

996 Brown et al

producing a cylindrical blast wave in a range-independentatmosphere Next a detailed numerical ray tracing approachis examined using moving point sources along the trajectoryin a range-dependent model atmosphere

INFRASONIC ANALYSIS FOR A CYLINDRICAL LINE SOURCE IN A

RANGE-INDEPENDENT ATMOSPHERE

As a means of examining the infrasound propagation in arange-independent atmosphere we can make use of thegeometrical acoustics approximation (wavelengths that aresmall compared to the pressure scale height the vertical scaleover which significant atmospheric pressure gradients canoccur) for which there are 2 constants of the motion in ahorizontally stratified steady state atmosphere that is anatmosphere with perfect stratification These constants are theheading of the wave normal (not the acoustic ray) from thesource and the characteristic velocity (Vk) generated at thesource In this approximation the arriving trace velocities atthe array are the same as the Vk values at the initial source

heights at which they were generated The characteristicvelocity can be thought of as the horizontal propagationvelocity modified for the effects of horizontal wind and entrygeometry (see ReVelle [1976] for a complete discussion)

Here we have reproduced the cylindrical line source blastwave approach developed by ReVelle (1976) In this methodthe characteristic velocity of the acoustic signal from the linesource is calculated as a function of altitude throughout theknown trajectory Due to non-steady effects or imperfectstratification (range dependent atmosphere effects etc) thevalue of the characteristic velocity is expected to be modifiedduring propagation In Figs 9 and 10 we have indicated theatmospheric structure parameters the so-called effectiveacoustic velocity (the signal propagation velocity includingwinds) and the calculated characteristic velocity (Vk) for therange of observed back azimuths from the infrasonicdetection at Freyung These parameters are all discussedfurther by Ceplecha et al (1998 p 380)

To model these acoustic arrivals we made use of theradiosonde data from Poprad Slovakia (~150 km ESE fromthe fireball) at 12 UT on May 6 2000 to define the

Fig 8 Observed trace velocities of the infrasound for each maximum in cross-correlation per bin

Table 3 Observed signal characteristics of the Moraacutevka fireball as seen from Freyung Germany on 6 May 2000 The start and end times are referenced to 115150 UT

Wave-train Start End DurationTime of max Azimuth

Peak amplitude

Trace velocity Period

Meansignal speed

(sec) (sec) (sec) (UT) (mPa) (kms) (s) (kms)

1 1180 1226 43 121142 685 638 0344 32 0302-0312plusmn07 plusmn72 plusmn0003 plusmn03

2 1247 1300 53 121257 667 2333 0355 41 0285-0297plusmn28 plusmn328 plusmn0013 plusmn08

3 1325 1490 165 ndash ndash 6 0353 ndash 0248-0279plusmn3 plusmn0026

The Moraacutevka meteorite fall Infrasonic and seismic data 997

temperature and wind field up to 30 km in altitude Above 30km we merged these radiosonde data with the MSIS-E (MassSpectrometer and Incoherent Scatter model) to produce thetemperature profile (cf Picone et al 1997) to a height of 140km inputting the appropriate geomagnetic indices for

May 6 2000 These indices significantly affect theatmospheric temperature and thus sound speed at heightsabove ~100 km The wind field above 30 km uses the HWM(Horizontal Wind Model) (Hedin et al 1996)

The propagation criterion within the geometricalacoustics approximation can be stated simply Whenever thecharacteristic velocity at the source exceeds the maximumeffective horizontal sound velocity over a given heightinterval ldquoraysrdquo will refract in such a way that they will reachthe ground (with sound waves bending away from regions ofincreasing temperatureincreasing sound speed gradients)

As indicated in Fig 10 for the altitude region from theground to ~118 km the maximum effective horizontal soundspeed is equal to 347 ms for our atmospheric conditions Forthose ldquoraysrdquo that have a Vk value greater than this valueldquorayrdquo paths exist between the line source sound generationaltitudes and points on the ground though in general only asmall subset will reach any given location (ie Freyung inour case)

Since the line source is a complicated acoustic raygeneration source we will first describe briefly the acousticradiation pattern In all cases where the velocity of themeteoroid is much higher than the local sound speed theradiation is perpendicular to the trajectory The only regionwhere this is not quite correct is near the bolide end heightwhere the Mach cone opens up substantially as the meteoroidis heavily decelerated shortly before the onset of dark flightand the fall of meteorites toward Earth Within the entryplane the vertical plane containing the trajectory that has anormal that is tangent to the earthrsquos surface immediatelybelow the mid-point of the fireball path the rays travel inexactly opposite azimuth to the heading of the bolide ietoward 3555deg (from the north) and have a downwardcomponent At the same time rays exist at all heights with anupward motion the heading of which is the same as the bolideie 1755deg but these do not generally reach the ground nearthe region of the fall ellipse and have not been examined hereAs the downward rays outside of the entry plane are examinedand we consider additional propagation directions we findthat the ray headings turn progressively toward less northerlydirections as the ray launch angle becomes less steepEventually as seen in Fig 11 the ray launch angle goes tozero (horizontally launched rays) at right angles to thetrajectory

Beyond this angle the rays have no initial downwardcomponent As further angular deviations from the entryplane are considered rays are launched at progressively largerhorizontal launch angles with an initial upward component totheir motion At horizontal launch angles of ~15ndash30deg andangular deviations from the entry plane of 110ndash115deg ie 20ndash25deg degrees above the horizontal the proper initial launchdirections are reached to enable rays to propagate to Freyung(arrival azimuths to Freyung of ~75ndash60deg where the arrivalazimuth is equal to the bolide heading (1755deg) minus theangular entry plane deviation) Note that these rays travel

Fig 9 Characteristic velocity as a function of height for the Moraacutevkabolide modeled as a line source explosion along with the effectivehorizontal sound speed as a function of height (far left hand curve asindicated)

Fig 10 Effective horizontal sound velocity versus height for ldquorayrdquopaths from the Moraacutevka trajectory over a range of azimuths (627deg to771deg) towards Freyung

998 Brown et al

upward first and are refracted downward by the zone of verylarge sound speed in the lower thermosphere These are theonly rays predicted to arrive at Freyung by the cylindrical linesource model

We summarize the predicted cylindrical line sourcebehavior by taking the vertical line from the ground effectivesound speed value until it crosses each of the respective Vk

contour lines for each direction with the minimum Vk valueequal to ~347 ms in Table 4

Having established that the only possible returns from aline source for Moraacutevka are rays launched upward initiallyand subsequently arriving after refraction from the lowerthermosphere below ~118 km (see also Fig 14 path 4) wemay estimate the region along the fireball trajectory fromwhich rays might be generated Our predicted lowest sourceheights for signal azimuths from 63ndash70deg for Moraacutevka as seenat Freyung are largely ~28 km in reasonable agreement withthe moving point source (see next section) and seismicresults We emphasize that the cylindrical line source modeldoes not show any downward stratospheric-type returns eventhough that such rays are observed in the infrasound seemsindisputable (see below)

Based on these calculations we plot the Vk value as afunction of the horizontal launch direction and of the entryplane deviations as shown in Fig 11 The computed line

source Vk values in Figs 10 and 11 vary from ~350ndash366 msfor source heights from ~28ndash36 km or 347ndash420 ms overazimuths at Freyung from ~63ndash77deg for all allowed sourceheights given in Table 4 The measured infrasonic tracespeeds (=Vk in a steady state horizontally stratifiedatmosphere assuming perfect stratification) are ~347ndash372 ms for azimuths at Freyung from ~62ndash702deg (see Figs 7 and 8)These calculations indicate the possible degree of errorinherent in infrasonic trace speeds at certain times effects dueto atmospheric range dependence non-steady effects localplanetary boundary influences or all of the above

INFRASONIC ANALYSIS OF A MOVING POINT SOURCE IN A RANGE-DEPENDENT ATMOSPHERE

If a significant fragmentation along the fireball trajectoryexists we expect that some rays will be launched at anglesother than purely normal to the trajectory To investigate thisscenario we shot rays from each point along the trajectorybelow 40 km in the direction of Freyung but with a widerange of elevation angles The rays were allowed to propagatethrough a steady state model atmosphere that allows forrange-dependence of atmospheric properties ie imperfectstratification effects including refraction in both thehorizontal and vertical planes The range dependence ispresent as a small change in the temperature (and thus thesound speed) at each height within the MSIS model Over therelatively short distance between the fireball and Freyunghowever this temperature change is on the order of 1deg or lessat most heights Clearly most of the differences between theresults from this model and from the cylindrical line sourcemodel arise primarily from differing initial launch geometriesfor the rays involved

We followed the complete acoustic path for each ray todetermine the delay time and arrival direction at the receiverof those rays passing within 10 km horizontally or verticallyand of the receiver array The wind field and temperatureprofiles used are shown in Fig 12 and the same atmosphericprofiles were used as in the range-independent analysisearlier

Fig 11 Contoured line source characteristic velocities (Vk) (ms) fora source height of 35 km for Moraacutevka as a function of the horizontalldquorayrdquo launch angle and the angular deviation from the entry plane Adeviation of 90deg is the dividing line between possible initial ldquorayrdquolaunch angles with upward (downward) paths for deviations gt90deg(lt90deg) Possible ldquorayrdquo paths to Freyung are indicated by the arrow forangular deviations from ~110ndash115deg and corresponding upward ldquorayrdquolaunch angles ~25ndash32deg The triangles represent computed Vk valuesand the labeled (connected) lines are the resulting contour values forVk The horizontal arrow shows the range of launch deviations andangular deviations for arrivals that could be observed at Freyung

Table 4 Possible infrasonic arrivals to Freyung from analytical solutions in the line source geometry and range-independent atmosphere

Azimuth arrival angle at Freyung (deg)

Angular entry plane deviation (deg)

Possible source altitudes (km)

627 1128 100andash695 651 1104 00andash690675 1080 280ndash650699 1056 280ndash640723 1032 345ndash595747 1008 345ndash590771 984 375ndash560

aThe Moraacutevka bolide did not maintain the necessary characteristics to be aline source explosion at such low heights

The Moraacutevka meteorite fall Infrasonic and seismic data 999

In this numerical model for a given elevation angle foreach launched ray the algorithm searches for ray pathsbeginning near the nominal great-circle azimuth between thepoint source along the fireball path and Freyung At eachiteration the closest approach distance between a test ray atsome launch azimuth and the receiver (Freyung) isdetermined and another ray at a slightly different azimuth ischosen in an attempt to decrease this distance and so forthThis iterative process continues until a ray launch azimuth isfound that meets the arrival criteria at Freyung or somespecified number of iterations made without success(typically on the order of several hundred at each launchelevation) This technique is used to find the full range ofpossible acoustic paths between each point along the fireballtrajectory and Freyung without any predetermination of thesource characteristics

The results of these acoustic runs are shown in Fig 13From the figure the modeled delay times clearly produceseveral sets of distinct arrivals at Freyung First an early setof model arrivals near 1180 sec corresponds well to the firstobserved maxima (train 1) in the amplitude record Second

2 major sets of acoustic arrivals starting at 1200 sec and 1330sec at low heights along the fireball trajectory and crossingnear 1280 sec at a source altitude of 42 km represent thesecond and largest maxima train 2 Finally 3 distinct sets ofarrival pathways beginning just before 1400 sec andcontinuing until 1550 sec correspond to the weaker train 3We will examine each of these arrival paths and label themchronologically from 1ndash6

The first of these paths (path 1) arrives with mean signalspeeds near 031 kms intermediate between the speedsexpected of tropospheric and stratospheric returns (cfCeplecha et al 1998 p 384) From Fig 13 these modeledarrivals are perhaps 10ndash20 sec earlier than the main signal fortrain 1 though they correspond with the beginning of thesignal at Freyung For the given travel times of ~1200 secthese errors amount to 1ndash2 which is a remarkableagreement given our approximations in the modeledatmosphere Figure 14 shows a typical arrival ray for thisacoustic path

Clearly this is an unusual ray path that resembles raysthat ldquoleakrdquo from the stratospheric waveguide and in so doing

Fig 12 Model atmospheric temperature profile (top) and wind field(bottom) used for numerical ray tracing and line source modelling

Fig 13 Modeled arrival times as a function of source height alongthe fireball trajectory (lower plot) compared to the observed signalamplitude at Freyung (top) The acoustic branch identifications givenin the lower plot follow the convention used in Figs 14 and 16 with(A) representing the anomalous ldquoleaky-ductrdquo path (S) stratosphericpaths and (T) thermospheric returns

1000 Brown et al

have shorter paths and thus higher average signal velocitiesthan normal stratospheric returns (cf Arase [1959] for anexample of this effect in the ocean) These waves propagateparallel to the Earthrsquos surface at the top of the stratosphericduct and ldquoleakrdquo back to the surface In previous work theinclusion of explicit range dependence of temperaturetypically results in these types of acoustic arrivals From oursimulation results the source heights responsible for thisinfrasound return are restricted to the interval from 34ndash40 kmaltitude along the fireball trajectory

We have found that removing the range dependence ofthe atmosphere does not remove this acoustic path Insteadwe were able to find this arrival only by searching with veryfine steps (01deg) in our numerical ray launch elevationsmodeled within the framework of a moving point source Fora given height only a very small range of launch anglesproduces this anomalous arrival path between the fireball andFreyung as shown in Fig 15 We find that for precisely theproper launch angle the ray paths appear to travel along thetop interface of the stratospheric duct where the turning pointat the local maximum in sound velocity is reached near 45 kmaltitude We also observe that generation of acoustic energyover this height interval is independently confirmed by themeasured arrival azimuth of 685deg which compares veryfavorably with our modeled range of ray arrival azimuths atFreyung for train 1 (67degndash69deg)

For train 2 the mean signal speed near 029 kms is

characteristic of stratospheric returns Typical raysassociated with these acoustic paths are shown in Fig 14 asa group of paths labeled 2 Clearly these paths arestratospheric arrivals corresponding to rays launched atslightly different downward angles along the flighttrajectory The timing of the arrivals relative to the sourceheights suggests sound generation primarily in the intervalabove 30 km The time of maximum for train 2 suggests apossible maximum in sound production near ~38 km thoughdifferences between the true atmosphere and our modelatmosphere make this number uncertain by at least severalkm The thermospheric path 3 also has an arrival timeconsistent with contribution to train 2 but this return islikely very weak (see below)

The final signal train (3) has a mean signal velocity near025 kms which is representative of thermospheric returnsFigure 14 shows the thermospheric ray arrivals typical ofpaths 4ndash6 Clearly all these paths represent thermosphericreturns For thermospheric returns to be the weakest of allinfrasonic signals is not uncommon due to the high signalabsorption at the top of the thermospheric waveguide (cfBeer [1974] for a detailed discussion) One of these arrivals(path 5) is an extremely high thermospheric arrival withconcomitantly high attenuation Thus path 5 probablycontributes little or not at all to the thermospheric signals Forthe same reason path 3 probably does not contributesignificantly to train 2

Fig 14 Examples of acoustic ray propagation from the fireball trajectory (here a point at 35 km altitude) to the station Freyung Path 1 isconfined to the top of the stratospheric channel (near 45 km altitude) and then leaks to the receiver This is the mode of propagation for thesignals associated with the observed train 1 The paths labeled 2 are confined to the stratospheric channel (between 5 km and 45 km) andform the train 2 Paths 3ndash6 are confined to the thermospheric channel (between ground level and 120ndash160 km) Path 3 may contribute totrain 2 while paths 4ndash6 form train 3

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

The Moraacutevka meteorite fall Infrasonic and seismic data 997

temperature and wind field up to 30 km in altitude Above 30km we merged these radiosonde data with the MSIS-E (MassSpectrometer and Incoherent Scatter model) to produce thetemperature profile (cf Picone et al 1997) to a height of 140km inputting the appropriate geomagnetic indices for

May 6 2000 These indices significantly affect theatmospheric temperature and thus sound speed at heightsabove ~100 km The wind field above 30 km uses the HWM(Horizontal Wind Model) (Hedin et al 1996)

The propagation criterion within the geometricalacoustics approximation can be stated simply Whenever thecharacteristic velocity at the source exceeds the maximumeffective horizontal sound velocity over a given heightinterval ldquoraysrdquo will refract in such a way that they will reachthe ground (with sound waves bending away from regions ofincreasing temperatureincreasing sound speed gradients)

As indicated in Fig 10 for the altitude region from theground to ~118 km the maximum effective horizontal soundspeed is equal to 347 ms for our atmospheric conditions Forthose ldquoraysrdquo that have a Vk value greater than this valueldquorayrdquo paths exist between the line source sound generationaltitudes and points on the ground though in general only asmall subset will reach any given location (ie Freyung inour case)

Since the line source is a complicated acoustic raygeneration source we will first describe briefly the acousticradiation pattern In all cases where the velocity of themeteoroid is much higher than the local sound speed theradiation is perpendicular to the trajectory The only regionwhere this is not quite correct is near the bolide end heightwhere the Mach cone opens up substantially as the meteoroidis heavily decelerated shortly before the onset of dark flightand the fall of meteorites toward Earth Within the entryplane the vertical plane containing the trajectory that has anormal that is tangent to the earthrsquos surface immediatelybelow the mid-point of the fireball path the rays travel inexactly opposite azimuth to the heading of the bolide ietoward 3555deg (from the north) and have a downwardcomponent At the same time rays exist at all heights with anupward motion the heading of which is the same as the bolideie 1755deg but these do not generally reach the ground nearthe region of the fall ellipse and have not been examined hereAs the downward rays outside of the entry plane are examinedand we consider additional propagation directions we findthat the ray headings turn progressively toward less northerlydirections as the ray launch angle becomes less steepEventually as seen in Fig 11 the ray launch angle goes tozero (horizontally launched rays) at right angles to thetrajectory

Beyond this angle the rays have no initial downwardcomponent As further angular deviations from the entryplane are considered rays are launched at progressively largerhorizontal launch angles with an initial upward component totheir motion At horizontal launch angles of ~15ndash30deg andangular deviations from the entry plane of 110ndash115deg ie 20ndash25deg degrees above the horizontal the proper initial launchdirections are reached to enable rays to propagate to Freyung(arrival azimuths to Freyung of ~75ndash60deg where the arrivalazimuth is equal to the bolide heading (1755deg) minus theangular entry plane deviation) Note that these rays travel

Fig 9 Characteristic velocity as a function of height for the Moraacutevkabolide modeled as a line source explosion along with the effectivehorizontal sound speed as a function of height (far left hand curve asindicated)

Fig 10 Effective horizontal sound velocity versus height for ldquorayrdquopaths from the Moraacutevka trajectory over a range of azimuths (627deg to771deg) towards Freyung

998 Brown et al

upward first and are refracted downward by the zone of verylarge sound speed in the lower thermosphere These are theonly rays predicted to arrive at Freyung by the cylindrical linesource model

We summarize the predicted cylindrical line sourcebehavior by taking the vertical line from the ground effectivesound speed value until it crosses each of the respective Vk

contour lines for each direction with the minimum Vk valueequal to ~347 ms in Table 4

Having established that the only possible returns from aline source for Moraacutevka are rays launched upward initiallyand subsequently arriving after refraction from the lowerthermosphere below ~118 km (see also Fig 14 path 4) wemay estimate the region along the fireball trajectory fromwhich rays might be generated Our predicted lowest sourceheights for signal azimuths from 63ndash70deg for Moraacutevka as seenat Freyung are largely ~28 km in reasonable agreement withthe moving point source (see next section) and seismicresults We emphasize that the cylindrical line source modeldoes not show any downward stratospheric-type returns eventhough that such rays are observed in the infrasound seemsindisputable (see below)

Based on these calculations we plot the Vk value as afunction of the horizontal launch direction and of the entryplane deviations as shown in Fig 11 The computed line

source Vk values in Figs 10 and 11 vary from ~350ndash366 msfor source heights from ~28ndash36 km or 347ndash420 ms overazimuths at Freyung from ~63ndash77deg for all allowed sourceheights given in Table 4 The measured infrasonic tracespeeds (=Vk in a steady state horizontally stratifiedatmosphere assuming perfect stratification) are ~347ndash372 ms for azimuths at Freyung from ~62ndash702deg (see Figs 7 and 8)These calculations indicate the possible degree of errorinherent in infrasonic trace speeds at certain times effects dueto atmospheric range dependence non-steady effects localplanetary boundary influences or all of the above

INFRASONIC ANALYSIS OF A MOVING POINT SOURCE IN A RANGE-DEPENDENT ATMOSPHERE

If a significant fragmentation along the fireball trajectoryexists we expect that some rays will be launched at anglesother than purely normal to the trajectory To investigate thisscenario we shot rays from each point along the trajectorybelow 40 km in the direction of Freyung but with a widerange of elevation angles The rays were allowed to propagatethrough a steady state model atmosphere that allows forrange-dependence of atmospheric properties ie imperfectstratification effects including refraction in both thehorizontal and vertical planes The range dependence ispresent as a small change in the temperature (and thus thesound speed) at each height within the MSIS model Over therelatively short distance between the fireball and Freyunghowever this temperature change is on the order of 1deg or lessat most heights Clearly most of the differences between theresults from this model and from the cylindrical line sourcemodel arise primarily from differing initial launch geometriesfor the rays involved

We followed the complete acoustic path for each ray todetermine the delay time and arrival direction at the receiverof those rays passing within 10 km horizontally or verticallyand of the receiver array The wind field and temperatureprofiles used are shown in Fig 12 and the same atmosphericprofiles were used as in the range-independent analysisearlier

Fig 11 Contoured line source characteristic velocities (Vk) (ms) fora source height of 35 km for Moraacutevka as a function of the horizontalldquorayrdquo launch angle and the angular deviation from the entry plane Adeviation of 90deg is the dividing line between possible initial ldquorayrdquolaunch angles with upward (downward) paths for deviations gt90deg(lt90deg) Possible ldquorayrdquo paths to Freyung are indicated by the arrow forangular deviations from ~110ndash115deg and corresponding upward ldquorayrdquolaunch angles ~25ndash32deg The triangles represent computed Vk valuesand the labeled (connected) lines are the resulting contour values forVk The horizontal arrow shows the range of launch deviations andangular deviations for arrivals that could be observed at Freyung

Table 4 Possible infrasonic arrivals to Freyung from analytical solutions in the line source geometry and range-independent atmosphere

Azimuth arrival angle at Freyung (deg)

Angular entry plane deviation (deg)

Possible source altitudes (km)

627 1128 100andash695 651 1104 00andash690675 1080 280ndash650699 1056 280ndash640723 1032 345ndash595747 1008 345ndash590771 984 375ndash560

aThe Moraacutevka bolide did not maintain the necessary characteristics to be aline source explosion at such low heights

The Moraacutevka meteorite fall Infrasonic and seismic data 999

In this numerical model for a given elevation angle foreach launched ray the algorithm searches for ray pathsbeginning near the nominal great-circle azimuth between thepoint source along the fireball path and Freyung At eachiteration the closest approach distance between a test ray atsome launch azimuth and the receiver (Freyung) isdetermined and another ray at a slightly different azimuth ischosen in an attempt to decrease this distance and so forthThis iterative process continues until a ray launch azimuth isfound that meets the arrival criteria at Freyung or somespecified number of iterations made without success(typically on the order of several hundred at each launchelevation) This technique is used to find the full range ofpossible acoustic paths between each point along the fireballtrajectory and Freyung without any predetermination of thesource characteristics

The results of these acoustic runs are shown in Fig 13From the figure the modeled delay times clearly produceseveral sets of distinct arrivals at Freyung First an early setof model arrivals near 1180 sec corresponds well to the firstobserved maxima (train 1) in the amplitude record Second

2 major sets of acoustic arrivals starting at 1200 sec and 1330sec at low heights along the fireball trajectory and crossingnear 1280 sec at a source altitude of 42 km represent thesecond and largest maxima train 2 Finally 3 distinct sets ofarrival pathways beginning just before 1400 sec andcontinuing until 1550 sec correspond to the weaker train 3We will examine each of these arrival paths and label themchronologically from 1ndash6

The first of these paths (path 1) arrives with mean signalspeeds near 031 kms intermediate between the speedsexpected of tropospheric and stratospheric returns (cfCeplecha et al 1998 p 384) From Fig 13 these modeledarrivals are perhaps 10ndash20 sec earlier than the main signal fortrain 1 though they correspond with the beginning of thesignal at Freyung For the given travel times of ~1200 secthese errors amount to 1ndash2 which is a remarkableagreement given our approximations in the modeledatmosphere Figure 14 shows a typical arrival ray for thisacoustic path

Clearly this is an unusual ray path that resembles raysthat ldquoleakrdquo from the stratospheric waveguide and in so doing

Fig 12 Model atmospheric temperature profile (top) and wind field(bottom) used for numerical ray tracing and line source modelling

Fig 13 Modeled arrival times as a function of source height alongthe fireball trajectory (lower plot) compared to the observed signalamplitude at Freyung (top) The acoustic branch identifications givenin the lower plot follow the convention used in Figs 14 and 16 with(A) representing the anomalous ldquoleaky-ductrdquo path (S) stratosphericpaths and (T) thermospheric returns

1000 Brown et al

have shorter paths and thus higher average signal velocitiesthan normal stratospheric returns (cf Arase [1959] for anexample of this effect in the ocean) These waves propagateparallel to the Earthrsquos surface at the top of the stratosphericduct and ldquoleakrdquo back to the surface In previous work theinclusion of explicit range dependence of temperaturetypically results in these types of acoustic arrivals From oursimulation results the source heights responsible for thisinfrasound return are restricted to the interval from 34ndash40 kmaltitude along the fireball trajectory

We have found that removing the range dependence ofthe atmosphere does not remove this acoustic path Insteadwe were able to find this arrival only by searching with veryfine steps (01deg) in our numerical ray launch elevationsmodeled within the framework of a moving point source Fora given height only a very small range of launch anglesproduces this anomalous arrival path between the fireball andFreyung as shown in Fig 15 We find that for precisely theproper launch angle the ray paths appear to travel along thetop interface of the stratospheric duct where the turning pointat the local maximum in sound velocity is reached near 45 kmaltitude We also observe that generation of acoustic energyover this height interval is independently confirmed by themeasured arrival azimuth of 685deg which compares veryfavorably with our modeled range of ray arrival azimuths atFreyung for train 1 (67degndash69deg)

For train 2 the mean signal speed near 029 kms is

characteristic of stratospheric returns Typical raysassociated with these acoustic paths are shown in Fig 14 asa group of paths labeled 2 Clearly these paths arestratospheric arrivals corresponding to rays launched atslightly different downward angles along the flighttrajectory The timing of the arrivals relative to the sourceheights suggests sound generation primarily in the intervalabove 30 km The time of maximum for train 2 suggests apossible maximum in sound production near ~38 km thoughdifferences between the true atmosphere and our modelatmosphere make this number uncertain by at least severalkm The thermospheric path 3 also has an arrival timeconsistent with contribution to train 2 but this return islikely very weak (see below)

The final signal train (3) has a mean signal velocity near025 kms which is representative of thermospheric returnsFigure 14 shows the thermospheric ray arrivals typical ofpaths 4ndash6 Clearly all these paths represent thermosphericreturns For thermospheric returns to be the weakest of allinfrasonic signals is not uncommon due to the high signalabsorption at the top of the thermospheric waveguide (cfBeer [1974] for a detailed discussion) One of these arrivals(path 5) is an extremely high thermospheric arrival withconcomitantly high attenuation Thus path 5 probablycontributes little or not at all to the thermospheric signals Forthe same reason path 3 probably does not contributesignificantly to train 2

Fig 14 Examples of acoustic ray propagation from the fireball trajectory (here a point at 35 km altitude) to the station Freyung Path 1 isconfined to the top of the stratospheric channel (near 45 km altitude) and then leaks to the receiver This is the mode of propagation for thesignals associated with the observed train 1 The paths labeled 2 are confined to the stratospheric channel (between 5 km and 45 km) andform the train 2 Paths 3ndash6 are confined to the thermospheric channel (between ground level and 120ndash160 km) Path 3 may contribute totrain 2 while paths 4ndash6 form train 3

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

998 Brown et al

upward first and are refracted downward by the zone of verylarge sound speed in the lower thermosphere These are theonly rays predicted to arrive at Freyung by the cylindrical linesource model

We summarize the predicted cylindrical line sourcebehavior by taking the vertical line from the ground effectivesound speed value until it crosses each of the respective Vk

contour lines for each direction with the minimum Vk valueequal to ~347 ms in Table 4

Having established that the only possible returns from aline source for Moraacutevka are rays launched upward initiallyand subsequently arriving after refraction from the lowerthermosphere below ~118 km (see also Fig 14 path 4) wemay estimate the region along the fireball trajectory fromwhich rays might be generated Our predicted lowest sourceheights for signal azimuths from 63ndash70deg for Moraacutevka as seenat Freyung are largely ~28 km in reasonable agreement withthe moving point source (see next section) and seismicresults We emphasize that the cylindrical line source modeldoes not show any downward stratospheric-type returns eventhough that such rays are observed in the infrasound seemsindisputable (see below)

Based on these calculations we plot the Vk value as afunction of the horizontal launch direction and of the entryplane deviations as shown in Fig 11 The computed line

source Vk values in Figs 10 and 11 vary from ~350ndash366 msfor source heights from ~28ndash36 km or 347ndash420 ms overazimuths at Freyung from ~63ndash77deg for all allowed sourceheights given in Table 4 The measured infrasonic tracespeeds (=Vk in a steady state horizontally stratifiedatmosphere assuming perfect stratification) are ~347ndash372 ms for azimuths at Freyung from ~62ndash702deg (see Figs 7 and 8)These calculations indicate the possible degree of errorinherent in infrasonic trace speeds at certain times effects dueto atmospheric range dependence non-steady effects localplanetary boundary influences or all of the above

INFRASONIC ANALYSIS OF A MOVING POINT SOURCE IN A RANGE-DEPENDENT ATMOSPHERE

If a significant fragmentation along the fireball trajectoryexists we expect that some rays will be launched at anglesother than purely normal to the trajectory To investigate thisscenario we shot rays from each point along the trajectorybelow 40 km in the direction of Freyung but with a widerange of elevation angles The rays were allowed to propagatethrough a steady state model atmosphere that allows forrange-dependence of atmospheric properties ie imperfectstratification effects including refraction in both thehorizontal and vertical planes The range dependence ispresent as a small change in the temperature (and thus thesound speed) at each height within the MSIS model Over therelatively short distance between the fireball and Freyunghowever this temperature change is on the order of 1deg or lessat most heights Clearly most of the differences between theresults from this model and from the cylindrical line sourcemodel arise primarily from differing initial launch geometriesfor the rays involved

We followed the complete acoustic path for each ray todetermine the delay time and arrival direction at the receiverof those rays passing within 10 km horizontally or verticallyand of the receiver array The wind field and temperatureprofiles used are shown in Fig 12 and the same atmosphericprofiles were used as in the range-independent analysisearlier

Fig 11 Contoured line source characteristic velocities (Vk) (ms) fora source height of 35 km for Moraacutevka as a function of the horizontalldquorayrdquo launch angle and the angular deviation from the entry plane Adeviation of 90deg is the dividing line between possible initial ldquorayrdquolaunch angles with upward (downward) paths for deviations gt90deg(lt90deg) Possible ldquorayrdquo paths to Freyung are indicated by the arrow forangular deviations from ~110ndash115deg and corresponding upward ldquorayrdquolaunch angles ~25ndash32deg The triangles represent computed Vk valuesand the labeled (connected) lines are the resulting contour values forVk The horizontal arrow shows the range of launch deviations andangular deviations for arrivals that could be observed at Freyung

Table 4 Possible infrasonic arrivals to Freyung from analytical solutions in the line source geometry and range-independent atmosphere

Azimuth arrival angle at Freyung (deg)

Angular entry plane deviation (deg)

Possible source altitudes (km)

627 1128 100andash695 651 1104 00andash690675 1080 280ndash650699 1056 280ndash640723 1032 345ndash595747 1008 345ndash590771 984 375ndash560

aThe Moraacutevka bolide did not maintain the necessary characteristics to be aline source explosion at such low heights

The Moraacutevka meteorite fall Infrasonic and seismic data 999

In this numerical model for a given elevation angle foreach launched ray the algorithm searches for ray pathsbeginning near the nominal great-circle azimuth between thepoint source along the fireball path and Freyung At eachiteration the closest approach distance between a test ray atsome launch azimuth and the receiver (Freyung) isdetermined and another ray at a slightly different azimuth ischosen in an attempt to decrease this distance and so forthThis iterative process continues until a ray launch azimuth isfound that meets the arrival criteria at Freyung or somespecified number of iterations made without success(typically on the order of several hundred at each launchelevation) This technique is used to find the full range ofpossible acoustic paths between each point along the fireballtrajectory and Freyung without any predetermination of thesource characteristics

The results of these acoustic runs are shown in Fig 13From the figure the modeled delay times clearly produceseveral sets of distinct arrivals at Freyung First an early setof model arrivals near 1180 sec corresponds well to the firstobserved maxima (train 1) in the amplitude record Second

2 major sets of acoustic arrivals starting at 1200 sec and 1330sec at low heights along the fireball trajectory and crossingnear 1280 sec at a source altitude of 42 km represent thesecond and largest maxima train 2 Finally 3 distinct sets ofarrival pathways beginning just before 1400 sec andcontinuing until 1550 sec correspond to the weaker train 3We will examine each of these arrival paths and label themchronologically from 1ndash6

The first of these paths (path 1) arrives with mean signalspeeds near 031 kms intermediate between the speedsexpected of tropospheric and stratospheric returns (cfCeplecha et al 1998 p 384) From Fig 13 these modeledarrivals are perhaps 10ndash20 sec earlier than the main signal fortrain 1 though they correspond with the beginning of thesignal at Freyung For the given travel times of ~1200 secthese errors amount to 1ndash2 which is a remarkableagreement given our approximations in the modeledatmosphere Figure 14 shows a typical arrival ray for thisacoustic path

Clearly this is an unusual ray path that resembles raysthat ldquoleakrdquo from the stratospheric waveguide and in so doing

Fig 12 Model atmospheric temperature profile (top) and wind field(bottom) used for numerical ray tracing and line source modelling

Fig 13 Modeled arrival times as a function of source height alongthe fireball trajectory (lower plot) compared to the observed signalamplitude at Freyung (top) The acoustic branch identifications givenin the lower plot follow the convention used in Figs 14 and 16 with(A) representing the anomalous ldquoleaky-ductrdquo path (S) stratosphericpaths and (T) thermospheric returns

1000 Brown et al

have shorter paths and thus higher average signal velocitiesthan normal stratospheric returns (cf Arase [1959] for anexample of this effect in the ocean) These waves propagateparallel to the Earthrsquos surface at the top of the stratosphericduct and ldquoleakrdquo back to the surface In previous work theinclusion of explicit range dependence of temperaturetypically results in these types of acoustic arrivals From oursimulation results the source heights responsible for thisinfrasound return are restricted to the interval from 34ndash40 kmaltitude along the fireball trajectory

We have found that removing the range dependence ofthe atmosphere does not remove this acoustic path Insteadwe were able to find this arrival only by searching with veryfine steps (01deg) in our numerical ray launch elevationsmodeled within the framework of a moving point source Fora given height only a very small range of launch anglesproduces this anomalous arrival path between the fireball andFreyung as shown in Fig 15 We find that for precisely theproper launch angle the ray paths appear to travel along thetop interface of the stratospheric duct where the turning pointat the local maximum in sound velocity is reached near 45 kmaltitude We also observe that generation of acoustic energyover this height interval is independently confirmed by themeasured arrival azimuth of 685deg which compares veryfavorably with our modeled range of ray arrival azimuths atFreyung for train 1 (67degndash69deg)

For train 2 the mean signal speed near 029 kms is

characteristic of stratospheric returns Typical raysassociated with these acoustic paths are shown in Fig 14 asa group of paths labeled 2 Clearly these paths arestratospheric arrivals corresponding to rays launched atslightly different downward angles along the flighttrajectory The timing of the arrivals relative to the sourceheights suggests sound generation primarily in the intervalabove 30 km The time of maximum for train 2 suggests apossible maximum in sound production near ~38 km thoughdifferences between the true atmosphere and our modelatmosphere make this number uncertain by at least severalkm The thermospheric path 3 also has an arrival timeconsistent with contribution to train 2 but this return islikely very weak (see below)

The final signal train (3) has a mean signal velocity near025 kms which is representative of thermospheric returnsFigure 14 shows the thermospheric ray arrivals typical ofpaths 4ndash6 Clearly all these paths represent thermosphericreturns For thermospheric returns to be the weakest of allinfrasonic signals is not uncommon due to the high signalabsorption at the top of the thermospheric waveguide (cfBeer [1974] for a detailed discussion) One of these arrivals(path 5) is an extremely high thermospheric arrival withconcomitantly high attenuation Thus path 5 probablycontributes little or not at all to the thermospheric signals Forthe same reason path 3 probably does not contributesignificantly to train 2

Fig 14 Examples of acoustic ray propagation from the fireball trajectory (here a point at 35 km altitude) to the station Freyung Path 1 isconfined to the top of the stratospheric channel (near 45 km altitude) and then leaks to the receiver This is the mode of propagation for thesignals associated with the observed train 1 The paths labeled 2 are confined to the stratospheric channel (between 5 km and 45 km) andform the train 2 Paths 3ndash6 are confined to the thermospheric channel (between ground level and 120ndash160 km) Path 3 may contribute totrain 2 while paths 4ndash6 form train 3

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

The Moraacutevka meteorite fall Infrasonic and seismic data 999

In this numerical model for a given elevation angle foreach launched ray the algorithm searches for ray pathsbeginning near the nominal great-circle azimuth between thepoint source along the fireball path and Freyung At eachiteration the closest approach distance between a test ray atsome launch azimuth and the receiver (Freyung) isdetermined and another ray at a slightly different azimuth ischosen in an attempt to decrease this distance and so forthThis iterative process continues until a ray launch azimuth isfound that meets the arrival criteria at Freyung or somespecified number of iterations made without success(typically on the order of several hundred at each launchelevation) This technique is used to find the full range ofpossible acoustic paths between each point along the fireballtrajectory and Freyung without any predetermination of thesource characteristics

The results of these acoustic runs are shown in Fig 13From the figure the modeled delay times clearly produceseveral sets of distinct arrivals at Freyung First an early setof model arrivals near 1180 sec corresponds well to the firstobserved maxima (train 1) in the amplitude record Second

2 major sets of acoustic arrivals starting at 1200 sec and 1330sec at low heights along the fireball trajectory and crossingnear 1280 sec at a source altitude of 42 km represent thesecond and largest maxima train 2 Finally 3 distinct sets ofarrival pathways beginning just before 1400 sec andcontinuing until 1550 sec correspond to the weaker train 3We will examine each of these arrival paths and label themchronologically from 1ndash6

The first of these paths (path 1) arrives with mean signalspeeds near 031 kms intermediate between the speedsexpected of tropospheric and stratospheric returns (cfCeplecha et al 1998 p 384) From Fig 13 these modeledarrivals are perhaps 10ndash20 sec earlier than the main signal fortrain 1 though they correspond with the beginning of thesignal at Freyung For the given travel times of ~1200 secthese errors amount to 1ndash2 which is a remarkableagreement given our approximations in the modeledatmosphere Figure 14 shows a typical arrival ray for thisacoustic path

Clearly this is an unusual ray path that resembles raysthat ldquoleakrdquo from the stratospheric waveguide and in so doing

Fig 12 Model atmospheric temperature profile (top) and wind field(bottom) used for numerical ray tracing and line source modelling

Fig 13 Modeled arrival times as a function of source height alongthe fireball trajectory (lower plot) compared to the observed signalamplitude at Freyung (top) The acoustic branch identifications givenin the lower plot follow the convention used in Figs 14 and 16 with(A) representing the anomalous ldquoleaky-ductrdquo path (S) stratosphericpaths and (T) thermospheric returns

1000 Brown et al

have shorter paths and thus higher average signal velocitiesthan normal stratospheric returns (cf Arase [1959] for anexample of this effect in the ocean) These waves propagateparallel to the Earthrsquos surface at the top of the stratosphericduct and ldquoleakrdquo back to the surface In previous work theinclusion of explicit range dependence of temperaturetypically results in these types of acoustic arrivals From oursimulation results the source heights responsible for thisinfrasound return are restricted to the interval from 34ndash40 kmaltitude along the fireball trajectory

We have found that removing the range dependence ofthe atmosphere does not remove this acoustic path Insteadwe were able to find this arrival only by searching with veryfine steps (01deg) in our numerical ray launch elevationsmodeled within the framework of a moving point source Fora given height only a very small range of launch anglesproduces this anomalous arrival path between the fireball andFreyung as shown in Fig 15 We find that for precisely theproper launch angle the ray paths appear to travel along thetop interface of the stratospheric duct where the turning pointat the local maximum in sound velocity is reached near 45 kmaltitude We also observe that generation of acoustic energyover this height interval is independently confirmed by themeasured arrival azimuth of 685deg which compares veryfavorably with our modeled range of ray arrival azimuths atFreyung for train 1 (67degndash69deg)

For train 2 the mean signal speed near 029 kms is

characteristic of stratospheric returns Typical raysassociated with these acoustic paths are shown in Fig 14 asa group of paths labeled 2 Clearly these paths arestratospheric arrivals corresponding to rays launched atslightly different downward angles along the flighttrajectory The timing of the arrivals relative to the sourceheights suggests sound generation primarily in the intervalabove 30 km The time of maximum for train 2 suggests apossible maximum in sound production near ~38 km thoughdifferences between the true atmosphere and our modelatmosphere make this number uncertain by at least severalkm The thermospheric path 3 also has an arrival timeconsistent with contribution to train 2 but this return islikely very weak (see below)

The final signal train (3) has a mean signal velocity near025 kms which is representative of thermospheric returnsFigure 14 shows the thermospheric ray arrivals typical ofpaths 4ndash6 Clearly all these paths represent thermosphericreturns For thermospheric returns to be the weakest of allinfrasonic signals is not uncommon due to the high signalabsorption at the top of the thermospheric waveguide (cfBeer [1974] for a detailed discussion) One of these arrivals(path 5) is an extremely high thermospheric arrival withconcomitantly high attenuation Thus path 5 probablycontributes little or not at all to the thermospheric signals Forthe same reason path 3 probably does not contributesignificantly to train 2

Fig 14 Examples of acoustic ray propagation from the fireball trajectory (here a point at 35 km altitude) to the station Freyung Path 1 isconfined to the top of the stratospheric channel (near 45 km altitude) and then leaks to the receiver This is the mode of propagation for thesignals associated with the observed train 1 The paths labeled 2 are confined to the stratospheric channel (between 5 km and 45 km) andform the train 2 Paths 3ndash6 are confined to the thermospheric channel (between ground level and 120ndash160 km) Path 3 may contribute totrain 2 while paths 4ndash6 form train 3

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

1000 Brown et al

have shorter paths and thus higher average signal velocitiesthan normal stratospheric returns (cf Arase [1959] for anexample of this effect in the ocean) These waves propagateparallel to the Earthrsquos surface at the top of the stratosphericduct and ldquoleakrdquo back to the surface In previous work theinclusion of explicit range dependence of temperaturetypically results in these types of acoustic arrivals From oursimulation results the source heights responsible for thisinfrasound return are restricted to the interval from 34ndash40 kmaltitude along the fireball trajectory

We have found that removing the range dependence ofthe atmosphere does not remove this acoustic path Insteadwe were able to find this arrival only by searching with veryfine steps (01deg) in our numerical ray launch elevationsmodeled within the framework of a moving point source Fora given height only a very small range of launch anglesproduces this anomalous arrival path between the fireball andFreyung as shown in Fig 15 We find that for precisely theproper launch angle the ray paths appear to travel along thetop interface of the stratospheric duct where the turning pointat the local maximum in sound velocity is reached near 45 kmaltitude We also observe that generation of acoustic energyover this height interval is independently confirmed by themeasured arrival azimuth of 685deg which compares veryfavorably with our modeled range of ray arrival azimuths atFreyung for train 1 (67degndash69deg)

For train 2 the mean signal speed near 029 kms is

characteristic of stratospheric returns Typical raysassociated with these acoustic paths are shown in Fig 14 asa group of paths labeled 2 Clearly these paths arestratospheric arrivals corresponding to rays launched atslightly different downward angles along the flighttrajectory The timing of the arrivals relative to the sourceheights suggests sound generation primarily in the intervalabove 30 km The time of maximum for train 2 suggests apossible maximum in sound production near ~38 km thoughdifferences between the true atmosphere and our modelatmosphere make this number uncertain by at least severalkm The thermospheric path 3 also has an arrival timeconsistent with contribution to train 2 but this return islikely very weak (see below)

The final signal train (3) has a mean signal velocity near025 kms which is representative of thermospheric returnsFigure 14 shows the thermospheric ray arrivals typical ofpaths 4ndash6 Clearly all these paths represent thermosphericreturns For thermospheric returns to be the weakest of allinfrasonic signals is not uncommon due to the high signalabsorption at the top of the thermospheric waveguide (cfBeer [1974] for a detailed discussion) One of these arrivals(path 5) is an extremely high thermospheric arrival withconcomitantly high attenuation Thus path 5 probablycontributes little or not at all to the thermospheric signals Forthe same reason path 3 probably does not contributesignificantly to train 2

Fig 14 Examples of acoustic ray propagation from the fireball trajectory (here a point at 35 km altitude) to the station Freyung Path 1 isconfined to the top of the stratospheric channel (near 45 km altitude) and then leaks to the receiver This is the mode of propagation for thesignals associated with the observed train 1 The paths labeled 2 are confined to the stratospheric channel (between 5 km and 45 km) andform the train 2 Paths 3ndash6 are confined to the thermospheric channel (between ground level and 120ndash160 km) Path 3 may contribute totrain 2 while paths 4ndash6 form train 3

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

The Moraacutevka meteorite fall Infrasonic and seismic data 1001

One puzzling aspect of the signal of train 3 is its lowtrace velocity (see Table 3) In general we expectthermospheric returns to be steeper than stratospheric returnswith higher trace velocities This points to the fact noted inMcIntosh and ReVelle (1984) that the elevation arrival anglemeasured by the horizontal trace velocity is inherently lessreliable as a parameter than is the plane wave back azimuthThis is due in part to local meteorological effects which attimes can change the elevation arrival angle considerablySimilar trace velocities are also found for other Moraacutevkaarrivals that have been ducted between the ground and theupper stratosphere and between the ground and the lowerthermosphere so we are very confident that themeasurements are correct The inherent error in these tracevelocity values is certainly larger than that inferred by themeasured standard error (see McIntosh and ReVelle [1984]for a more complete discussion of this effect)

We also caution that the individual ray arrival timescomputed here are in reality the center of a wave train emittedby each moving point source along the trajectory in the contextof our modeling This wave train experiences dispersion alongthe propagation route (not taken into account in our geometricray approximation) which acts to smear out the overall signalyielding the longer wave trains actually observed

Figure 16 shows the deviations of individual rays fromthe direction perpendicular to the fireball trajectory Only therays corresponding to path 4 and launched at heights of~25ndash35 km are sufficiently close to the perpendiculardirection to be considered part of the cylindrical blast waveThis confirms the finding of the previous section that only

thermospheric returns are possible at Freyung from acylindrical line source As outlined in this section howeverthe strongest infrasonic signal at Freyung (train 2) wasproduced by stratospheric returns from a moving pointsource which we interpret to be most likely individualfragmentation events

The analysis of the video and seismic data for Moraacutevkapresented in Boroviegrave ka and Kalenda (2003) shows that alarge number of fragmentation events clearly occurredbetween 29ndash37 km lending further support to thisinterpretation We note that train 1 also was produced by amoving point source as the deviation from the perpendiculardirection was larger than ~5 degrees The fact that much of thesignal detected at Freyung was caused by fragmentationevents is not sufficient to conclude that in overall termsfragmentation was the main source of sounds associated withthe fireball In fact the geometric configuration and actualatmospheric conditions may have led to preferential detectionof acoustic energy produced from point sources at theparticular location of Freyung The propagation of cylindricalline source energy to Freyung would be greatly attenuated dueto the thermospheric nature of any such signals

In summary we find that at least 3 distinct soundldquochannelsrdquo provided signals at Freyung The 2 stratosphericchannels dominate the signal energy but noticeable energyfrom thermospheric returns is also recorded late in the recordThe earliest arrival is notable as being due to leaky-duct-typepropagation not normally recorded for atmosphericexplosions

Fig 15 Ray paths from point source at 35 km near elevation launchangle needed to form leaky duct solutions Here each ray is launchedand incremented 01ordm in elevation relative to its neighbor The changebetween stratospheric leaky duct and thermospheric arrivals occursover less than 03ordm difference in launch elevation at the interface Thisdemonstrates the sensitive dependence of this solution on preciselythe right launch angle for this particular height and our adoptedatmospheric parameters

Fig 16 The deviations of the individual ray launch directions fromthe direction perpendicular to the fireball trajectory plotted as afunction of source height along the fireball trajectory The rays aremarked by signal types (thermospheric stratospheric anomalous)and path numbers (see Figs 13 and 14)

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

1002 Brown et al

CONCLUSIONS

Acoustic energy from the Moraacutevka fireball was generatedat the source as both a cylindrical line source blast wave andfrom fragmentation events (which we term an extended linesource) in the height interval of ~30ndash40 km with a probablemaximum for the fragmentation-produced sound near 38 kmas measured at the location of Freyung These conclusions areconsistent with the results of Borovi egrave ka and Kalenda (2003)who measured directly the fragmentation as occurringprimarily between 29ndash37 km altitudes

The direct arrival of the cylindrical line source blast waveproduced the strongest signal on seismic stations located onboth sides of the fireball trajectory Stations located up rangeof the fireball terminal point registered the arrival of a nearlyspherical blast wave propagating from the terminal pointHowever the first though weaker waves arriving at allstations were air-coupled P-waves These are sonic wavestransformed to the ground P-waves and propagating quicklynear the surface of the Earth as described in Brown et al(2002b) The first waves originated at the fireball terminalpoint ie the lowest point of the trajectory and the P-waveswere followed by directly-coupled airwaves and largeramplitude Rayleigh waves

The seismic record also contains signatures of individualfragmentation events The fragmentations mimicked smallexplosions and formed quasi-spherical shock waves Deepunderground stations also detected the seismic signature of thefireball Reconstruction of the trajectory of the fireball waspossible based on seismic data alone to accuracies of 1deg inelevation of the fireball radiant and 35deg in the azimuth of theradiant as compared to the video-determined trajectory(Borovi egrave ka et al 2003a) This demonstrates the expectedaccuracy in seismic-only trajectory solutions Somewhatbetter precision might be obtained by including winds in thesolutions to modify the effective sound velocity

The propagation of sound to larger distances wasgoverned mostly by the geometry of the trajectory combinedwith the actual atmospheric conditions At Freyung aninfrasonic station located 360 km from the fireball 3 distinctsignal trains were measured The cylindrical blast wave mayhave contributed only the weakest signal by a refraction ofsound in the thermosphere at the height of ~120 km Thestrongest signal must have been produced by moving pointsources along the trajectory ie by the individualfragmentation events and recorded at the receiver by doublerefraction at the heights of 5 and 45 km The deviations of theacoustic ray launch angles from the perpendicular in thesefragmentation events was found to be between 5degndash30deg as seenfrom Freyung substantially larger than the few degrees ofdeviation expected from a purely cylindrical line sourcemodel The first signal arrival was propagating through thestratosphere horizontally and then leaked to the receiver Thisis the first time to our knowledge that such an anomalous

hybrid horizontal-stratospheric mode of acoustic propagationhas actually been observed for an atmospheric source

AcknowledgmentsndashSeismic data were provided by J Holecko(DPB Paskov) J Pazdirkova (Masaryk University Brno) PWiejacz (Institute of Geophysics Polish Academy ofSciences) and W Wojtak (Silesian Geophysical ObservatoryRaciborz) infrasonic data and calibration information werekindly sent by G Hartman (German Federal Institute forGeosciences and Natural Resources Hannover) Supportingmeteorological data were obtained from J Lukacko (SlovakHydrometeorological Institute Ganovce) P Zarsky and MSetvak (Czech Hydrometeorological Institute Praha)Infrasonic modeling of point sources was done using theInframap utility developed by BBN technologies a specialthanks to D Norris for providing support with this modelingP G Brown acknowledges support in the form of a director-sponsored post-doctoral fellowship at Los Alamos NationalLaboratory P Jenniskens provided valuable comments on anearlier version of this manuscript

Editorial HandlingmdashDr Donald Brownlee

REFERENCES

Anglin F M and Haddon R A W 1987 Meteoroid sonic shock-wave-generated seismic signals observed at a seismic arrayNature 328607ndash609

Arase T 1959 Some characteristics of long-range explosive soundpropagation Acoustical Society of America Journal 31588ndash595

Beer T 1974 Atmospheric waves New York Halsted Press p 315 Borovi egrave ka J Spurny P Kalenda P and Tagliaferri E 2003a The

Moraacutevka meteorite fall 1 Description of the events anddetermination of the fireball trajectory and orbit from videorecords Meteoritics amp Planetary Science This issue

Borovi egrave ka J Weber H W Jopek T Jake sup1 P Randa Z Brown P GReVelle D O Kalenda P Schultz L Kucera J Haloda JTyacutecovaacute P Fryacuteda J and Brandstaumltter F 2003b The Moraacutevkameteorite fall 3 Meteoroid initial size history structure andcomposition Meteoritics amp Planetary Science This issue

Borovi egrave ka J and Kalenda P 2003 The Moraacutevka meteorite fall 4Meteoroid dynamics and fragmentation in the atmosphereMeteoritics amp Planetary Science This issue

Brown P Whitaker R W Rodney W ReVelle D O and TagliaferriE 2002a Multi-station infrasonic observations of two largebolides Signal interpretation and implications for monitoring ofatmospheric explosions Geophysical Research Letters 2914-1ndash14-4

Brown P ReVelle D O Tagliaferri E and Hildebrand A R 2002bAn entry model for the Tagish Lake fireball using seismicsatellite and infrasound records Meteoritics amp PlanetaryScience 37661ndash676

Ceplecha Z Borovi egrave ka J Elford W G ReVelle D O Hawkes RL Porub egrave an V and Šimek M 1998 Meteor phenomena andbodies Space Science Reviews 84327ndash471

Cevolani G 1994 The explosion of the bolide over Lugo di Romagna(Italy) on 19 January 1993 Planetary and Space Science 42767ndash775

Cumming G L 1989 Alberta bolide of June 1 1982 Interpretation

The Moraacutevka meteorite fall Infrasonic and seismic data 1003

of photographic and seismic records Canadian Journal of EarthSciences 261350ndash1355

Evers L and Haak H 2001 Sounds from a meteor and oceanicwaves Geophysical Research Letters 2841ndash44

Folinsbee R E Bayrock L A Cumming G L and Smith D G W1969 Vilna MeteoritemdashCamera visual seismic and analyticrecords Journal of the Royal Astronomical Society of Canada 6361ndash86

Hedin A E Fleming E L Manson A H Schmidlin F J Avery SK Clark R R Franke S J Fraser G J Tsuda T Vial F andVincent R A 1996 Empirical wind model for the uppermiddle and lower atmosphere Journal of Atmospheric andTerrestrial Physics 581421ndash1447

Ishihara Y Tsukada S Sakai S Hiramatsu Y and Furumoto M2001 Determination of the fireball trajectory using dense seismicarrays Bulletin of the Earthquake Research Institute Universityof Tokyo 7687ndash92

McIntosh B A and ReVelle D O 1984 Traveling atmospheric

pressure waves measured during a solar eclipse Journal ofGeophysical Research 894953ndash4962

Picone J M Hedin A E Coffey S L Lean J Drob D P NealH Melendez-Alvira D J Meier R R and Mariska J T 1997The Naval Research Laboratory Program on empirical modelsof the neutral upper atmosphere In Advances in theastronautical sciences edited by Hoots F R Kaufman BCefola P J and Spencer D B San Diego AmericanAstronautical Society 2184 p

Qamar A 1995 Space shuttle and meteroid-tracking supersonicobjects in the atmosphere with seismographs SeismologicalResearch Letters 666ndash12

ReVelle D O 1976 On meteor-generated infrasound Journal ofGeophysical Research 811217ndash1240

ReVelle D O 1997 Historical detection of atmospheric impacts oflarge super-bolides using acoustic-gravity waves Annals of theNew York Academy of Sciences 822284ndash302