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ACTA MONTANA 1992Series A, No. 3(89), 89-110

SEISMIC SOUHCE SELF-ORGANIZING

a Vladimir Aksenov, a Jan Kozák, a Vladimír Rudajev, a Jan Vilhelmand b Tomáš Lokajíček

a Institute of Geotechnics, Czechoslovak Academy of Sciences,V Holešovičkách 41, 182 09 Prague, Czechoslovakia

b Geophysical Institute, Czech. Acad. Sci., Boční II, 141 31 Prague,Czechoslovakia

Abstract: In the paper the results of the frequency analysis ofthe elastic pulses fr.om the loaded rock sample source models, ofthe rockbursts records and of the seismograms of selected shallowearthquakes are presented. For all the three categories of studythe fundamental symptoms of non-linear processes in seismie fociwere found and demonstrated as clearly pronounced. Namely, themodulation of elastic waves generated in the source under load,the self- synchronizing the individual. components of the wavefield and the coherent wave radiation were repeatedly observedwhich can be understood as the pr.ecur sor s of the final stage ofelastie radiation in which the shift of the maximum in frequencyspeetra to lower values oceur, what is reflected in a release ofthe maximum amount of seismie energy. All this indicates that.'le non-linear processes can participate in a seismic sourceduring the energy release. Also, certain weak points of "linear"theories of the seismic source (such as, e.g., the seismic sourcesize, etc.) can be easily understand and explained from the viewpoint of non-linear dynamies.

Key words: seismic source physics, frequency analysis, non-lineardynamics, self-organizing processes.

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1. INTRODUCTION

.In the last 20 years numerous theoretical models of a seismicsource were introduced and applied for the solution of individualseismic events, see, e.g., J. N. Brune (1970), J. N. Brune at al.(1979), V. Grosser at al. (1979), R. Madariaga (1976) and V.

Rudajev (1986). These models were altogether based on the physicsof linear dynamics, in which the principles of wave superpositionruled the process of interaction and interfering the seismicwaves. As the fundamental characteristics of a seismic source thefollowing parameters have been considered. Size of a seismicsource (volume V, radius r, length 1), magnitude M, stress droptJ. (5" , Burger's vector u, seismic moment Mo' slip velocity vsI'rupture velocity vr' source radiation characteristics, and time tof the displacement iniciation and propagation.

In the classical concepts of the seismic source models theincrease of the earthquake magnitude is explained by the increaseof the source volume/dimensions (see, e.g., Sadovski 1984, Brune1970). Fur ther , the observed narrowing down the spec t ra andgrowth of the wave period T as a function of increasing magnitudeM is believed to occure due to the extending the time (duration)of seismogenic processes in a seismic foci.

As for the natural events, however, the seismic sizp(volurne) computed frorn spectral properties of radiated waves, asshown e.g., in the works of Brune (1970) and R. Madariage (1976)reached unrealistically large values, especially as concerns thelarge earthquakes, H > 6. To reduce this apparent disagreernentbetween observed and cornputed focus size, an the artificialcoefficient K was introduced, what actually ment that the shearwave ve loc ity {3 value was in the cornputations reduced S to 10times.

These observed changes of the frequencies in the re.Iation tomagnitudo can be explained also using the supposttion ofnonlinear processes in the seismic source. This supposition hasits response in thé nonlinear superposi tion of seismic waves(amplitude modulation, coherent radiation, narrowing down thespectraJ.

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These mentioned characteristics, connected e.g. with nonconstant displacernent velocity in the seismic source, wereobserved in the large scale of radiated seismic energy - from SApulses, rockbursts, to the earthquakes.

2. THE NONLINEAR EFFECTS RESPONSED IN RADIATED WAVES

Linear approach, which is mostly used up to date, is based onthe principle of superposition of radiated waves, i.e. theresu1ted seismic signa1 is done by the surnmation of the signalsof the individual elernentar sources

n

IY Y.1

i=lThe principle of superposition of the seismic waves is valid inthe case of constant displacement ve10city in the source and whenthe focus is situated in the Hooke's medium.

In the case of the non constant displacement Crupturelvelocity or the non-Hooke' s medium, the principle ofsuperposition is not generally valid, and the re1ations ofnonlinear physics can be used. These facts resu1tes to theamp1itude modulation of seismic radiated signals from individualsources, what can be described as follows :

Y = ao [1 + m.f(t)] sin (wot + ~ol,

where sin (wot + ~o) is rnodulated signal and [(tj is modulatingsigna1, m is called the modu1ation depth. This is reflected inthe spectral pattern of resulting radiation: instead of the twofrequencies characterizing both inter-acting radiations, the

+{o- ~f: the value of 6f is the

modulating radiation [(t), after Kharkievich, 1953.

w /2rr ) ofo

frequenciesmodu1ated radiation and

the frequency fo (

two other (sate1ite)three frequencies will occure. Namely,

frequency of

Another phenomenon important in non-linear dynamics is theprincip1e of forced synchronization, firstly discovered' byHuygens on the behaviour of mechanica1 systems, La ter explainedby Poincaré (1928) and Mendelstham (1950) on the platform ofnon-linear differential equations. In the recent works, see e.g.,Nicolis (1986), the effect of self synchronization is sometimescalled 'self-organizing'. Commonly, it can be described asfollows: During mutual interaction of non-linear oscillators the

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mutual energy exchange occurs. Gradually, due to internalrela tions, the energy interchange results í nt,o the osci llat ionphases synchronization. Finally, a coherent radiation isestab li shed . Dur ing this process, the energy of the wave fieldgrowths considerably, because as concerns coherent radiation its

energy W is proportional to the square number of interactingoscillators W - E n~ in' contrast to non-coherent radiation forwhich W - E n.

After Nikolis (1986), during such a coherent radiation, thevalue of frequency can decrease.

The physical processes in a seismic source propagate wi thvariable displacement velocity (slip velocity) and therefore theelementary source oscillators mutually interchange their energy,what is reflected in the variations of their phases, so that theresulting radiation can be proper ly described in' terms ofnon-linear dynamics.

In the following an attempt is presented to detect theprinciples of seismic source self-organizing in a wide range ofenergy release fromlevels: these levels extend'seismoacoustic emission recorded in laboratory, up to tectonicalearthquakes.

3. LABORATORY EXPERIMENTS

An extent series of laboratory experiments on biaxiallyloaded rock samples was performed in order to detect thesymptoms of non-linear processes described above.

As physical models triples of rectangular blocks of magnesitewere used, see Fig. 1. The blocks were located in a special modelstructure, in which they were subjected to confining force P2'

After.fixing the desirable value of the load PZ' the models werepressed by load P1 so that the inner block was pressed againstthe outer blocks. Prior to loading, two p í ck -ups were fixed onthe model surface, one (No.l) in the vicinity of the displacementplane, the other (No.2) ácros s it. Pick-up No.l was anaccelerometer and recorded acoustic emission, pick-up No. Z wasof a gauge type and recorded the mutual displacement of modelblocks.

Load P 1 was uniaxial, 1inearly increasing force. It was

the

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appLi ed up to the values of cca 60 kN (which corresponds the-1stress vaIue ~1 = ZO MPa). Loading rate was cca 500 Ns. It was

expected that in the course of increasing the P1 compression fastseismogenic dispIacements' along the displacement plane wouldoccur.

Confining load Pz was fixed in several load levels, wiťh astep of approx. 3.3 kN. After fixing the Pz Ioad and increasingthe Pl load, seismogenic displacements occurred. The emitedseismic pulses were recorded by pick-ups Nos 1, 2 and stored intransienť recorder DL 912 in the digital formo Sampling rate was10 HHz. The dead time (during data transfer) was O.Z S. The FFTanaIysis of the recorded pulses was performed by means of currentroutines.

In the given set up of the experiment, the requiredconditions of mechanical friction coupling were satisfied, whatresuIted in sťick-slip occurrence. Let us have a look at the waveform of the pulses radiated by the stick-slip instabíIitites.Coming from the level ~2 = 3.0 HPa to level 0'2 = 4.65 HPa, we cansee a stress formation of the originally complex/chaoticwavefield consisting of numerous frequency components i."ntoa moresimple, monochromaťic-like waveform in which the high-frequencycomponents appear only in the front part of the pulse. At thelast Pz level (0'2 = 5.Z HPa) the wave form resumes a more complextype again, see Fig. Z. An interesťing tendency can also be seenin the pulse envelope curves as related to individual Pz levels.From the level O'z = 3.0 HPa up to level O'z = 4.65 HPa a cleartendency can be detected from the originally chaotic pulsation ofthe recorded signal to a clearly modulated one. This modulationdisappears for the pulses recorded at level O'z = 5.2 HPa.

The above features are clearly reflected in the amplitudefrequency spectra af these pulses, see Fig. 3: going from the 1.level (O"'Z = 3.O HPa) over the 2.individual spectra harmonics merge;

Leve I (O'2 = 3.55 HPa) thethis makes the spectra more

simple, which physically meahs more coherent. This effectculminates at the 3. P2 level (O'Z = 4.1 HPa), characterized by anearly monochromatic spectrum Cfmax 36 kHz) with wellpronounced satellite components. For the 4. level (~Z = 4.65 HPa)this monochromatic behaviour is st i II preserved, however, thefrequency maximum is shifted from 36 kHz, the spectrum satellite

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eomponents being quite marked1y expressed. At the last 5. 1evel(~2 = 5.Z MPa) the previous self- organizing of the wave fie1d islost and the speetrum resumes to its initia1 complex/chaoticstate.

The aim of the seeond series of laboratory measurementsperformed was to verify whether the dependenees obtained in theprevious measurements (on magnesite samp1es) wil1 be true a1sofor the other roek materials. model sizes and contact conditions.As for the roek media fine grained sandstone (grain size sma11erthen 0.5 mm) and coarse grained sandstone (grains 4-8 mm) weretested. Coneerning the model size, the structures of 150x150x.60mm and 40x40x60 mm were treated; in such a way the models of1arger and smaller dimensions were investigated than thesemagnesite ones of the first series. Two types of the eontactsurfaces were tested, name1y the ordinary surfaee obtained afterthe samp1e eut by a diamond saw, and, seeond1y, the finepo1ished, eontact surfaces. The experimental set up was the sameas the previous arrangement of the measurement on magnesitesamples. As coneerns the eonfining load Pz it was kept eonstantfor al1 the experiments being se1eeted within the zone ofstick-slip seismie souree eharaeter.

In Fig. 4 the two examples of pulses (and their speetra)from loaded magnesite mode1s are g í ven. The 1eft hand pulse iseharacterized by a non-eoherent radiation with the wide/eomplexspectrum and relatively low amplitude. The right hand pieturepresents another type of the pulse, already modulated, what isreflected in clearly expressed satelite spectra components.

Also the two series in Fig. 5 presenting the pu1ses radiatedfrom loaded model eomposed of fine grained sandstone (Upperseries, pu1ses 1 - 3) and of eoarse grained sandstone (bottomseries, pulses 4 - 6) demonstrate the typieal stages of seismieenergy release revea1ed a1ready in the measurements on themagnesite models. Independently on the grain size of both theroek materials, the radiated pu1ses are (f í.rst Ly ) eharaeterizedby a low intensity and by spectra with numerous loeal maxima, seethe two pietures in the first eo1lumn of Fig. 5. An inerese ofthe amplitude is evident in the middle collumn of the picture inwhich the pulses with modulated wave-pattern are shown. Thepulses given in the third collumn of the picture present fully

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coherent radiation for all the rock material?Also, a clear shift of the maximum amplitude spectral

component to lower frequeney vaIues is elearly seen in Fig. '5 :

from app. 80 kHz to app. 40 kHz for the fine grained sandstone(see the upper series, the second and third record) and from forapp. 112 kHz to app. 16 kHz .(7 times) for the eoarse grainedsandstone, bottom series, .aecond and third picture).

The componental difference (grain s í ze) of both the rockmaterials are well reflected in the discussed spectra. For thecoarse grained sandstone the radiation works on higherfrequeneies, beeause the stress coneentration is eonsiderablyhigher on the large grain eontacts of the border faee incomparison with, more or less, regularly distributed stress fieldalong the eontaet sample faees for the fine grained sandstone.Aecording to this, the shift of the frequency maxima, to lowervalues is larger for the eoarse grained sandstone model.

Thus , it is demonstrated here , that the frequeney reeordeddoes not depend on the dimensions of the focal zone, but on thestate of the rock, on its composition and on the contactconditions along the seismogenie fault.

The results obtained clearly demonstrate strenghtening thenon-linear processes as a funetion of eonfining pressure; as itincreases the spectrum of radiated waves beeomes more simple, seethe levels 3 and 4 in Figs 2 and 3. This phenomenon refleets thegrowing degree af generated oseillations' eohereney. In thisphase of loading the "satelite" Ioeal maxima in amplitude speetraoccur as well as the shift of the frequency of maximum amplitudeto lower frequencies what fits wel! the Poincaré/Mendelsthamtheory. In the highest degree of the coherency of radiatedoscillations the energy of the vave field reaches its maximum

value. Further, loading the model results in the return ofcoherent wave field into its initial chaotic state. AIl thisspeaks in favour to non-linear processes in a seismic sourcesimulated in laboratory conditions.

4. ROCKBURST fOCI IN MINES

The rockbursts belong to the typical seismic phenomena whichoccure as a result of interaction between the tectonical stress

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field changes and an undeground man-activity. The time pattern ofthe focal zone fracturing can hardly be described by means ofsimple physical models in most cases because the rupture processcannot be explained by a force dipole only, in contrast to thetectonic earthquakes. The natural space distribution of stressedin a rock massif which interferes with the effects of localstress redistributions due to mining excavation (expIor-a t icn ),results into a complex way of fracturing and also to thetime-variable radiation of seismic energy. The time pattern of asource function depends on the mechanical parameters of the rockmassif, source geometry and rupture mechanism. Due to smallepicentral distances the dimensions of the rock-burst focusshould not be neglected.

It was expected t.hatthe time variable pattern of fracturínghad a character of a non-linear dynamica1 processes. For theverification of this hypothesis the 39. rockburst records frornthe Ostrava coal basin (Nord Moravia), ranging the time intervalApr-Nov 1988 were subjected to the frequency- arnplitudeanalysis.The treated series of recordings was selected of the large arnountof seisrnograms of rockbursts from a given region, which werelocated in a small room. They were believed to represent onefocal zone. The type analysis of the appurtenant seismogramsconfirmed that these quakes belonged to the same rockburstfami1y; nine records of the treated series are shown in Fig. 6.The 1ast rockburst of this series (4.10.1988) beLorige d to thestrongest quakes of the studied sequence,· its magnitude wasMl = 1.73, see No. 37 in Fig. 6. The weakest tremor of the serieswas classified by magnitude Ml 0.25.

The results of the frequency analysis of the rockburstseismograms are in agreement with the non-linear principles g.fseismic energy radiation, c.f. the spectra given in Fig. 7, whichbelong to the seismograms from Fig. 6; here the amplitude maximumis denoted by the asteriks. It is we11 seen in the picture, thatthe spectrum maxima (except No. 37) always lie in the narrow

+frequency band 3.6 - O.5 Hz. As for the record No . 37, themaximum in its spectrum lies at 1.2 Hz, so that the thirdharmonics of this pulse is identical with the amp1itude maxima ofthe previous pulses. By the other hand the wave period enlargedthree times. This is in good agreement with the theory by

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Poincaré/Mandelstham who formul.ated the possibility of enlarging

the wave period n-times, where n is a natural number, for

non-linear systems. Also the satelite local maxima al-e well

developed in the spectra - some of them are denoted by black

point. What also speaks in favour for non-linear processes in the

rockburst foci.

5. SEISMICDATAANALYSIS

For testing possible non-linear processes in tectonical

earthquake foci, a series of 6 recordings of aftershock events

which followed the main 1989 Spitak earthquakes were analyzed. A

relatively srnall nurnber of suitable seisrnic event s at our

disposal was due to the principle that only those seismograms

couId be analyzed which were recorded right in the epicentre of

the earthquake or in the near zone. The recordings from larger

epicentral distances were not treated, since due to numerous

reflections, dissipation and local effects, they considerably

distort the information on the wave process in earthquake focus.

For the same reason only shallow earthquakes were taken into

consideration. (In principle also seismograms recorded in larger

epicentral distances could be utilized if only proper signal

filtration had been applied, which eliminated the above signal

deformationsJ.

In Figs 8 and 9 seismograms of s í x strong 1988/89 Spitak

aftershocks are plotted which occurred in period Dec 19-31, 1988

(Fig. 8) and in Jan '1-8, 1989 (Fig. 9), respectively. (The main

shock occurred on Dec 7; 1988). In Fig. 8 the horizontal

components recorded in W-E direction are plotted in which the

largest values of acceleration were recorded; the sei.smograms are

complemented with the amplitude-frequency spectra.

In Figs 8 and 9 - from top to bot tom - characteristic changes

in seismogram forrris are displayed. In this series the amplitude

of accelerograms gradually increases in time. This increase

corresponds to magnitude Mb increase, from Mb= 4.2, over Mb ;:

4.3 up to Mo = 4,9 (for Fig. 8). A similar series is given for

Fig. 9 where Mb 4.1, 4.4, and 4.8., respectively.

The changes in complexi ty of the wave form in both the

1988/89 Spitak aftershocks series, see Figs 8 and 9, can be

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considered as the transformation from linear to non/linearprocesess. The spectra of these aftershocks change from complexand wide spectra which originaUy have numerous components in thehigh-frequency band (for lower Mb values) to modulated coherentspectra with the side satellite .components (for the higher Mbvalues). This indicates that the process of automodulation due toincreasing confining pressure has a more common character andunde r certain conditions can be found in both, laboratory andnature conditions. It is assumed that with increasing Mb valuesalso the confining pressure growth when the same focal region isconsidered. This spectra evolution is demonstrated in figs 10 and11. It fo11ows that a given structure can release the maximumelastic energy under full coherency of radiated pulses, what canbe explained using the principles of non-linear dynamics.

The effect of coherency observed in the investigatedaftershocks from Spitak series (1988/89) was also found in thecase of the three aftershocks Oroville (1975, Aug 05, 06 and 11).

CONCLUSION

It is considered in the presented contribution, that therelease of seismic energy can be characterised as a non-linearprocess. The main considered aspects of this approach werenon-linear superposition, represented by the amplitudemodulation, the synchronisation, the coherency and a frequencyshift of the resulting elastic radiation.

These aspects were found in the seismie records in widefrequency band seismoaeoustie signals (laboratory tests),records of loeal seismic network (rockbursts in coal mines) andseismograms of teetonieal earthquakes. In all three thesecategories cf measurement the symptoms of non-linearity ofseismogenie process were detected and manifested: of wave-fieldmodulation (satelites in speetra), synchronization (spectrasimplification, their transformation to narrow spectral band),frequency shift to lower values (which does not result fromenlarging the source size but from increasing degr-ee of theproeess of non-linearity) and finally radiation coherency. Underthis presumptions the seismic souree can be eharacterised by ahigh degree of self-organizing and earry much higher energy (for

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a given vol ume) than this one derived on the basis of linear

approach (the radiated energy is not proportional to the summof

elementary sub-sources, but to the square of this summ). On this

basis also the disagreement between the source size observed in

the nature and computeď by means of linear physics, can be

explained.

The non-linear approach can also be used as a new tool for

the assessments of a maximum possibly released energy of the

ear thquake Lat the moment of highest degree of radiated waves

coherency) which is - for a focal/seismic zone - an important

parameter for the seismic hazard classification.

REFERENCES

Brune, J.N. (1970). Tectonic stress and the spectra of seismicshear waves from earthquakes, JGR,Vol. 75, 4997-5009.

Brune, J.N., Archuleta, R.J., Hartzel, S. (1979). Far field S-wavespectra, corner frequencies and pulse shapes, JGR, Vol. 84,No. ES, 2262-2272.

Cao, T., Aki, K. (1986). Effect of slip rate on stress drop,Pageoph, Vol. 124, No. 3, 515-53.0.

Chai.kin , S. E. (971) Fizitscheskie osnovy mechaniki, in Russian,

(Physical Fundaments of Mechanicsl, Nauka, Moscow.

Kharkievich, A.A. (1953) Spektri i analiz (Spectra and ana l ys i s l ,

in Russian, GITTL, Moscow.

Davi s , J. P., Sa.cks , 1. S., Linde , A.T., (1989). Source complexity

of small earthquakes near Matsushira, Japan, Tectonophys.,

166, 175-187.

Gorelik, G.S. (1959) Kol.ebany í a i vol ny , in Russian, CVibration

and Waves), Nauka, Moscow.

Cr-ose r , H., Poppitz R., Knoll, P. (1979). The Problem of the

Focal Mechanism of Seismic Events in Mining Regions. Acta

Montana, 50, p.39.

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Ke i1is-Borok, V. I . (1990). The 1i thosphere of the earth as anonlinear system with implications for earthquake prediction,Rewiews of Geophysics, 28, l/February 1990, 19-34.

Ki m , W. -Y., Hahlstrom, R., Usk i , M., (1989). Regional spectralscaling relations of source parameters for earthquakes in theSaltic Shield, Tectonophys., 166, 151-161.

Liu, D., Wang, J., Wang, Y., (1989). Application of catastrophetheory in earthquake hazard assessment and earthquakeprediction researeh, Tectonophys., 167, 179-186.

Hadar í aga , R. (1976). Dynamics of an Expanding Circular Fault.Bull. Seism. Soc. Am. Vol. 66, No. 3, 639-666.

Mandelshtam, L. I. (1950) Polnoye sobranyie spisov (Comp Ie t ecollection of works), In Russian, Vol. III, 89-178, Izd. Akad.Nauk, MoseO\,.

Nicolis, J. S. (1986) Dynamics of Hierarchical Systems, anEvolutionary Approaeh, Springer Verl., Berlin u. Heidelberg.

Poincaré, A. (1928) Sur les courbes definies par une equa t i.ondifferentielle. Oeuvres, V.I., Paris.

Rudajev, V., Te í sseyr e , R., Kozák, J., and Šílený, J., (1986).Possible Mechanism of Rockbursts in Coal Mines, Pageoph, 124,Nos 4/5, 841-855.

Fig. 1. Model set-up. Threemagnesite bIocks compressedby the confining force P2;central block is pressedagainst the two outer blocksby load PI.1 - piezoe1ectric pick-up

accelerometer,2 - tensometer recording the

displacement values.Hode1 size is given in mm.

I;, =,1<50 5050

- 101 -

o 300 .00 300 <200 {500

t [Ms]

Fig. 2. Form of the stick-slip signals radiated in 5 different

levels af confining pressure ~2'

A .. amplitude, t - time.

- 102 -

~o 1.5" so ss: fOO ,ZI"

f [kHz.]

Fig. 3. Amplitude/frequency spectrum of the signals given in

Fig. 2 . The spectra patterns are given in linear

normalized scale. . f 1 maximum of the spectra in

coherent stage of radiation.

1.0

0.0 .o

"E~-1.0 ...

~-c3~O.5a..

~-e

~~ 0.0"..

- :; -'-'--'-'--r-r-r-r-r-r-~-'-'-"-,.--r-r--r-r--r-rr--t-'·1-'-~0.0 0.2 0.1 O.G

1.0 lime [ms]

.-cB'a,0.5 :~ f-'

OW

0.0· --r-T"r-r-r-r-T"'-'-'-'-'''''''''-''-'''1"1 ......,....,.-,.O 50 100

Ir cqu en cy (kHz)150 200

a seismic source (upperFig. 4. Two seismoacoustic pulses from loaded magnesite model of

amplitudespectra (lower part, rel. units).

part) and their

_ III I

i",ď:,~l~~~O.G 0.2 0.1 0.6

1.0 Uroe(m~

1

I~)v~~r"",\"""""hr~50 100 150 200

frequency (kJl.)

0.0 ~O

1.04

"'O2 0.0-P.E.

-1.00

-+.0"""-'-'-'-''''''-''-0.''2 -v-r-v-r , , , 0.'1 '

10 Urno (ms]

{ o.s j Ul,~ 0.0 ~,--rrF~~rrrr."..,-T" :»r-,-;>,-,,.,., ,'T7"i"?f'A;..,.c:

O 50 100 150 200Ir-cque ncy (kHz)

~.'Gi , I

2.02

2:.u - 3

-2.0 •0.0

1.0

'l'--y-r-r-, i i • I ' , i i I , , i ( I I I , ,''''-' •• i I i • • I I

0.2 O": O,Utí me (ma)

-2.0 ":-"'T"""T"'T""T~r-r, i I I I. , , , I r-r-v-r-v-i +t--.-.-rr--l'-,·--r·"\0.0 0.2 0.1 o.e

LO tfme (mo)

1.0

0.0

6

.s:O 50 100 150 200

rrequeccy (kHz)

~ 1.01

t~:J~,~,,~r+r- .-,~."'fT"T~~'řř:

0.0 0.4 0.01.0 Urno (ma)

5

.'O

~ 0.0·p.Só

-1.00.0

1.0

.-r-r-r-r,-~!"""""'-'--I-I--.--r-r-r-r-'-'-'0.2 0.1 O.G

Llme (ma)

"-c3'20.5S.

MJ ,Jl,-,-;bt r-r-r-r-r-r-r •• , ? , l' t'rií50 100 150 200

řr-eque acy (kHz)

Fig. 5. Three acoustical pulses, 1, 2 and 3 from loaded fine grained sandstone soruce model and their ampli·tude spectra,see the row under the pulses 1-3. In the lower half of the figure three acoustical pulses 4, 5 and 6 from loadedcoarse grained sandstone source model are ShOl1TItogether with their ampli tude spectra (bottom row) . Both thesamples were taken Irom the Kladno coal region.

0.0 •o

OSTRAVA

36

35

34

32

30

29

f--

0.0+1----·1--·----+ .----t--------+---- 1-1---

5_1 6.4 7.7 9.0 10.2 11.51

12.8

Fig. 6. Seismic records of nine rockburst events taken from theOstrava coal region, which were selected from onelocality in a time interval Apr-Nov 1988. Time is givenin seconds, the amlitudes are normalized.

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OSTRAVA

)f, M

1.1.3

36. 0.94

:1..46

E o.ss;..o.s:::

32. d.. n/I

-a...E 3i. O. 5'3ess::.~-:I

0.3930.

29. Q. 66

0.39

i.281.50

J [Hz]

Fig. 7. AmpIitude frequeney speetra of the pulses from Fig. 6 ina lin/lin representation. By the asterisk the maximum

thevalues fo + +point show the sateIite loeal maxima fo - ~fo or foin individual speetra are denoted,

~2fo

- 107 -

o~~~

-011 , , ,0.0 1.0 2.0

I

Il.O,s,O G O trS]

°O'~~~

-0.1 ~f---r-, --.,--, --....-----,-----",---,---0.0 :LO 2.0 3.0 f{.O S.O S.ot [S]

30.i2.gg

o '1-o: Ji-J"'I,}{""-"rVV, WVV'\./"v--...--v"",,\,NI,III \

i.O0.0 2.0 3.0

3U2.Sg

,lJ.O

I

S'.O 6'.0 t [S]

Fig.8. Three 1988 Spitak earthquake aftershocks, recorded by

accelerometers, see the dates under seismograms, t -

time, g - acceleratioL.

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-2g[cm s 1

-0.10.0 :LO 2.0 3.0

04.01.85&.0 trs]s.o

:1.0I

2.0I3.0 ~.O

05.0i.89

0.0 :1.0 2.0 3.0

08.01.89'1.0 ,.0 b.O [[s]

Fig.9. Three 1989 Spitak earthquake aftershocks recorded by

accelerorneters, see the date under seisrnograrns. t - tirne,g - acceleration.

- ~09 -

gi.S.i2.88r.sM ~1f.2..

'1.0

0.5 ~

0.00J

b.O 30.12.88M ~ 4.3

«»

2.0

~~0.030.0

3:U2.88

60.0 M "tl.S

40.0

20.0

0.0

0.0 li. O s.o ~2.0 fb.O Zo.O f [Hz)

Fig.l0. Frequency spectra (lin/lin) of the accelerograms in Fig.

8. f - frequency, g - acceleration.

- llO -

g 1.5 O!J.Oi.8S

M : 'U

s.e

4.0

2.0

O.DL'--L-r----,......:...-~--~---=.~

60.0 08.01.89

M::: Lf.8

0.0 /.{.D 8.0 {2.0 rs.e 20.0[(Hz]

Fig. 11. Frequency spectra (lin/lin) of the accelerogramsin Pig. 9. f - frequency, g - acceleration.