Journal of Volcanology and Geothermal Research 177 (2008) 635–647

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Journal of Volcanology and Geothermal Research

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Moment tensor inversion of very long period seismic signals from Strombolianeruptions of Erebus Volcano

R. Aster ⁎, D. Zandomeneghi, S. Mah, S. McNamara, D.B. Henderson, H. Knox, K. JonesDepartment of Earth and Environmental Science and Geophysical Research Center, New Mexico Institute of Mining and Technology, Socorro, New Mexico, United States

⁎ Corresponding author.E-mail address: aster@ees.nmt.edu (R. Aster).

0377-0273/$ – see front matter © 2008 Elsevier B.V. Aldoi:10.1016/j.jvolgeores.2008.08.013

a b s t r a c t

a r t i c l e i n f o

Article history:

Strombolian eruptions from Received 8 February 2007Accepted 22 August 2008Available online 13 September 2008

Keywords:volcanismmagmaexplosive eruptionsseismology

the long-lived lava lake of Erebus volcano, Ross Island, Antarctica, generaterepeating Very Long Period (VLP) signals, containing energy between approximately 30 and 5 s, that persistfor several minutes and through the post-eruptive refilling of the lava lake. The initial approximately 10 s ofthis signal is moderately variable, particularly with respect to its initial polarity, while the following VLP codahas been observed to be stable since the earliest VLP observations were made (1996). To estimate forces andforce couples consistent with the Erebus VLP signature, we perform moment tensor inversions for pointsources using high signal-to-noise data stacks from the six-station, 18-component broadband seismographicnetwork and Green's function forward calculations that incorporate topography. We infer a shallow(approximate depth of less than 400 m below the lava lake surface) source centroid that underlies the centerto the northwestern rim of the main crater, east and north of the lava lake. Integrated Mii functions over thepredominant (180 s) signal duration of VLP events show that the net scalar moments for these events are onthe order of 4×1013 N m (corresponding to a moment magnitude mw ≈3) for typical sized VLP events.Moment rate tensors which characterize force couple components are dominated (85–97% of variance) bydilatational components. Approximately 25% of the data variance is attributable to single forces that areattributable to oscillatory reaction forces caused by fluid transport, however, the relative contributions ofvertical forces and couples with this sparse network is poorly resolved for these shallow sources. Thegenerally high degree of repeatability in the VLP signal across thousands of eruptions over the past decadeindicates that the response of the conduit system to gas slug ascent and subsequent gravitationaldisequilibrium is stable, consistent with the generally unchanging surface manifestation of the convectinglava lake system, and arguing for a thermally and dynamically stable conduit system beneath the lava lake.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction and background

ErebusVolcanohas exhibitedpersistent Strombolian activity from itsphonolitic lava lake fordecades (e.g., Giggenbach et al.,1973;Kaminuma,1994; Kaminuma et al.,1985; Dibble et al., 2008-this issue). The exposedErebus magmatic system facilitates repeated close-range (to withinseveral hundred meters; Fig. 1) study of diverse vent activity, with themost common eruptive activity by far consisting of characteristiceruptions from the lava lake. These eruptions are the explosivedecomposition of large, generally single gas slugs that can reach 10s ofm in diameter at the lava lake surface (Dibble, 1988, 1994; Aster et al.,2003; Johnson et al., 2003; Aster et al., 2004a; Jones et al., 2008-thisissue). Erebus shows a distinct lack of internal earthquakes or volcano-tectonic events (Rowe et al., 2000), consistent with a long-term openmagmatic system that does not readily accumulate internal deviatoricstress or pressurization. Very long period (VLP) seismic signals at Erebus(Rowe et al.,1998; Aster et al., 2003) belong to a class of signals recorded

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at a number of active volcanoes (Sassa, 1935; Chouet et al., 1999;Arciniega-Ceballos et al.,1999; Aster et al., 2000; Kawakatsu et al., 2000;Nishimura et al., 2000; Almendros et al., 2002; Chouet et al., 2003;Augeret al., 2006; Waite et al., 2008, Arciniega-Ceballos et al., 2008) thatprovide unique information on eruption- or transport-induced forceswithin volcanoes at periods ranging from seconds to hundreds ofseconds. For sufficiently close seismographs (i.e. on the orderof a seismicwavelength), these signals are observed as near-field elastic displace-ments that must be interpreted using near-field theory (as opposed tothe more familiar far-field theory for P, S, and surface waves). ErebusVery Long Period (VLP) signals to date are uniquely associated withimpulsive Strombolian eruptions from the lava lake system.

Volcano instrumentation (Fig. 1) currently consists of a network oflong-operational short-period seismic stations combined with infra-sound, tiltmeters, geodetic GPS, gas, infrared, environmental, and state-of-health sensors installed since2001 (Asteret al., 2004a).Most recently,seismic recording on Erebus has been greatly expanded with a 23-station supplemental network of temporary IRIS PASSCAL (Aster et al.,2005) stations installed in 2007 scheduled to operate through early2009, coupled with a tomographic shot program (Chaput et al., 2008;

Fig. 1.Map of Erebus shaded summit topography, seismic, and video station locations showing locations of seismic stations and the video site (VID). Station RAY was destroyed by aneruption in 2007. Crater rim morphology taken from Csatho et al., 2008-this issue.

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Zandomeneghi et al., 2008). In the first study of Erebus VLP signals,accomplishedwith IRISPASSCAL seismographsduring1996–1997, Roweet al. (1998) noted the persistent association of VLP signals withStrombolian eruptions with vertical polarities uniformly directeddownward, indicating a deflationary and/or downward-directed forceoperating on the elastic volcano volume during the VLP onset.Subsequent observations from 1999 onwards showed that some laterevents had upward initial polarities, corresponding to an inflationary,and/or upward-directed force. Mah (2003) performed an examinationand classification of VLP signals using data from the prolifically activeperiods of 1999, 2001, and 2002, a period of elevated activity precedingan 18-month quietus in eruptive activity that ended in 2004. Mah hasnoted that, when the initial polarity and other characteristics could beeasily discerned, the seismograms could be classified into 3 groups byinitial polarity (assessed by crosscorrelation and confirmed by visualinspection), time function shape, and spectral content (Fig. 2). Group 1eruptions show positive initial vertical motions (Fig. 2A). Group 2eruptions show negative initial vertical motions (Fig. 2B) that tend tohave lower frequency content. Group 3 eruptions are very rare (only 4observed examples) and exhibit a relatively simple pulse-like shape (Fig.2C). AlthoughGroup3 events showclearhigh-frequency seismoacousticarrivals consistentwith Strombolian eruptions, eruptive and vent detailsare unknowndue to their rarity and lack of accompanying video or othercorroboration for the handful of observed cases.Many lava lake eruptionsignals are too noisy and/or emergent for to discern a definite characterfor the initial polarity and were classified by Mah as “indeterminate”.

To greatly increase signal-to-noise and thus facilitate study of theextended VLP source signal (e.g., Dreier et al., 1994; Aster et al., 2003),Mah (2003) and Aster et al. (2003) stacked events from each of theidentified group populations (131 and 113 events fromGroups 1 and 2,respectively). Fig. 3 shows normalized stacked displacement seismo-grams and corresponding power spectra. The characteristic VLPspectral peaks centered at T0=20.7, T1=11.3, and T2=7.8 s are nearlyidentical between the Group 1 and Group 2 events. Group 3 eventsshow only a single very broad spectral peak near 25 s. Despite initialpolarity differences, and timing relative to the short-period seismoa-coustic signal created by the eruption, Groups 1 and 2 events shownearly identical VLP codas (Fig. 4), indicating that the post-eruptiveVLP source mechanism for Group 1 and Group 2 events (which spansthe lava lake refill period following the eruptive removal of theuppermost few 10's of meters of conduit material) is highly similar.

Video taken approximately 350 m from the lava lake (Fig. 1) revealskey eruptive differences between Group 1 and Group 2 events. Fig. 5shows a characteristic and well-observed Group 1 VLP vertical-component displacement signal at station E1S with correspondingvideo frames in 1 s intervals. The first frame shows the undisturbed lavalake just prior to the eruption. The second and third frames show avertical jet-like eruption. Remaining frames show the immediateevisceration of the lava lake following eruption and a thermal ash andvapor plume. Fig. 6 similarly depicts a characteristic Group 2 eruption,where the video record reveals substantially different eruptioncharacteristics from the Group 1 eruption shown in Fig. 5. The first

Fig. 2. Representative self-scaled vertical-component displacement seismograms for each eruption family, showing characteristic differences, especially Group 1: positive initial VLPpolarity), Group 2: negative initial VLP polarity, and Group 3: pulse shape. All data recorded at station E1S.

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frame shows an undisturbed pre-eruptive lava lake surface. The secondframe shows the lava lake surface start to noticeably inflate, a featurenot observed in the Group 1 eruption, and is followed by somewhat

Fig. 3. Stacked vertical-component displacement seismograms and correspond

asymmetric westward (left in the video field of view) ejecta. Precursoryinflation is associated with a prolonged (up to 10 s) initial downwardVLP signal characteristic in Group 2 events. The onset of the explosive

ing power spectra (normalized power units) for the event types of Fig. 2.

Fig. 4. Stacked vertical-component displacement seismograms for the event types ofFig. 2, taken from Fig. 3 (vertical gray line marks the approximate source origin time ofthe explosive seismoacoustic signal) showing pre-eruptive differences in polarity andtiming, and the strong post-eruptive similarity in the post-eruptive VLP signal.

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eruption in both cases (time zero) is revealed by the beginning of themuch weaker seismoacoustic signal generated by the explosion.Analysis of a number of well-observed events by Mah (2003) appearsto confirm the consistency of these eruptive differences. Mah (2003)further noted that Group 1 and Group 2 events are interspersed in timeand overlap in size (with Group 2 events tending to be systematicallylarger), but display evolving proportions from season to season. It isimportant to note in the context of this paper that Group 1 and Group 2events differ essentially solely in their first approximately 5–10 s of VLPsignal, and their VLP signals are highly similar thereafter (Fig. 4).

2. Moment rate tensor and force inversions

VLP signals generated by ascending gas slugs in Strombolian systemsarise due to the integrated influence of inertial and pressurization forces

Fig. 5. Vertical-component displacement seismogram and corresponding video frames for a Gapproximately 250m of the inner crater from east to west going from left to right. The eruptinby a P-wave (2.1 km/s) estimated propagation delay. Note the predominantly sub-vertical e

within a conduit system acting upon the surrounding volcano, usuallyassumed tobe elastic at these longperiods and lowstrain rates (typicallyon the order of nanostrain or less). The seismograms are a convolutionbetween forcing source time functions and an elastic (Green's function)impulse response. Therefore, responsible moment rate functions andforce histories can be estimated as a linear inverse (deconvolution)problem. Increasingly, such results can be interpreted in the context ofimproved experimental and numerical modeling under increasinglyrealistic physical conditions. To investigate underlying forces and/ormoment couples and the source location responsible for VLP signals atErebus, we performed inversions (e.g., Chouet et al.,1999; Legrand et al.,2000; McNamara, 2004) utilizing data from events recorded by sixthree-component long-term broadband (Guralp 40-T, 30 s cornerperiod) seismometers deployed at sites E1S, CON, HUT, NKB, RAY, andHOO (Fig. 1; Aster et al., 2004a). Our method of solution is essentiallythat of Ohminato et al. (1998) with Green's functions calculated using a50-m resolution topographic model of the volcano using the method ofusing the TOPO finite-difference code (Ohminato and Chouet, 1997)generously provided to us with documentation by P. Dawson of the U.S.Geological Survey. Uniform elastodynamic parameters used in themodel (Vp=2.2 km/s, Vs=1.27 km/s, and ρ=2400 kg/m3) were based onthe results of near-summit refraction experiments by Dibble et al.(1994).

Moment rate and single force source functions were parameterizedusing 50% overlapping0.5 s-wide triangular basis functions, b(t), to solvefor K 200 s source time functions (M=200/0.5−2=398 basis functions)using 200 s of 40 sample/s displacement seismogram data (N=8000points) for each seismic component. The general forward model is

unj tð Þ ¼ ∑K

i¼1si tð Þ⁎Gijn tð Þ ð1Þ

where un is the nth component of displacement at seismic station j,si(t) is the time function corresponding to solution function i, ⁎ denotes

roup 1 event, taken at the camera position (VID) shown in Fig. 1. The field of view spansg vent at the left of the video frames is the lava lake. The seismograms have been shiftedjecta.

Fig. 6. Vertical-component displacement seismogram and video frames for a Group 2 event, shown as in Fig. 5. The seismograms have been time-shifted by an estimated P-wave(2.1 km/s) propagation delay. Such events show a characteristic asymmetry in ejecta towards the right (west), as can be seen by the large sheet of magma ejected to the right.

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convolution, and Gijn(t) is the appropriate Green's function for solutionfunction i, station j, and component n, including the Guralp 40T (30 s)seismometer response. Parameterization to solve for the amplitudes,Bil of the triangular basis functions, b(t−τl ), where i again denotes theindex of the moment tensor source component and τl is the centertime of the lth basis function, yields

unj tð Þ ¼ ∑M

l¼1∑K

i¼1Bil b t−τlð Þ⁎Gijn tð Þ� � ð2Þ

The system of equations

d ¼ Ax ð3Þis formulated in terms of a composite data vector, d, of length D=NS,where S is the total number of single-component seismograms in thedata set (18, in this case), and a very sparse system matrix of size D byKM. The rows of A are the given by time reversed responses of thesystem to appropriate unit height basis functions (which are easilygenerated using convolution and time shift operations).

The resulting system is iteratively solved for theweighting functionsBil (assembled into the composite vector x) using the conjugate gradientleast-squares (CGLS) algorithm (e.g., Aster et al., 2004b). The K timefunctions corresponding to the moment rate and forcing functions arefinally reconstructed from basis function weights as

si tð Þ ¼ ∑M

l¼1Bilb t−τlð Þ ð4Þ

Upon convergence (typically approximately 1500 iterations for sixcouples and three force functions), CGLS produces a least-squaresmodel that maximizes the variance reduction

V ¼ ∑Di¼1d

2i −∑

Di¼1 di−dpred;i

� �2∑D

i¼1d2i

� 100k ð5Þ

and dpred is the composite data vector (the concatenation of all 27individual seismograms) predicted by the solution.

Individual events at Erebus are typically too noisy for robustmomentrate tensor inversion, because of the persistent and high microseismicnoise of coastal Antarctica in the VLP band (Aster et al., 2008). Noiselevels are particularly high during the summer months when the entirebroadbandnetwork of six stationswas operational due to favorable solarpower and field support conditions. To optimize VLP signal-to-noise toallow for examination of the entire (minutes-long) VLP signal, includingits relatively low-amplitude, minutes-long coda, we here performinversions using a stacked data set from 293 similar Group 2 VLP lavalake eruptions that occurred between January 30, 2005 and April 18,2006. The composite stack is representative of the larger downwardinitial motion events typical of this stacking period, and the VLP codaafter about 30 s is highly representative of the VLP process as observedsince1996 (Fig. 7). This timeperiod corresponds to a strong resurgence ineruptive activity that followed a lava lake eruption quietus betweenapproximately November, 2002 through June, 2004 (Jones et al., 2008-this issue). Each set of eruption seismograms, in native seismometercomponents, was aligned using station E1S vertical seismogram bestlags. Seismograms were normalized by maximum amplitude, stacked,and then rotated into a (vertical, radial, tangential) right-handed lava-lake-centric (radial component outwards), right-handed coordinatesystem. In cases where individual seismogram components were notavailabledue to stationdowntime, stackingwasperformedona subsetofthe data collected during operational periods. The correlation method,which relies on the agglomerative assembly of a consistent stack byselecting events that correlate with the total stack, initially with arelatively low correlation threshold (0.6) and culling those that do not,unbiasedly selects an ensemble of high signal-to-noise events forstacking. The maximum vertical displacement amplitude at station E1Sfor the stacked data set was nominally scaled to 10 µm, which iscomparable to the signal amplitude experienced duringmedium to largesingle events that generate infrasonic overpressures at E1S of approxi-mately 40 Pa (Johnson et al., 2003, 2004; Jones et al., 2008-this issue).Wenote that the largest recently observed eruptions (January 2005–January2007)were approximately five times this size asmeasured by infrasonic

Fig. 7. E1S vertical component displacement seismograms (293 similar events between January 30, 2005 and April 18, 2006, selected based on high mutual crosscorrelation andaligned to minimize all 2-event crosscorrelation lags; Rowe et al., 2002) plotted in greyscale (white = up). Stacked E1S vertical component seismogram used in moment tensorinversion shown at right. The stacked data is representative of a Group 2 (first motion down) event, as can be seen in the stack trace and characteristic dilatations (black, downward)signature. Data are low-pass filtered at 5 s. This data period was selected to encompass the optimal operational period for the six-station broadband network (Aster et al., 2004a).

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overpressure. To remove short-period energy generated by the distinctsurface explosionprocess that is not due to theVLP seismic source (Asteret al., 2003) seismogram stacks were low-pass filtered at 0.2 Hz using azero-phase 4-pole bidirectional Butterworth frequency response.

We calculated moment rate tensors for force couples and forcesusing a 600 m by 600 m, 150 m-spacing grid of source epicentroidlocations and source depths across a search volume (175 sources). Thelateral boundaries of the search region were constrained by the least-squares azimuthal disagreement between the observed VLP signal andthe (geometric) station-source radius (Fig. 8). We justify this procedurebecause we expect the VLP source to be dominated by pressurization

Fig. 8. Contoured particle motion azimuthal fit function, F (Eq. 6; maximum = 0.802) used to laepicentroids across the maximum region of F is shown. The maximum of F occurs approxima(Fig.1), but the function is nearlyflat in a triangular region boundedby the locations of stationsRfrom moment tensor inversion are indicated. Epicentral source search region is shown by the

and vertical force terms that will tend to produce radial VLP particlemotions, an assumption that is bolstered by the predominantly radialparticle motions observed in the data and shown in Fig. 8). Theazimuthal fitness function applied in this determination

F ¼ 1L∑L

i¼1librid be1;i� �2

ð6Þ

has a theoretical maximum value of 1 and is based on the eigenvalue–eigenvector decomposition of the variance tensor of horizontaldisplacement particle motions at all L stations, where the linearity, l

terally bound a search region for the VLP centroid source. The applied grid of trial sourcetely 330 m WNW of the lava lake, in the vicinity of the northwestern-central main craterAY, E1S andNKB. Locations of the lava lake (Fig.1),minimum F, and the epicentroid inferredblack box. Extent of the Erebus crater and lava lake location are those shown in (Fig. 1).

Fig. 9. Variance reduction (5) for six couple, three force solutions as a function of source position and depth, with best-fit locations indicated by stars. The lateral location of searchregion corresponds to the black box in Fig. 8. The location of the main crater rim from Fig. 1 is shown for reference.

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(e.g., Aster and Shearer, 1990) is defined by the eigenvalues, λi as l=(λ1−λ2)/(λ1+λ2), rb is the station-source unit vector, and ê1 is the uniteigenvector corresponding to the largest eigenvalue, λ1 (and is theunit least-squares best-fit vector to the horizontal particle motion).Each of the 25 epicentroid location shown in Fig. 8 was indexed to thenearest (50-m spacing) node in the finite-difference model of thevolcano. Greens functions were calculated using the TOPO code forsource elevations of 3300, 3200, 3100, 1050, 2800, 2500, and 2200 m.For comparison, the tip of the magmatic conduit as indicated by themean lava lake surface is at an elevation of approximately 3350 m(Csatho et al., 2008-this issue).

Initial inversions were performed (Aster et al., 2006) utilizing theAIC metric, and approximate half-space Green's functions (Johnson,1974). In this work, moment tensor inversion was explored forascending degrees of source complexity, using moment and forcecomponents appropriate for a fluid pressure and/or mass transportsystem (Aster et al., 2006). Models tested included 1) A single-component isotropic Mogi (Mogi, 1958) source (K=1); 2) A 3-component dilatational source (K=3); 3) A 3-component dilationalsource plus a vertical single force (K=4); and 4) A 3-componentdilatational source plus three orthogonal single forces (K=6), and a fullmoment tensor of six couples plus three forces. Solution appropriate-ness (number of source components versus goodness of fit) wasevaluated by finding the minimum of the Akaike information criterion(Akaike, 1974) under normally distributed error assumptions

AIC ¼ 2KMσ2 þ R ð7Þwhere R is the square of the residual 2-norm, σ is the noise standarddeviation (estimated from the pre-event noise in the VLP data), andthe product KM is the total number of parameters in this inverseproblem.

Aster et al. (2006) suggested a best solution for K=6 rate functionsand a source hypocentroid 150 m north of the minimum azimuthalerror epicentroid and approximately 330 m west–northwest (283° Eof N) of the center of the lava lake at an elevation of approximately3100 m. However the inversions discussed here, using significantlymore complex topographically corrected Green's functions calculatedusing the TOPO code, clearly produce best-fit solutions for a full suite ofK=9 forces and couples. These inversion results are shown in terms oftheir color-contoured variance reduction in Fig. 9 as a function of depth,with corresponding solution locations indicated by stars. Correspondingmaximum variance reduction solutions for each depth are shown inFigs. 10 and 11. Representative data fits (for the maximum variancesolution at 3300 m elevation) are shown in Fig. 12. We summarize thedata fit and some useful solution metrics in Tables 1 and 2.

3. Discussion

The best-fitting solution is found for an extremely shallow source(3300 m; V=0.89), it is clear from the spatial pattern of variancereduction (Fig. 9) that there are a range of almost equally suitablesolutions from the standpoint of fitting the data. However, all of thebest-fitting solutions show common features that suggest somerobustly resolved features of the VLP source.

One robust feature is that the distribution of best-fitting solutionsclearly indicates a very shallow VLP source; data fit falls offdramatically below 3050 m. This source region is consistent withearlier work (Aster et al., 2006), and indicates that the VLP sourcecentroid lies in the upper extent of the volcano, at a depth that we canstate with a high degree of uncertainty is less approximately 400 mbeneath the lava lake (2900 m). If the VLP centroid represents asignificant feature within the conduit system, this bodes well for

Fig. 10.Moment rate and force rate functions corresponding to the maximumvariance reduction solutions for elevations of 3300, 3200, and 3100 m (Fig. 9). Coordinate convention is(x̂1, x̂2, x̂3) = (East, North, Up).

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ongoing tomographic efforts to examine the velocity structure of theupper mountain above the 2000 m contour (Chaput et al., 2008;Zandomeneghi et al., 2008). An additional common best solutionlocation feature is that they all lie from 150m to 300m east and from0to 150 m north of the lava lake. Depending on depth, this places theVLP centroid clearly to the west of the lava lake and beneath thecentral to northeastern quadrant of the main crater, consistent withour aforementioned particle motion analysis (Fig. 8). The implicationis that the magmatic conduit system at shallow depths resides moretowards the center to northwest of the crater complex, rather thanbeneath the significantly off-center lava lake (Fig. 1; Csatho et al.,2008-this issue). The presence of a substantial underlying magmaticsystem to the west of the lava lake is also supported by theintermittent presence of a second small lava lake near the westernedge of the inner crater that has produced a few very smallStrombolian eruptions since 2005.

Absolute source size can be estimated from moment rate tensorfunctions using a scalar moment rate function (e.g., Stein andWysession, 2003)

Mr0 tð Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑iMii tð Þ2

rð8Þ

which can be integrated to obtain a net scalar moment

M0 ¼ ∫∞0 Mr0 tð Þdt: ð9Þ

For these results, we find a range of net scalar moments rangingbetween 3.2×1013 and 5.3×1013 N m. For comparison to general

seismic sources, this scalar moment can be converted into a momentmagnitude (e.g., Hanks and Kanamori, 1979), using

mw ¼ 2=3 log10M0−9:1ð Þ: ð10Þ

The corresponding mw of a typical Erebus eruption VLP signal isthus approximately 3–3.1. This is substantially larger than the lower-bound moment magnitude equivalent estimated from the first pulseamplitude using a Mogi source approximation,mw≈1.9, by Aster et al.(2003) for comparably sized VLP signals. This apparent discrepancyarises because the scalar moment calculated here is for the integratedcontribution across 200 s of oscillatory source activity.

Because the VLP process is obviously causally linked to forcesarising from the transport of a gas slug to the vent and subsequentrecovery of the conduit system after eruptive removal of ejecta (Jameset al. (2006), one might expect the moment rate functions to bedominated by dilatational components, as the pressurization of anear-summit magmatic system would propagate at P wave speedsand, for a system within the uppermost extent of the volcano, suchpressurization would occur rapidly relative to VLP periods. Anexamination of the shear couples in the solutions show that theshear couple moment rate functions are, as expected, relatively small,but not entirely negligible. The ratio of the dilatational to total netscalar moments ranges between 85 and 97%. VLP source non-coupleforces might similarly be expected to include reaction forcesgenerated by the acceleration of conduit fluids. All solutions showsingle force terms that are predominantly in the (x 1,x 3), or (east,vertical) plane, where the initial force is downward and eastward. Thisis consistent with oscillatory upward and westward mass advection

Fig. 11. Moment rate and force rate functions corresponding to the maximum variance reduction solutions for elevations of 3050 and 2800 m (Fig. 9). Coordinate convention is(x̂1, x̂2, x̂3) = (East, North, Up).

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and with the western trend of ejecta in Group 2 eruptions (Fig. 6).However, the eruption time scale, as observed by infrasound and short-period seismic radiation, is much shorter than the VLP time scale, andthe single force components tend to showperiod content near 7–8 s (seefurther discussion on this point below). We note that the maximumamplitudes of the Mii and Fi components for characteristic Erebuseruptions are of a similar size to those reported for Stromboli by Chouetet al. (2003);Mii,max≈2×1012 N m/s and Fi,max≈5×108 N here comparedto Mii,max≈2×1012 N m/s and Fi,max≈1×108 N at Stromboli, with amaximum force-to-maximummoment rate ratio (Table 1) on the orderof 10−4 m−1 in both cases. However, the Erebus VLP signal has asignificantly more sustained duration than that of Stromboli(several minutes at Erebus versus approximately 20 s at Stromboli).

The above quantification and localization of the VLP source isconsistent across the best suite of VLP inversions shown in Figs. 10and 11. We next discuss the differences between the solutions. Alargest progressive difference as the test hypocentroid depth increasesis a transition in the dilatational terms between a solution that isdominated by a vertical (M33) force couple (e.g., 3300 m), such asmight be produced by a pressurized subhorizontal crack or sill, to onethat is dominated by M11 and M22 couples (e.g., 2030 m), as might begenerated by a prolate, vertical conduit or chamber. Mii ratios,decomposed as eigenvectors and eigenvalues of the moment ratetensor, can provide key information on the orientation and aspectratios of the VLP source (Davis, 1986; Yang et al., 1988; Chouet et al.,2003). A consistency check is thus to examine the correlation betweentheMii functions. To be consistent with the pressurization of a crack or

more general cavity, we would expect the dilatational terms to be inphase so that the correlation of the respective time functions arehighly positive. These metrics are reported in Table 2. The correlationbetweenM11 andM22 is moderately high for all best solutions, rangingfrom 0.71 (3200 m) to 0.89 (3050 m). The correlation between M11

andM33 (Table 2; Figs. 10 and 11), however, is highly variable, showingrelatively high correlations for the shallow and deep (3300 m and2800m) solution endmembers of 0.79 and 0.66, respectively, but verylow correlations between these depths. The corresponding nighdegree of anticorrelation between M33 and F3 for the shallow depthsis highly suggestive of poor resolution in the inversion. The tradeoffbetween these two source terms is expected for shallow sources in aleast-squares inversion because of similarities in the Green's functionsfor M33 and − f3 (Uhira and Takeo, 1994; Chouet et al., 2003). We thuscontend that the low correlation between the horizontal and verticalmoment rate terms is due to this effect.Mii ratios between the verticaland horizontal components are therefore highly affected by thistradeoff.M11 toM22 amplitude ratios vary between 2.85 (3300 m) and1.06 (3100 m), showing that the azimuthal aspect of the source is alsonot particularly well constrained, although the trial source locationsbelow 3300m have a relatively consistent ratio between 1.38 and 1.06,suggestive of an equant azimuthal source geometry.

The modeling here incorporates two significant approximations.First, the source is modeled as a superposition of couples and singleforces applied at a common point within the volcano, and is thereforea highly idealized representation of a spatially distributed source.However, the point approximation is a good one when scaled to the

Fig. 12. Data, forward modeling, and residual corresponding to the 3300 m maximumvariance reduction solution of Fig. 10.

Table 2Solution summary metrics, continued. H is elevation, c values are correlationcoefficients between indicated rate functions, and RM is the proportion of datavariance due to the moment tensor terms alone in the forward calculation

H (m) c(M11,M22) c(f3,M33) c(M11,M33) |M11|/|M22| |M11|/|M33| RM (%)

3300 0.80 −0.89 0.79 2.85 0.45 753200 0.71 −0.86 0.02 1.33 0.74 743100 0.84 −0.97 −0.29 1.06 1.83 783050 0.89 −0.92 0.09 1.15 2.93 792800 0.86 −0.26 0.66 1.38 1.86 76

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wavelength of seismic waves at these periods (10 km or longer) andthe total size of the array (on the order of an S wave wavelength),similar inversions on other volcanoes and synthetic tests have shownthat this issue may not be highly significant except for very sparsenetworks (P. Dawson, pers. commun.). Second, we incorporate theeffects of topography using a fairly crude approximation with a 50 mfinite-difference node spacing. Topographic effects should be espe-cially notable for station RAY, which was nearly perched on the craterrim overlooking the lava lake (Fig. 1). We suspect that Green'sfunctions for RAY are significantly less accurate than for the other

Table 1Solution summary metrics for the five best (and shallowest) maximum variancereduction solutions, with corresponding time functions shown in Figs. 10 and 11. H iselevation, V is variance reduction (5),M0 is the integrated seismic scalar moment,MΔ isthe integrated seismic moment for the dilatational (Mii) components, F0 is theintegrated total force

H (m) V (%) M0 (N m) MΔ (N m) %Δ F0 (N) F0 /M0 (m-1)

3300 89 5.5×1013 5.3×1013 97 1.8×1010 3.3×10−4

3200 88 3.2×1013 3.0×1013 94 1.6×1010 4.9×10−4

3100 88 4.1×1013 3.4×1013 85 1.8×1010 4.5×10−4

3050 87 4.8×1013 4.1×1013 85 1.8×1010 3.8×10−4

2800 83 5.4×1013 4.9×1013 90 1.9×1010 3.5×10−4

stations, and this suspicion is borne out in the relatively large misfit forseismograms at this station (Fig. 12. A probably smaller source ofmodeling error is the use of a uniform elasticity and density structure,which was constrained using the near-summit refraction estimates ofDibble et al. (1994). A simple test of the veracity of the Dibble et al.velocitymodel is to examine the crosscorrelation lags betweenobservedand forward modeled waveforms for the various VLP pulses across thenetwork. We find this fit to be generally consistent relative to the longperiods that characterize the VLP data. The largest such discrepancy, asmeasured by the entire VLP signal crosscorrelation lags between thecomplete observedandpredicted three-component signals of Fig.12, is anegative residual of approximately 2 s seen at HOO, located 5.5 km fromthe source epicentroid. This indicates, not surprisingly that the elasticmoduli of the volcanic edifice far outside of the central conduit region(Fig. 1) are appreciably higher than the velocity model. Conversely, thenear-summit stations LEH and NKB show positive residuals of 0.1 and0.38 s, respectively, suggesting that the northern sector of the near-summit region out to ranges of approximately 2 km is more compliantthan specified by the half-space parameters. The best lag for the netcrosscorrelation between observed and predicted data across all 18components is zero to sample resolution.

The contribution of the single force components to total variancereduction in this inversion is consistently approximately 25% for allsolutions (Table 2). Single forces also appear as a primarily post-eruptive component of the source. Single forces are expected to begenerated by magmatic momentum change within the conduit. Formass-conserving systems like the Erebus conduit during its post-eruptive magmatic refill phase, the generated internal forces aresimply the spatial integral of the magma density multiplied by itscorresponding acceleration distribution

f ¼ ∫Vρ Vð Þa Vð ÞdV : ð11Þ

The initial abrupt ejection of materials from the Erebus lava lakegenerates a single force that undoubtedly contributes to the short-period signal (Henderson, 2007). However, this jet force has a periodcontent that is peaked near 1 s, as observed in infrasound (Jones et al.,2008-this issue), which is much shorter that of the 5–30 s VLP band(Aster et al., 2003). Indeed, the eruption onset, as defined by thebubble burst, does not visibly appear as a feature on the VLP signals ormoment rate functions when the data are low-passed below severalseconds. In a rough calculation we can assume that the total force inthe prolonged VLP signal is due to rapid shallow accelerations ofmagma in a constricted upper conduit region during lava lake refill.Using the eviscerated volume from the eruption (roughly cylindricalwith a radius of 25m and a depth of 20m) as an approximation for thedimensions of the volume of magma in motion during subsequentrefill, and using an approximate shallow Erebus magma density of2000 km/m3 estimated by Dibble (1994), we obtain estimated totalmass in motion of approximately 8×107 kg. Eq. (11) then implies thatthe inverted force magnitudes on the order of the observed 1×108 Ncould be generated by a mass of this magnitude undergoing a vectoraverage acceleration with a magnitude on the order of 1 m/s2.

An interesting consistent aspect of these moment tensor inver-sions is the asymmetric spectral partitioning of VLP spectral energy

Fig.13.Normalized power spectra for representativemoment (M11) and force (F3) components of the rate functions of Fig.10. VLP spectral components are denoted (Aster et al., 2003)as T0 ≈20.7 s, T1 ≈11.3 s, and T2 ≈ 7.8 s. The unequal partitioning of energy between the Mii moment components and the Fi single forces, with the single force accounting for themajority of the shortest period (T2) spectral component, is a general feature of these solutions.

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peaks (Fig. 3) between the vertical and horizontal Fi and Mii ratefunctions (Fig. 13), particularly with respect to the T2=7.8 s period peakbeing predominantly fit by the single force and/or M33 components.Single forces inferred from moment rate inversions are ideallyattributable to magmatic recharge acceleration forces, but (as describedabove) showahigh level of correlation in this study (Eq. (11)) thatmaybea resolution artifact of the inversion. This suggests that the T2 componentof theVLP spectrummight be linked to adistinct process compared to theT0 and T1 spectral components. This partitioning is seen in all solutions,and is most apparent for the deepest solution (2800 m) shown in Fig. 11(however this solution has significantly degraded variance reductionrelative to shallower solutions). One hypothesis, that could be tested inthe future with higher resolution data sets from an augmentedbroadband network is that the partitioning of the T2 component intothe (predominantly vertical) force component system suggests that theresonance time for surging recharge into the eviscerated post-eruptivelava lake is distinct from the pressurization resonances of the system (T0and T1). The stability of the VLP periods further implies that, despitethousands of Strombolian eruptions during the past decade, therepeating and self-reconstructing conditions of the lava lake and VLPsystem have been maintained. If the T2 component of the VLP spectrumwere the fundamental “surging” excitation of the lava lake system togravitational disequilibrium, then modeling this component of the VLPsignal as a volcanic analogue of a hydraulic “slug test” in a high-permeability aquifer bounded by impermeable strata (e.g., Guenther andMohamed,1986; Guenther et al.,1987)might be fruitful. In this analogue,a near-summit magma chamber/conduit system corresponds to theaquifer. The height of themagma column is only intermittently visible invideo records during its highest amplitude excursions because of thecameraviewbeingobscuredbyashandvapor. Itmaybepossible in futuremodeling efforts to estimate this parameter, however, by doublyintegrating the inferred acceleration derived from the F3 component ofthe moment rate tensor inversion, under the assumption of homo-geneous oscillatory laminar flow of an appropriate conduit segment.

We note that ascribing the T2 component of the VLP spectrum tooscillatory recharge is consistent with previously noted videoevidence in that rare, exceptionally clear views of the immediatepost-eruptive lava lake were observed to display surging behaviorwith a period of 8.8±1.6 s. Additionally, source Q estimates of theprincipal VLP modes from spectral peak widths, showing that thedecay of the T2 component is significantly more rapid than the T1 and

T0 components, with Q2=4, Q1=18, and Q0=11, again suggesting thatit may be associated with distinct processes (Aster et al., 2003).

Notable other studies of conduit-associated VLP signals at activevolcanoes includeAso, Japan (Kawakatsuet al., 2000; Legrandet al., 2000),Stromboli (Chouet et al., 1999, 2003), and Popocatepetl (Arciniega-Ceballos et al., 1999; Chouet et al., 2005). In the case of Aso volcano, asimilar gravitationally-driven inertial mechanism to that proposed herefor Erebus is suggested, with the important distinction that a mixture offluid and rock interacting with a sub-crater hydrothermal reservoir(heated by deeper magma) is invoked at Aso to model the mechanism ofoscillation. Preferred models for VLP moment tensor inversions forStromboli and (vulcanian) Popocatepetl eruptions, however, invokemagmatic transport through constrictive, single- or multiple crack-likeupper conduit structures embedded in compliantmedia (Chouet,1996). Inthis respect Erebus, with its highly oscillatory and exceptionally long-duration VLP signals may constitute a near end-member “open” or“underdamped” example of such systems,where inertial forces generatedby the relatively unimpeded transport and back-flow of rechargingmagma are dominant, as opposed to shorter duration VLP signals largelycontrolled by amore restrictive crack-like conduit geometry. A long-livedstable open conduit system is furthermore consistent with geochemicalmodeling of characteristic abundant anorthoclase feldspar phenocrystserupted from the lava lake system, which require long-term (e.g., decadesto millennia) convective circulation of magma at depth (betweenapproximately 400 m and the surface) for their formation (Dunbar et al.,1994). The displacement of the VLP source centroid by approximately330m from the lava lake, and somewhat closer to the geometric center ofthe main crater and the consistent orientation of single forces in thesemoment rate inversions are consistent with a shallow kink in themagmatic system beneath the lava lake.

4. Conclusions

Strombolian eruptions from the Erebus lava lake consistentlyproduce repeating VLP signals that show high degrees of correlationacross their several minute durations, but which show variable firstmotion polarity encompassing the first approximately 5–10 s. Firstmotion differences are correlated with ejecta direction characteristicsobserved in video observations and are thus reflective gas slugdelivery and eruption and the immediate conduit response. Asidefrom these early seismogram variations, time- and frequency-domain

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characteristics of VLP signals are notably invariant across a decade ofobservation, despite widely varying eruptive frequency at the volcano,ranging from many events per day to months-long quiet periods. Thisdegree of consistency in the VLP signature indicates a stable, self-reconstructing VLP source and stable upper conduit system, where theunderlying plumbing system dynamically responds in a reproduciblemanner to departures in gravitational equilibrium induced by the gasslug-mediated removal of magma from its tip. Moment rate tensorinversion of a high signal-to-noise six-station, 18-component dataconstructed by stacking VLP signals produce solutions that constrainthe source centroid to lie less than about 400 m below the lava lakeand to be laterally displaced by up to several hundred meters to thewest and north. Mii component ratios are variable with trial sourcedepth, and tradeoffs between vertical forces and vertically-orientedmoments are large due to the ill-posed nature of the inverse problemfor this small network. These tradeoffs unfortunately make chamberand other geometric constraints on the summit magmatic systemunfeasible with this limited network geometry. Net scalar momentsrange between 3.2×1013 and 5.3×1013 N m. Energy partitioningbetween spectral components of the VLP signal may indicate that theshortest-period predominant VLP mode (T2≈7.8 s) is preferentiallyassociated with the single force system, and may thus reflect resonantrecharge of magma into the post-eruptive lava lake system.

Acknowledgments

We thank UNAVCO and the IRIS PASSCAL Instrument Center at NewMexico Tech for facility support and field assistance on Mount Erebus.Donations of equipment from Extreme CCTV and VideoComm Technol-ogies were essential for video observations. We thank the manyRaytheon Polar Services Company individuals and groups at McMurdowho made this field effort possible. The development and testing ofinverse methodologies was assisted by Brian Borchers and ChristianLucero (Lucero, 2007). The manuscript was significantly improved inrevision following comments by P. Dawson and an anonymous reviewer.We additionally thank P. Dawson for providing uswith the TOPOGreen'sfunction calculation code. This research was supported by NSF AwardsOPP-9814291, OPP-0116577, OPP-0229305, and ANT-0538414 and byNew Mexico Tech Research and Economic Development.

References

Akaike, H., 1974. A new look at the statistical model identification. IEEE Trans. Automat.Contr. AC-19 (6), 716–723.

Almendros, J., Chouet, B., Dawson, P., Bond, T., 2002. Identifying elements of theplumbing system beneath Kilauea Volcano, Hawaii, from the source locations ofvery-long-period signals. Geophys. J. Int. 148, 303–312.

Arciniega-Ceballos, A., Chouet, B., Dawson, P., 1999. Very long-period signals associatedwith vulcanian explosions at Popocatepetl volcano, Mexico. Geophys. Res. Lett. 26,3013–3016.

Arciniega-Ceballos, A., Chouet, B., Dawson, P., Asch, G., 2008. Broadband seismicmeasurements of degassing activity associated with lava effusion at PopocatepetlVolcano, Mexico. J. Volcano. Geotherm. Res. 170, 12–23.

Aster, R., Shearer, P., 1990. Quantitative measurements of shear-wave polarizations atthe Anza seismic network, southern California—implications for shear-wavesplitting and earthquake prediction. J. Geophys. Res. 95, 12449–12473.

Aster, R., Lees, J., Neuberg, J., 2000. Broadband seismic and acoustic observations ofvolcanic seismicity (editorial). J. Volcanol. Geotherm. Res. 101, vii–viii.

Aster, R., Mah, S., Kyle, P., McIntosh, W., Dunbar, N., Johnson, J., 2003. Very long periodoscillations of Mount Erebus volcano. J. Geophys. Res. 108, 2522. doi:10.1029/2002JB002101.

Aster, R., McIntosh, W., Kyle, P., Esser, R., Bartel, B., Dunbar, N., Johns, B., Johnson, J.,Karstens, R., Kurnik, C., McGowan, M., McNamara, S., Meertens, C., Pauly, B.,Richmond, M., Ruiz, M., 2004a. New instrumentation delivers multidisciplinaryreal-time data from Mount Erebus, Antarctica. EOS trans. AGU. 85 (10) March 9.

Aster, R., Borchers, B., Thurber, C., 2004b. Parameter Estimation and Inverse Problems.Elsevier Academic Press. 301 pp.

Aster, R., Beaudoin, B., Hole, J., Fouch, M., Fowler, J., James, D., et al., 2005. IRIS PASSCALprogram marks 20 years of scientific discovery. EOS. trans. AGU 86 April 26.

Aster, R., Kyle, P., McIntosh, W., Lucero, C., Borchers, B., 2006. Very long periodStrombolian eruption-associated seismic signals observed in the near field atMount Erebus volcano. The Physics of Fluid Oscillations in Volcanic SystemsWorkshop, Lancaster, U.K., 7–8 September.

Aster, R., McNamara, D., Bromirski, P., 2008. Multi-decadal climate-induced variabilityin microseisms. Seismol. Res. Lett. 79. doi:10.1785/gssrl.79.2.194.

Auger, E., D'Auria, L., Martini, M., Chouet, B., Dawson, P., 2006. Real-time monitoring andmassive inversionof sourceparametersof very longperiodseismic signals: anapplicationto Stromboli Volcano, Italy. Geoph. Res. Lett L04301. doi:10.1029/2005GL024703.

Chaput, J., Jones, K., Yarbrough, H., Zandomeneghi, D., Aster, R., Johnson, J., Kyle, P.,McIntosh, W., Snelson, C., Oppenheimer, C., Gerst, A., 2008. Seismological andrelated research at the Mount Erebus Volcano Observatory. Annual Meeting of theSeismological Society of America, Santa Fe, NM, Seismol. Res. Lett., 79(2).

Chouet, B., 1996. New methods and future trends in seismological volcano monitoring.In: Scarpa, R., Tilling, R.I. (Eds.), Monitoring and Mitigation of Volcano Hazards.Springer, New York, p. 2397.

Chouet, B., Saccorotti, G., Dawson, P., Martini, M., Scarpa, R., De Luca, G., Milana, G.,Cattaneo, M., 1999. Broadband measurements of the sources of explosions atStromboli volcano, Italy. Geophys. Res. Lett. 26, 1937–1940.

Chouet, B., Dawson, P., Ohminato, T., Martini, M., Saccorotti, G., Guidicepietro, F., DeLuca, G., Milana, G., Scarpa, R., 2003. Source mechanisms of explosions at StromboliVolcano, Italy, determined frommoment-tensor inversion of very-long period data.J. Geophys. Res. 108, 2019. doi:10.1029/2002JB001919.

Chouet, B., Dawson, P., Arciniega-Ceballos, A., 2005. Source mechanism of Vulcaniandegassing at Popocatepetl Volcano, Mexico, determined fromwaveform inversionsof very long period signals. J. Geophys. Res. doi:10.1029/2004JB003524.

Csatho, B., Schenk, T., Kyle, P., Wilson, T., Krabill, W., 2008. Airborne laser swathmapping of the summit of Erebus volcano, Antarctica: applications to geologicalmapping of a volcano. J. Vol. Geotherm. Res.177, 531–548 (this issue). doi:10.1016/j.jvolgeores.2008.08.016.

Davis, P., 1986. Surface deformation due to inflation of an arbitrarily oriented triaxialellipsoidal cavity in an elastic half-space, with reference to Kilauea Volcano, Hawaii.J. Geophys. Res. 91, 7429–7438.

Dibble, R., 1988. Time comparisons between video and seismic signals from explosionsin the lava lake of Erebus Volcano, Antarctica. Bull. Disaster Prev. Res. Inst. KyotoUniv. 38, 147–161.

Dibble, R., 1994. Velocity modeling in the erupting magma column of Mount Erebus,Antarctica. In: Kyle, P.R. (Ed.), Volcanological and Environmental Studies of MountErebus, Antarctica, Antarctic Research Series. American Geophysical Union,Washington DC, pp. 17–33.

Dibble, R.R., Kyle, P.R., Rowe, C.A., 2008. Video and seismic observations of Strombolianeruptions at Erebus volcano, Antarctica. J. Volcanol. Geotherm. Res. 177, 619–634(this issue). doi:10.1016/j.jvolgeores.2008.07.020.

Dreier, R., Widmer, R., Schick, R., Zürn, W., 1994. Stacking of broad-band seismograms ofshocks at Stromboli. Acta Vulcanol. 5, 165–172.

Dunbar, N., Cashman, K., Dupŕe, R., 1994. Crystallization processes of anorthoclasephenocrysts in the Mount Erebus magmatic system: evidence from crystal composi-tion, crystal size distributions, and volatile contents of melt inclusions. In: Kyle, P.R.(Ed.), Volcanological andEnvironmental StudiesofMount Erebus, Antarctica,AntarcticResearch Series. American Geophysical Union, Washington DC, pp. 129–146.

Giggenbach, W., Kyle, P., Lyon, G., 1973. Present volcanic activity on Mt. Erebus, RossIsland, Antarctica. Geology 135–156.

Guenther, R., Mohamed, F., 1986. Well response tests: I. The direct problem. InverseProblems 2, 83–94.

Guenther, R., Lundy, R., Mohamed, F., 1987. Well response test: II. The numericalsolution. Inverse Problems 3, 407–419.

Hanks, T., Kanamori, H., 1979. A moment magnitude scale. J. Geophys. Res. 84,2348–2350.

Henderson, D.B., Analysis of seismic similarity in Strombolian eruptions from MountErebus, Antarctica, M.S. Thesis, NewMexico Institute ofMining and Technology, 2007.

James, M., Lane, S., Chouet, B., 2006. Gas slug ascent through changes in conduitdiameter: laboratory insights into a volcano-seismic source process in low-viscositymagmas. J. Geophs. Res. 111, B05201. doi:10.1029/2005JB003718.

Johnson, L.R., 1974. Green's function for Lamb's problem. Geophys. J. R. Astron. Soc. 37,99–131.

Johnson, J., Lees, M., Ruiz, M., McChesney, P., Aster, R., Kyle, P., 2003. Interpretation andutility of infrasonic records from erupting volcanoes. J. Volcanol. Geotherm. Res.121, 15–63.

Johnson, J., Aster, R., Kyle, P., 2004. Volcanic eruptions observed with infrasound. Geop.Res. Lett. 31, L14604. doi:10.1029/2004GL020020.

Jones, K., Johnson, J., Aster, R., Kyle, P., McIntosh, B., 2008. Infrasonic tracking of largebubble bursts and ash venting at Mount Erebus. J. Volcanol. Geotherm. Res. 177,661–672 (this issue). doi:10.1016/j.jvolgeores.2008.02.001.

Kaminuma, K., 1994. The seismic activity of Mount Erebus in 1981–1990. In: Kyle, P.R.(Ed.), Volcanological and Environmental Studies of Mount Erebus, Antarctica.Antarctic Research Series. American Geophysical Union, Washington DC, pp. 35–50.

Kaminuma, K., Ueki, S., Kienle, J., 1985. Volcanic earthquake swarms at Mt. Erebus,Antarctica. Tectonophysics 114, 357–369.

Kawakatsu, H., Kaneshima, S., Matsubayashi, H., Ohminato, T., Sudo, Y., Tsutsui, Y., Uhira,K., Yamasato, H., Ito, H., Legrand, D., 2000. Aso94: Aso seismic observation withbroadband instruments. J. Vol. Geotherm. Res. 101, 129–154.

Legrand, D., Kaneshima, S., Kawakatsu, H., 2000. Moment tensor analysis of near-fieldbroadband waveforms observed at Aso volcano, Japan. J. Volcanol. Geotherm. Res.101, 155–269.

Lucero, C., Seismic moment rate function inversions from very long period signalsassociated with Strombolian eruptions at Mount Erebus, Antarctica M.S. Thesis,New Mexico Institute of Mining and Technology, 2007.

Mah, S., 2003. Discrimination of Strombolian eruption types using very long period(VLP) seismic signals and video observations at Mount Erebus, Antarctica. M.S.Independent Study, New Mexico Institute of Mining and Technology.

647R. Aster et al. / Journal of Volcanology and Geothermal Research 177 (2008) 635–647

McNamara, S., 2004. Source mechanism inversion of very long period signals associatedwith Strombolian eruptions at Mount Erebus, Antarctica. M.S. Independent Study,New Mexico Institute of Mining and Technology.

Mogi, K., 1958. Relations of the eruptions of various volcanoes and the deformationsof the ground surfaces around them. Bull. Earthq. Res. Inst. Univ. Tokyo 36,99–134.

Nishimura, T., Nakamichi, H., Tanaka, S., Sato, M., Kobayashi, T., Ueki, S., Hamaguchi, H.,Ohtake, M., Sato, H., 2000. Source process of very long period seismic eventsassociated with the 1998 activity of Iwate Volcano, Northeastern Japan. J. Geophys.Res. 105, 19135–19147.

Ohminato, T., Chouet, B., 1997. A free-surface boundary condition for including 3Dtopography in the finite difference method. Bull. Seismol. Soc. Am. 87, 494–515.

Ohminato, T., Chouet, B., Dawson, P., Kedar, S., 1998. Waveform inversion of very longperiod impulsive signals associated with magmatic injection beneath Kilaueavolcano, Hawaii. J. Geophys. Res. 103, 23839–23862.

Rowe, C., Aster, R., Kyle, P., Schlue, J., Dibble, R., 1998. Broadband recording ofStrombolian explosions and associated very-long-period seismic signals on MountErebus volcano, Ross Island, Antarctica. Geophys. Res. Lett. 25, 2297–2300.

Rowe, C., Aster, R., Kyle, P., Dibble, R., Schlue, J., 2000. Seismic and acoustic observationsat Mount Erebus Volcano, Ross Island, Antarctica, 1994–1998. J. Vol. Geotherm. Res.101, 105–128.

Sassa, K., 1935. Volcanic micro-tremors and eruption-earthquakes (Part 1 of thegeophysical studies on thevolcanoAso).Mem.Coll. Sci., Univ. Kyoto, Ser. A 19, 255293.

Stein, S., Wysession, M., 2003. An Introduction to Seismology, Earthquakes and EarthStructure. Blackwell Publishing, Oxford, p. 498.

Uhira, K., Takeo, M., 1994. The source of explosive eruptions at Sakurajima Volcano,Japan. J. Geophys. Res. 99, 17,775–17,789.

Yang, X., Davis, P., Dieterich, J., 1988. Deformation from inflation of a dipping finiteprolate spheroid in an elastic half-space as a model for volcanic stressing.J. Geophys. Res. 93, 4249–4257.

Waite, G., Chouet, B., Dawson, P., 2008. Eruption dynamics at Mount St. Helens imagedfrom broadband seismic waveforms: interaction of the shallow magmatic andhydrothermal systems. J. Geophys. Res. 113, B020305.

Zandomeneghi, D., Yarbrough, H., Snelson, C., Kyle, P., Aster, R., Chaput, J., Johnson, J.B.,Jones, K., 2008. Seismological observations and modeling at Erebus volcano,Antarctica. Proc. IAVCEI General Assembly, Reykjavik, Iceland.