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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. B10, PAGES 23,879-23,894, OCTOBER 10, 2000 Evidence for temporal variation of seismic velocity within the upper continental crust GStz H. R. Bokelmann • Department of Geophysics,Stanford University, Stanford, California Hans-Peter Harjes Institut fiir Geophysik, Universit/it Bochum, Bochum, Germany Abstract. Observationsof systematictemporal variations of seismicanisotropy are presented for an induced-seismicityexperiment at 9 km depth. These observations were made under particularly well-controlled conditionsin the German Continental Deep Drilling Program (KTB) borehole,usingshearwave splitting from similar events recorded at a three-component instrument located at 4 km depth from a hydraulic fracturing experiment at 9 km depth. In a large set of seismicevents recorded during the experiment, many can be associatedwith multiplets exhibiting essentially identical waveforms. Since they must have approximately the same source location and source radiation pattern, these events are particularly useful for testing the hypothesisof time-dependentanisotropy.Anisotropy itself is clearly a very prominent feature in the data. A simple approachfor waveform matching of split shear waves allows unprecedented resolution of variations in shear wave splitting. Importantly, the variation of shear wave splitting with time is a relative measurement, which can be performed with higher accuracy than the associated absolute measurement. In particular, the relative measurementis not affected by timing errors nor by event distancevariations. During the experiment the difference betweenshear wave velocitiesdecreasesby -• 2% within -• 12 hours. After that, the medium apparently approachesa state which is stable for at least 5 hours. We suggestthat the temporal variation is due to the tectonic stressreleasefrom seismic events causedby the fluid injection. This model requiresthe presenceof fluid-filled cracks at depths larger than 4 kin. 1. Introduction the saxneorder of magnitude and often similar angle dependence,which makes a distinction usually rather There is little doubt that anisotropy is an important difficult, unless some of the effects can be ruled out feature of elastic wave propagation throughout many on other grounds. Generally, however, all of these efregionsof the Earth: It affectsapparent velocitiesof P fects are present, and the questionis only to which dewaves[e.g.,Hess,1964],polarizationof P waves[e.g., gree they contribute to the observations.An important Bokelmann,1995a],and particularlyshearwaves[e.g., questionis whether or not effectiveanisotropy changes Ando et al., 1983]. Sucheffectiveanisotropyat seismic with time. Suchtemporal variations(at least thoseon wavelengths of l0 -• to 102km canbe causedby a va- timescalesof yearsor less),if they canbe found,narrow riety of effects, all of which are associated with some down the choiceto just few effects. More importantly, type of ordering in the medium. These effectsrange however,temporalvariationswouldshowthat (and perfrom preferentialorientationof minerals(eachwith its haps how) anisotropyreacts sensitivelyto changesin ownintrinsicanisotropy),layering,to preferentiallyorithe stressfield and it might perhaps serve as a simple ented cracks or faults. These effects may have about means for measuring crustal stresschangesat reasonable cost[Crampinand Zatsepin,1997]. Several observationshave been suggested,which ap•Previously at Institut fiir Geophysik,Ruhr-Universit/it Bochum, Germany. pear to show a time dependenceof anisotropy. These observations are in all cases associated with variations Copyright 2000 by the American GeophysicalUnion. in shear wave splitting. Gupta [1973]presentedap- Paper number 2000JB900207. parent observationsof very large temporal variations, which were soon disputed on grounds that they might also be explained by scattering and phase conversions 0148-0227/ 00/ 2000JB900207509.00 23,879 23,880 BOKELMANN AND HARJES: TEMPORAL VELOCITY within the crust [Ryall and Savage,1974]. Peacocket a) al. [1988]and Crampin et al. [1990]presentobservations of shear wave splitting from local events near the Anza Gap in California, where one station apparently showsvery large variations of shearwave splitting over just weeksbefore and after a nearby event. These splitting delay time data, however, were disputed by VARIATION KTB FracNetwork (seen from above) 4OOO OThree Components ßVertical only ,, 2OOO ß Aster et al. [1990],who useda differentapproachof •' ,•VB o estimating shear wave splitting: while Peacocket al. [1988]and Crampinet al. [1990]extractedthe time separationbetween the two shear wave phases(splitting delay) by visually inspectingwaveforms,Aster et al. (1990) estimatedthe splitting delayas the length of the time interval of linearly polarized shear wave motion. Most of the data both groups used were from indiscriminate regional seismicity. We believe, however, that the argument can be sharpened considerably by specialtechniquesfor similarevents(doublets), or at least take the focal mechanism •,•hot 3 : o , 0 •, .9. 4OOO I1km o 6000 4000 2000 0 2000 4000 6000 East (meters) KTB FracNetwork (seen from South) b) which are nearly colocated and similar in source radiation pattern. In contrast, regional seismicity contains eventsof strongly varying character. However, depending on the focal mechanisms,which may differ between events, relative amplitudes of fast and slow shear wave phasesmay differ substantially. This may affect either method. An ideal approach would either use identical events o 2000 2000 6E 10E 14E II 4000 dif- 6000 ferencesinto account explicitly. In our study, similar events are found by a cluster analysis procedure: Since 8OOO 46N j"Main events are often remarkably similar in sourcelocation 6E 10E 14E HB and focal mechanism,a waveform matching technique 10000 allows determination of variations in shear wave split6000 4000 2000 0 2000 4000 6000 ting with unprecedentedresolution. Using severalclusEast (meters) ters of events, we show that the delay between split Figure 1. The "Kontinentale Tiefbohrung" KTB shear waves indeed varies with time. Distance variation in the Oberpfalz region of southeasternGermany; inof the events within a cluster are estimated with similar strument deploymentduring the Frac Experiment 1994 resolution. Anisotropy,as recordedby the shearwave shown(a) top and (b) sideview. Three-component receiversare shownby opencircles,single(vertical)comsplitting variesby •- 2.5% overjust a few hours. ponent instrumentsby dots. Note the location of the boreholeinstrument "Vorbohrung"VB in Figure lb), which suppliedthe data in this paper, and the bottom of the KTB drillhole("Hauptbohrung"HB), wherefluid The "KontinentaleTiefbohrung"(German Continen- wasinjectedduringthe experiment. The locationof one tal Deep Drilling Program) KTB is a scientificdeep particularlylarge event ("main event") and a surface drilling project in the Oberpfalz region of southeastern shot (shot 3) are alsoshown. Germany(Figure 1). Since1990,drillinghasprogressed 2. Experiment to the final depth of 9101 m below the surface. One of the last experiments performed at that depth was the KTB Frac Experiment 1994, which is discussedin detail large number of seismicevents were generatedduring by Zobackand Harjes [1997].The goalsof that experi- eachof thesephases.There were 376 eventswith magment were related to studying the behavior of the crust at that deeplevel in the crust during hydrofracturing;in particular, onegoal wasto determinethe stressfield acting at that depth, which has never beforebeenobtained by direct observation.Pumping started at 2202:15UTC on December 17, 1994, and lasted for about a day. During and after the experiment, flow rate, pressure,and nitudes of at least -2.1, the b value is 1.1. More details of the event location distribution and focal mechanisms are givenin Zobackand Harjes [1997]. 2.1. Main Event and Anisotropy During the 2-day interval a magnitude 1.2 event occurred, which was more than a magnitudelarger than seismicitywere closelyrecorded(Figure 2). The exper- the secondlargest event. That event, which we refer to iment was conductedin two phases:first the frac-phase as the "main event", a recordedwith excellentsignal-tolasting for -• 9 hours and secondthe main fluid injec- noise ratio on all stations temporarily installed for the tion phase lasting until •- 23 hours after the start. A experimentand alsoon stationsof the German Regional Flow 23.881 i I i 15 20 25 I I 1 600 prE' 500 • 400 •-. 3oo 200 loo I o ,Ir•I=-'11 i 0 5 ,..P 10 4O Time [h], To=1994:351:22 02:15.0 UTC Temporal Event Distributionand Pressure b)•,60 I I 5 10 I I I I I 15 20 25 30 35 •o i4o- • 30 ,,>, 20 -•o o o Time [hi, To: 1994:351:22 02:15.0 UTC, dt=10 min Figure 2. (a) Fluid flow and (b) pressureand inducedseismicity(histogram,light shading) during the KTB Frac Experiment. Events with magnitude-1.0 or larger are shownin the solid histogram. b) a) Component Orientations (Borehole Instrument) Main Event on Original Components Shear Waves North i 2 Az.317deg •' 1 Az.43deg ~ horizontal 'A.•-- ' ' 6.0 62 6.4 6.6 Time in Seconds Figure 3. Borehole instrument orientation and waveformsof P and $ wavesfor the main event: (a) the instrumentorientationas seenfrom above(the third componentis essentiallyverticalwith positiveupward). (b) The "Main Event" (origintime, day 352 at 1526:30.225UTC) showing excellentP and S waveforms,recordableat suchboreholesites. The S wave window is enlarged to showthe typical S wavedelaybetweenthe first (horizontal)componentrelativeto the second. That delay was consistentlyobservedfor all eventsin the boreholedata analyzed in this study. By chance, orientations of components1 and 2 correspondmore or less to the slow and fast directions(Az.-azimuth). 40 23,882 BOKELMANN AND HARJES:TEMPORAL VELOCITY VARIATION a) Shot 3 Raw Data Shear Waves •10• "110 11• 11, 116 ' '• Time in Seconds •) Lows-pass-Filtered Data Shear •aves Time in Seconds Figure4. P andSwaveforms fora surhce sho[(sho[ 3 onday350a[ 14:34:50.000 UTC)on [heoriginal componen[s. Bo[hrawda[ainFigure 4aandlow-pass-fil[ered da[a(8Hz,causal) in Figure4b showS phases arrivingon [hesecond componen• earlier[hanon•hefirst. The polariza[ion agrees qui[ewellwi[h[heorien[a[ion of[hesecond componen[. Manualde[erminalionofspli[[ing delayisdifficul[ [hough, asdocumen[ed by[hediffering es[ima[es of39msand 23msfor[hespli[[ing delayts2- tsz,depending onwhe[her [heband-pass is usedor no[. If goodaccuracy is required, moresophis[ica[ed [echniques mus[be used. Seismic Network(GRSN)in southern Germany andthe pendiculardirection(Figure 1). Still, the S arrival is GermanExperimental Seismic System(GERESS)ar- fasteron the secondcomponentfrom the surface.This ray,whichislocated-• 160kmto thesoutheast. Figure feature,an indication of anisotropy, is in generalagree3 showsa recordingof that event on the three channels mentwith previous studiesin the area[Liischenet al., of theborehole instrument in the"Vorbohrung" (VB). 1991],and it also agreeswith valuesfor the crust in Theinstrument orientation wasdetermined byusingP CentralEurope[Babu•kaand Cara,1991].FromFig- wave polarization data recordedfrom four surfaceshots. The instrument is tilted to the south in accordancewith the local deviation of the boreholeout of the vertical to the north. The early secondcomponent is seenfor all eventsin this study,whichis illustratedin Figure4 usinga calibrationshotarrivingfrom an almostper- ure 3 we estimatethe time separationbetweenthe shear waveson the two horizontalcomponentsas -• 14 ms for the mainevent.We obtainthe relativedifference 6/• betweenthe two shearwavevelocities/•1 and/•2, aver- agedoverthe path length(fromHB to VB, Figure1), if we can estimate the source-receiver distance D: BOKELMANN AND HARJES' TEMPORAL VELOCITY VARIATION 23,883 izontal interface. The latter would predict a radially approximatelynorth-southpolarizedfast arrival. Similarly, the effectof conversionoff a dippinginterfacecan with the velocityratio ? = a/• m x/•. This shows be ruled out, sincethe structure dips to the northeast. thatwemayobtain6• frommeasurement of threearrival times only with knowledgeof ?. We do not need to know the source-receiver 2.2. Spatial Distribution of Sources distance D. The calibration All of the eventsoccurin a spatially confinedregion: Figure 5 showsdirectionsfrom the VB boreholeinstru(1.9%or 3.2%) than the mainevent,nomatter whiches- ment to the locationsof the 35 strongestevents(lower timate of ts2-ts• we use. The most likely explanationis hemisphereplot). Incidenceis alwaysrather steepand that effectiveanisotropygenerallyincreasestoward the all azimuths are in the third quadrant near 120ø. Time surface, for example, due to increasingcrack-induced separations t$• - tp (approximatelydistance)are also anisotropy. This increase in anisotropy near the sur- given. The scatter indicatesthat distancesof the events face is consistentwith severalvertical profiling studies from the VB instrumentvary by lessthan +8%, which [e.g., Aster and Shearer,1991]. There are indications includes the statistical scatter of observations. In fact, that seismic anisotropy near the KTB borehole may we will see in section 2.3 that most of these events can alsobe affectedby foliationdirections[Rabbel,1994], be associatedwith severalclustersof very tight spatial shot(Figure4) givesriseto muchlargervalues of • as was found to be the dominant effect under the G ER- ESSarray160km to the southeast[Bokelmann, 1995b]. However, even at 9 km depth, there may still be a component of crack-inducedanisotropy if high fluid pressuresare present. Figures 3 and 4 together give clear evidence that the time separation t s2 -ts• is caused by anisotropyand not by S-to-P conversionfrom a hor- confinement. An ideal experiment for testing the time-dependent anisotropy(TDA) hypothesiswouldconsistof repeated identicalsources(samefocalmechanismand samesource time function)at the samelocation.High-qualitythreecomponentreceiverswould be distributed such that identical ray paths through a crustal region are ob- Histogram of S-P Differential Times Direction to the Sources (Lower Hemisphere) i i i i 2O i 9o 18 16 14 12 10 4 - 0 I 0 0.2 0.4 0.6 0.8 Time Delay in Seconds Figure 5. Receiver(borehole instrument)to sourcedirections (lowerhemisphere) and ts• - t• differentialtime delaysfor the strongest35 events. The eventsare within a spatiMlyconfined regionasdemonstrated by the smallscatterin distance(• ts•- t•) andanglesfromthe borehole instrument. Closerstudy showsthat many of them form groups(clusters)of eventshaving remarkablewaveformsimilarity.This suggests specialtechniques of waveformmatchingto find subtletemporalchangesof material parametersalongthe sharedpath. 23,884 BOKELMANN AND HARJES: TEMPORAL VELOCITY VARIATION i 12 --Frac Phase -- --Injection Phase-o 10 o oo o o o o O 0 o co O0 5 G•D o o o I o o of Main Event oo I 1•0 o o -Time I 0 15 2•0 2•5 Time in hours Figure 6. Temporaldistribution(in hours)of five clustersof similarearthquakesat a required similarity level of at least 0.8 . The diameter of the symbolsshowsthe magnitude of the events (maximumof-0.3, minimumof-1.2). A few otherclusters(2,3,4,6,7)are too confinedin time to be of interest in this study. served,which may be describedby a simple model. The receiverswould preferably be located in deep boreholes to circumvent complex interferencesfrom near-surface structure and to produce a high signal-to-noiseratio. Essentially,all of thesecriteria are met by the KTB Frac Experiment: Figure 3 showsthat the three-component instruments record remarkable P and S waveforms,even at frequenciesof 150 Hz. As sourceswe use data from well-defined clusters of events. We also have some prior effectsthat must be soughtby highly accuratewaveform comparisonof the events within a cluster. As will be seenin section2.4, the degreeof similarity between events of the same cluster is in fact remarkable. The existence of such "doublets" is well-known for seismicenergyreleaseacrossmanydifferentlength scales,rangingfrom earthquakeseisinology [Gellerand Mueller, 1980; Poupinet et al., 1984; Nadeau et al., 1995]to inducedmicroseismicity [Moriyaet al., 1994]. knowledge of effectiveanisotropy in the region[Liischen The long time window in this study containsboth et al., 1991; Rabbel,1994]. The clusteranalysisis de- the P and S phasesand the coda and secondaryphases. scribed in section 2.3. Highly similar events(and only these)must sharethe 2.3. Event Clusters samepath, sinceit is extremely unlikely that any other path can causethe same(kinematicand dynamic)pat- We obtain nearly colocatedeventswith similar source tern of reverberationsat the receiver. Clearly, locations radiationby clusteranalysis[$chulte-Theis, 1995]of the of sucheventsare displacedfrom eachother by at most 100 strongestevents. In that procedure, waveform sim- a small fraction of the wavelength. Geller and Mueller ilarity is measured by the maximum value of the cross [1980]estimatedthe maximumdistancebetweentwo correlation(we requireat least0.8). Successively, event eventsin a doublet, which are similar up to a wavelength pairs are distributed into different clusters of events. A, as A/4. This was confirmedby numerousauthors Generally,we obtain more clustersfor longertime windows, but with a reduced maximum cross correlation value. For our purpose, we use time windowsof 1.5 s, containingboth P and S waveenergy. Could this procedurebias the time dependenceanalysis? Such a cluster analysisprocedurewould bias a possibletime dependenceto smaller valuesrather than to larger onesbecauseevent pairs displayingtemporal variations are then lesssimilar and might therefore be rejected from the cluster. On the other hand, the existenceof highly similar doubletsover sometime interval showsthat temporal variationscan not be very large; instead, subtle variations are likely to be second-order thereafter,with somestudiessuggesting that A/4 may be overly restrictive, perhaps due to the strong effect of somestation site responses.By the same reasoning, theseeventsmust also have nearly identical focal mechanisms. Thus such events are ideal sourcesfor testing the TDA hypothesis, since they give nearly identical signalspropagatingalong nearly the same paths with appreciabletime separations. Out of the 100 strongestevents,57 can be associated with 11 clusters at the similarity level of at least 0.80 (crosscorrelationmaximum). Sevenof theseclusters are quite confinedin time, each lasting not longerthan 5 hours. On the other hand, four clusters are more BOKELMANN AND HARJES: TEMPORAL VELOCITY VARIATION spreadout in time with durationsof up to 12 hours. We may conceptuallyseparatethe time spanof the experiment into three intervals,the frac phaseand the early and late injectionphases,whichrefer to the injection periodsbeforeand after the main event. Two of the clusterscoveralmostall three time intervals(see Figure6). Theseare the mostvaluableclustersfor our study,but we alsousethree other clusterswith useful temporal coverageas they give us the opportunity to study the variation of shear wave splitting over time 23,885 aresufficiently large. Shearwavesagreeverywellon all components: To seesubtlechanges in the waveforms, closerinspectionis required. For the five clusters studied in this paper, Table 1 givesinformation for the associated events.The relative time delaysA(tse -tsx) and A(tsx -tp) with respectto a reference eventcanbe determined with high accuracy.Givenestimatesfor the reference event,the time separations tse - ts• andts• - tp are determined toestimate thedifference ofshear wavevelocities SlY(t). and also between these intervals. 2.4. Similarity 2.5. Waveform Matching Technique of Waveforms In Figure 7 we have seen how remarkablysimilar Figure7 showsP and S waveforms for the four events waveforms are within the same cluster. Now we turn to in cluster 9. It is evident that both P and S waveforms are indeedvery similar,at leastwheresignalamplitudes the determinationof relative delaysbetweenthe phases for two events,particularlythe relative splitting delay, the observable of prime interestin this paper. Are the small variations between the waveforms visible in Fig- a)4[Component 2 pWaveforms for Four Events ._-_: ure 7 systematicor not? To determinethesevariations, we displaypairsof seismograms u• (t) and u2(t) (each component)usingan initial alignmentby waveformcorrelationon a large time windowfor eachcomponent,to roughlyalign the waveforms.For eachcomponentwe E comparethe two seismograms in detail(seeFigure8). Figure8 showsthat waveforms are virtually identical (•4[Component 3 aside from the small time shifts. Thus the waveform ,... comparison is donemostconvenientlyby a slidingcross correlation window, interpolating and monitoring the <• 0 10 20 S Waveforms 30 Time in msec delayof the maximum[seealsoBokelmann, 1992],dependingon time. We obtainmeasurements of At• and Ate with very high accuracy,far below the sampling interval of 1 ms. The capabilityof measuringsuchsubsamplingtime delaysis in agreement with otherstudies for Four Events 2 [seee.g.,Poupinetet al.,1984]:Thelimitingaccuracy is controlledby waveformsimilarity,not by the sampling interval. We especiallywant to determine variations 4 A(t$2 - t$•) of the delayt$2 - t$• betweenthe two shearwave phases,which we obtain simply from the two quantitiesAtse and At$•, whichwe can determine Component 2 very well I 2 i i i i i i i Component 3 10 A(t$2-- rS1)-- (t$2-- rS1)-- (t$2-- t$1)ref = (rS2-- +ref- (ts 20 3•0 Time • in'msec Figure 7. P and $ waveformsfor eventsin cluster9, +ref )- -- •S1 - ' (2) We usethe delayestimatesof the fast (S1) waveon the secondcomponentand the slow(S2) waveon the first component,sincetheir amplitudesare largest on thesecomponents.Our delay estimatesare composed of the crosscorrelationmaximumlagsaveragedwithin (a) P ontheradial(2) andvertical(3) components, and the chosen time windows for the fast and slow shear (b) shows$ on all components. Notethe highdegreeof wave phases. similarityof eventswithin clusters.This is remarkable, The standarderror of the delay betweenthe two shear considering that dominantfrequencies are•,, 150Hz. As waves is 5 = V/(St$•)2 +(Stse)2, withthescatter a consequence, wemayusedetailedcomparisons of such and 5tse of the delay relative to the referenceevent. eventsto study time-dependentvariationsof medium properties. For this figure, raw waveformdata have This is a very simplebut effectivemethodfor determinbeen interpolated,time-shifted,and amplitude-scaled ing the relativesplittingdelay(or moregenerallybeonly. tweenany two phases).The approachdoesnot require 23,886 BOKELMANN AND HARJES: TEMPORAL Table 1: Clustersof Similar Events Used in This Studya ml ms ms ms Cluster ms •2• 1 0.00 579.00 0.00-t-0.05 14.50 1.058 25 352-0421:19.808 -0.8 -0.86 578.14 -0.18+0.07 14.32 1.047 16 352-0519:32.028 -0.7 -O.O6 578.94 -0.10+0.03 14.40 1.051 19 352-0521:59.744 -0.7 -0.44 578.56 -0.10+0.06 14.40 1.052 76 352-0533.54.897 -1.2 -0.36 578.64 -0.15-t-0.05 14.35 1.048 34 352-0538:03.481 -0.9 -0.08 578.92 -0.15-t-0.05 14.35 1.048 29 352-0559:09.019 -0.8 -0.38 578.62 -0.10-t-0.06 14.40 1.052 67 352-0654:51.035 -1.1 -0.56 578.44 -0.13-t-0.05 14.37 1.050 43 352-1317:15.312 -0.9 -0.02 578.98 -0.26-t-0.06 14.24 1.040 49 352-1321:39.923 -1.0 -0.30 578.70 -0.23-t-0.08 14.27 1.042 (24) 352-0351:30.880-0.8 39 352-1432:19.950 -0.9 0.16 579.16 -0.23-t-0.08 14.27 1.044 48 352-1527:21.615 -1.0 0.16 579.16 -0.34+0.07 14.15 1.036 47 352-1531:22.067 -1.0 -O.36 578.64 -0.37+0.12 14.13 1.032 1.063 Cluster 26 352-0121:10.691 -0.8 (17) 352-0252:37.508-0.7 554.40 -0.06+0.21 13.94 0.00 554.50 0.00-t-0.05 14.00 1.067 32 352-0353:53.902 -0.8 0.18 554.68 -0.08+0.07 13.92 1.060 27 352-0530:39.227 -0.8 -0.34 554.16 -0.09-t-0.18 13.91 1.061 86 352-1338:34.507 -1.2 -0.08 554.42 -0.14+0.25 13.86 1.057 75 352-1514:51.335 -1.2 -0.02 554.48 -0.13-t-0.20 13.87 1.057 97 352-1739:11.455 -1.2 -0.02 554.48 -0.39-t-0.13 13.61 1.037 Cluster 0.00-t-0.05 13.00 1.027 352-2129:03.308 -0.3 -0.02 534.98 -0.04+0.04 12.96 1.024 42 352-2308:11.075 -0.9 -0.04 534.96 0.06ñ0.08 13.06 1.032 18 353-0040:43.140 -0.7 0.06 535.06 0.02+0.04 13.02 1.029 0.00 576.40 0.00:h0.10 14.50 1.063 0.04 576.44 -0.19ñ0.22 14.31 1.049 0.00 535.00 Cluster (35) 352-0805:07.707-0.9 90 352-1510:50.274-1.2 Cluster 583.20 0.00+0.10 14.50 1.051 -0.9 -0.32 582.88 -0.21+0.09 14.29 1.036 62 352-1445:21.357 -1.0 0.38 583.58 -0.01+0.14 14.49 1.049 0.00 581.07 0.00+0.10 14.50 1.055 0.34 581.41 -0.05+0.22 14.45 1.050 Cluster (20) 352-1153:46.358-0.7 69 352-1625:46.000 -1.1 The only interactive part in the approachis in choosing time windows for the procedure to operate on. At that time the user is shown only the waveforms,and no indication of the time of the event, which prohibits subjective biases. 3. Results Another waveform example from cluster i is displayed in Figure 9, which showsa much smaller delay t$2 -- rS1 compared with Figure 8. Figure 10 shows showsthe results of this analysis for all events in cluster 1. Figure 10a comparesdifferent sets of time delay t$1 -- t?. Two sets of estimates obtained from manual picking scatter much more than the data set obtained from our procedure. Obviously, the uncertainty of estimates from the waveform matching is at least an order of magnitude smaller. The standard deviation is 0.3 ms. This confirmsthat (1) all eventlocationsin the cluster are very near eachother and (2) relative arrival times can be determined with accuracies of at least a third of the samplinginterval which is I ms. The limits of uncertainty which can be reachedis primarily determined by waveformsimilarity,not by the samplingrate [Bokelmann,1995b].The quantityts•- tp = D f(/31,c•),with f(/31,c•) -- [1//•1 - 1/c•], which is computedfor each 5 352-1323:04.487 0.00 between the waveforms of S1 and S2. 11 44 (61) 352-1115:20.956-1.0 the approach makes no assumption about the relation 9 3 (8) 352-1931:49.888-0.5 ple [seefor exampleBokelmann,1992]. In particular, 10 -0.10 VARIATION strong assumptionson the type of anisotropycausing the effects.Basically,the weak assumptionit doesmake is that as elastic propertiesvary with time by a small amount, eachobservedwave phasechangesprimarily in travel time and amplitude but not in waveformshape. This assumptioncan be justified from Fermat's princi- Event 6OriginTime, Mag,Actsl_p,t•l_p, Day:-UTC VELOCITY event, dependson the source-receiverdistance D and on medium velocities/31 and c•. Since D and the latter are unrelated quantities, we infer from the constancy of t$1 -t? for all events in cluster 1 that both D • 8 constand f(/3•, c•) , const= c. The formermeansthat distancesvary by < 2 meters. The latter imposesa con- a A few eventsare left out due to low signal/noise:Theseare events77, 89, and 95 for cluster 1 and event 94 for cluster 9, Event 7 was discarded dition relating the variationsof c•(t) and /31(t). If we write c•(t) = c•(0)+ Ace(t)and/3•(t) =/3• (0)+ A/3•(t), from cluster 5, becausethe magnitude was very different from the others we obtain (-0.4). I q-C•1(0) I - c/• (0) • Eventnumbersweregivenbasedon decreasing magnitude.Reference events(24, 17, 8, etc) are indicatedby parentheses. Theseeventsare used (t), (a) tocompute A/•. Forthese events, uncertainties forA(ts2-ts•)arespecified subjectively. c A refersto the differenceof a quantity with respectto the value for the referenceevent. In both cases,(1) for determiningthe relative shearwave splittingdelayand (2) the relativedelaybetweenfasterS waveand P wave, the high-resolution methodis used;accuracies for ACts2_s•are typicalfor both. d Herets2-s• = rs2 - ts• andts•-? = tsl - t?. e Here 5/3 is the differencein shearwavevelocitybetweenfast and slow whichsuggests Ace(t) m 2.4A/3•(t). However,this can be explainedmorenaturally,if both c•(t) and/31(t) are constant. After all, the constancyof f(/•l, o•) for varying c• and /3• may not be coincidental. Therefore it appearsmore likely that the temporal changeoccursin the slower shear velocity/32. Observedshearwavesplitting delaysshowa remarkable decrease,which is statistically significant. With velocity averaged overthe ray path5/• = /32-/3•//31withfll ---6.2/•¾-• estimates of ts• - t• and ts2 - ts• we obtain estimates km/s. of5/•fromequation (1) using r/ - x/•. Thetimede- BOKELMANN AND HARJES: TEMPORAL VELOCITY VARIATION 23,887 EventComparison afterFitting:352152715(solid)and352035125(dashedline),D•fference: -0.32 +/- 0.06msec >' ß • •Component 1 ,....',.•_, • -0.5 -• • (D t0.15 +0.02 msec'• • -1 -1.51 Ii • • I I I Component 3 0.5 I I I I -• . • • I I f•-'..- -. • I f' \ •o .5 1 i I I 10 20 30 Time in msec 40 Figure 8. Illustrationof the waveformmatchingtechniquefor determiningrelative delays betweentwo seismograms.Overlayingtwo three-component seismograms allowsdetermination oftherelative splitting delayA(t$2- tsz)- (rs2-*ref ref (thickdashedline,in ms),The •$2)-(t$• -tsz) crosscorrelationoperateson a sliding15-mswindowwith a Hanning-typetaper. Averagingover the windowsshowsby the verticaldashedlinesresultsin a relativesplittingdelayA(ts2 - tsz)= -0.32 + 0.06 ms. Clearly, this procedureallowssubsampleaccuracy. EventComparison afterFitting:352051925(solid)and352035125(dashed line),Difference: -0.10 +/- 0.03 msec 1[ ' ' ' ' ' ' ',f•,' i' ' ' ' >, 0.5 Component 1 .• -0.5 • 0.19 Component 3 A " x• •x• \.,,/'" 10 / "• / ',\ 20 -• • " ••I I 30 '•/'• '/ ',• ;/ ',/ /• 4• ,/•,' / '• '1 , I 50 60 Timeinmsec Figure 9. Waveforms andrelativesplitting delays foranother eventpairfromcluster1 (24-25). The timelagis shownonlyfor the chosen timewindows of S1 andS2 (displayasin Figure8). After approximatealignmentthe pair shows"earlier"time delaysfor both shearwavephases, while the examplein Figure 8 showeda later S2. This documentsan increasingtime delay between the two shear waves from event to event. 23,888 BOKELMANN AND HARJES' TEMPORAL VELOCITY VARIATION a)Cluster 1-Estimating tsl-tP b) Observed Splitting Delay , 590 585 +++ ++ .06 + )55 + ++ c) Temporal Variation of S Velocity Difference , .05 )45 580 )35 575 +: Routine Processing x: Own Manual .03 Estimates o: Relative Delay Analysis 10 20 Time in hours )25 0 10 20 Time in hours 0 10 20 Time in hours Figure 10. Resultsfrom cluster1. (a) A comparisonof differentsetsof is1 - tp valuesfor the eventsin cluster 1. Plusesindicate data from routine manual picking, crossesindicate data from an additional attempt using manual picking, and circlesindicate valuesobtained from waveform matching. Clearly, the waveformmatchingproducesstandard errors,which are at least an order of magnitude smaller than those of manual picking, and distance variations of the events in cluster 1 are all within 10 meters (seetext). (b) Observedvaluesof relative splitting delay as a functionof timeduringthe experiment assuming r/= x/• (timeis givenrelativeto 1994,day 351 at 2202:15.0UTC), (c) The shearwavevelocitydifferencein percentas a function of time. There is a clear decreaseby -• 2% overjust 12 hours. pendenceof that effectis clearly statistically significant with a variation of -• 2% within 12 hours. The effect of the time window choice has been extensively tested insuring that it has only minor influenceon the result. Hence the method is objective in the sensethat its resuits do not contain subjective biases. eventerrorsenterintotheoffsetlevelof rS/}(absolute measurement), say(•/• + •/•2)/2,morestrongly byan orderof magnitude. Theimp•ortant^feature is that the timedependence of•/•, say•/•2- 6fi2isnotaffected. In addition to the larger errors in the relative delaysof the referenceeventdifferentialarrival times,one must check effectsof timing errors during the experi3.1. Error Analysis ment. Generally,timing errorsmay be groupedinto two types, both of which might affectthe waveformdata of Whicherrors mayaffectestimates of6/•andmayperour experiment: First, timing might sufferfrom a conhapscause artifacts?We notethat results of •/• are stant offset, and second,there might be a drift in the alsoaffectedby errorsin referenceeventvalues[seealso Bokelrnann,2000]. To understandits influence,con- time signal, which would effectivelyspread or shrink the waveform data along the time axis. Since we exsider that equation (1) is in our procedureusedas clusivelyuse relative arrival times in this study, errors of the first type can not affect our analysis. On the other hand, a time drift with constant rate over the 0.6 s windowcontainingboth P and S phases,wouldspread or shrink waveformsand consequentlyaffect estimates of ts• - tp and ts2 - ts• similarly by a constant facwhere the first terms in numerator and denominator tor. That is the caseif we use either equation(1) or (referenceeventvalues)are of size 102 and 103 ms. (4). Equation (1) showsthat throughthe quotient,this outandtheestimates of 6/• areunThese valuescarry errorsof the order of 1 ms. The other factorwouldcancel (ts2 --tp) ts)er +X(ts2 - ts)V-r/ ' (4) rer+A(t$-tP) termsare of size10-• msandcarryerrorsof 10-2 ms. affected. For the data set in this paper, in fact, we are Weareinterested inthetemporal variation of• be- fortunate to have good knowledge of the true timing tweentwoevents, say•2 -6fi•. Wechoose thesecond signal during the experiment. Variation in this timing event as the referenceevent and develop the denomina- signal is only of the order of microseconds.However, also in the caseof a less-knowntiming signal, the sugis of order10-6). Thenweseethat the temporalvaria- gested type of analysis is robust in the sensethat it tion is of size10-2 (percent)with errorsof order10-3 offersat the same time very high accuraciesand is also arisingprimarily from the errorsin A(t$1 - tp). The insensitiveto timing errors, which may easily bias other reference events errors enter into the order 10-4. Theretypes of studiesof time-dependenteffects,at least if the fore,thetemporal variation of• isnotaffected byref- size of the temporal variations are of the order of only erence event errors. On the other hand, the reference a few percent. tor of •/•2 keeping thefirst-order term(thenextterm BOKELMANN 3.2. Other AND HARJES: TEMPORAL 3.3. Clusters VELOCITY VARIATION 23,889 Total Temporal Variation In order to study temporal variationsalong the total duration of the experiment we need to take into account The samewaveformanalysiswas applied to data from the other clusters. For cluster 10, waveform similarity different absolute levelof 5• fordifferent is generallysomewhatsmallerthan for cluster 1 (Ta- theperhaps ble 1). Nevertheless,we obtain a similar result: small clusters. A conservative approac•h of doingthisis to fit shearwavesplitting variationsfor event pairs with time a straight line to the valuesof 5fi for eacheventand to separationsof just a few hours. For larger separation, constrain these extrapolations to coincidein the center splitting delays vary more. Differential times t$1 - tp of overlappingtime intervals or the center of the gap again show a near constancywith time, while splitting for nonoverlappingtime intervals. This proceduregives delays decrease significantly. The5• clearly varies with the temporal variation shownin Figure 12, where the time consistent with the results of cluster 1, although adjustmentis in agreementwith the data for the three uncertaintiesare larger for cluster 10. Clusters 1 and small clusterscoveringthe transition (Table 1), which 10 essentially have similar temporal coverageand are shows a milddecrease in 5•. Thetotalvariation is of hence easily comparable: Both consistentlyshow that the order of 2%. Interestingly, the differenceof shear the difference between the two shear wave velocities dewave velocities decreasestill the main event and stays creases with time. constant after that. Polarization directions do not show How does5• behaveafter the mainevent? The suchsystematicchangeswithin clusters,neither for P largest remaining cluster, cluster 9, coversa time inter- waves nor for the faster S waves. val of 11 hours after the main event. Figure l l shows waveforms and relative splitting delays for an example event pair from cluster 9. Waveform similarity for 4. Discussion events in cluster 9 is remarkable. Visually comparing The main results from this study are (1) that the the event pairs, we notice that time variation of shear medium propertiesdo in fact vary with time and (2) wave splitting is clearly small. This is also apparent that we may indeedobservesucheffects.However,it is in the results (Table 1), where uncertaintiesare very also of great interestto understandthe nature of this small, reflectingthe excellent similarity. Variations of time dependence. We will in the followingsectiondisdifferential times t$l -tp are never larger than 0.6 ms. cuss possible causes for the temporal variation which Also the shear wave delays hardly vary: Temporal variin mechaniation of shear wave splitting in the latter part of the are (1) the injectedfluid, and (2) changes cal stressdueto (a) the inducedseismicityor (b) solid experiment is negligiblefor cluster 9. EventComparison afterFitting:352212855(solid)and352193145(dashed line),Difference: -0.04 +/- 0.04 msec Componont• •" 11 % i i I , Component 2 (1)•0 , /'% • • , •'• i • ,,, i • • i • I - rr 0.03 __21 I i 0.5 Comp'onon, :• / -- >•o -1' I I 10 I I 20 I I 30 I 40 50 Timein msec Figure l l. Waveformsand relativesplittingdelaysfor an exampleeventpair from cluster9 (events8 and 3). The displayis similarto Figure 8. 23,890 BOKELMANN AND HARJES' TEMPORAL VELOCITY VARIATION I Main ,Event 1.06 1.05 () 1 .o4 1.03 0 5 10 15 Time 20 25 in hours Figure 12. Temporal variation of shear wave splitting over the length of the experiment (clusters1 and 9). Seethe text for discussion. Earth tides. Can any of thesefactorsexplain a variation of-• 2%in •/• (oralternatively in jes, 1997].Theseare consistent with the regionalstress field (NW-SE compression), suggesting that a substan- Figure 13 showsthe volume of the first Fresnel zone tial fraction of the releasedseismicenergyis due to a refor the dominant frequencyof 150 Hz, which consists laxation of tectonicstress.Changesof stressdifferences of all pointsgivingrise to time delaysAT _<T/4 rel- may have a considerableeffect on effective anisotropy ative to the first arrival time. A good approximation [e.g., Zatsepinand Crampin, 1997], especiallywhen to the wave field can be made by assumingthat only fluid-filled cracks are present throughout the medium. this volumecontributesto the data [$niederand Lo- Events in this study produced stressdrops on the order maz, 1996].The volumeof that bodyis approximately of 10s Pa (bars)andfracturesizesof fewtensof meters. l08 m3. Prior to the main event, about 126 m3 of On the other hand, the sensitivity of relative velocity fluid was injected at 9 km depth. We take the most changeswith respect to stresschangeshas been sugfavorableview and assumethat all fluid propagates gestedto be of order10-s or even10-7 Pa-1 nearthe into the Fresnel volume where it can affect the obsersurface[De Fazioet al., 1973].A studyin southernGervations. Although unlikely,it givesa viable argument many usingcontinuousman-madesignals[Baischand 1999]produced an upperboundof 10-s about whether the injected fluid can explain the obser- Bokelmann, vationsat all. The 126m3 offluidmaychange themean Pa-1 With an averagestressdropof several104Pa fluid contentin the volume(mean excessporosity)by (assumingthat stressreleaseoccurson a "fault plane" 10-6. Can sucha smallchangein fluid contentcause throughoutthe Fresnelvolume) we may, in principle, su•ciently large variationsin •/? Randomlyoriented explain the magnitude of the observedeffectsby teccircular cracksas computedfrom a self-consistent ap- tonic stresschangein an anisotropicmedium containing proachfollowingO'ConnellandBudiansky [1974]would fluid-filled cracks. This mechanism should also explain require a mean excessporosity of the order of a few percent to explain the temporal variation of 2%. This is further characteristicsof the observations,namely that 4 ordersof magnitudelarger than can be explainedby variation occurs(most likely) in the slowerS velocity (1)5• decreases withincreasing stress dropand(2)the the injectedfluid(10-6). Thusthe injectedfluidcannot /•2, which is polarized in NW-SE direction. Figure 14 illustratesour interpretation. The cracks explain the observedeffects,at least if the pore spaces are isotropic.In the followingsectionwe will be dealing are oriented in or1direction, perpendicular to or3.Figure 14b showsthat tectonic stressdrop causesthe normal with anisotropicpore spaces. stress on the cracks an = or3to increase. This leads to 4.1. Tectonic Release The hydraulicfracturing set of a largenumberof seis- miceventswith strike-slipmechanism [ZobackandHat- a flatteningof the cracks(decreaseof aspectratio c•). Figure 14cpresentsthe resultsfrom a modelof random alignedcracks[Hudson,1981]. Specifically,the two S velocities are shown for a number of aspect ratios. We BOKELMANN Partial KTB frac-Network I -3000 J - AND HARJES' TEMPORAL VELOCITY VARIATION 23,891 (seen from South) see that indeed 5• = • -/• decreasesfor decreasing aspectratios for all angleswhich produceconsiderable I S wavesplitting. Furthermore,this model predictsthat the slower S wave velocity •2 varies, while • is constant. We can match the size of the observationsby a 1% changeof the aspectratio if the angleof propagation is 45ø from the symmetry axis. This would be the case if the cracks were roughly aligned with the foliation, VB whichdipswith -• 50ø to the northeast[Harjes et al., 1997]. A moreverticalorientationof the crackswould requirelarger changesin aspectratio in this model. -4000 We illustrated that the nature of the velocity change canbe explainedby a changein meanaspectratio of the cracks. The crack density was chosenas e - 0.05. This model is certainly simplistic. A more realistic treatment would also allow a varying orientation distribu-5000 tion of opencracks[e.g.,Zatsepinand Crampin,1997]. - However,this simplecrack model doesqualitatively reproducethe relevantfeaturesof the observedtemporal variation. 4.2. -6000 Solid-Earth Another - Tides stress field which we need to address is that arisingfrom solidEarth tides, whichgive riseto periodic changesof stresswithin the crust. These are of the or- > o derof 103Pa, smallerthan the coseismic stresschanges. J• However,they act throughout the entire crust. Unfortunately, the time duration of our experiment was not o longenough to ruleouta periodic change of 5• with > -7000 period of about 1/day and 2/day directly. Therefore - -8000- the possibility of tidal effects cannot be ruled out entirely given the uncertaintiesinvolved. A longer-time observationof shear wave splitting using doublet data would be an important test to better distinguishthis effect from tectonic causes. In any case, such a test givesa measurefor the extent of open compliantcracks in deeper levels of the crust. The possibilityfor such a long-time monitoring of seismicvelocitieshas been Main addressed for continuouslygenerated(machine)signals from the surface[Bokelmannand Baisch,1999;Baisch and Bokelmann,1999]. -9000 4.3. - Comparison With Other Studies Poupinetet al. [1984]found temporalvariationsof i -1000 -500 0 i 500 1000 East (meters) Figure 13. Closerview of the geometryof the experiment: A circle of 50 m radius is drawn around the point of fluid injection(HauptbohrungHB); The rayspropagate from the sourcelocation,for example,"main"to the VorbohrungVB. The first Fresnelvolume(zone) is shownfor 150 Hz (100 timesexaggerated in width). S velocitiesby • 0.2% before and after a magnitude 5.9 event in California using a coherence-based method operating on full seismogramsof events with similar waveform. In contrast to our paper, the split shear waveswere not specificallyaddressed,but that method is also capable of resolvingvery small time shifts. In fact, the size of temporal variation that it suggestsis similar to the effectin our paper. The ideal approachto studyingtime-dependentvariationsis certainly the approachusingdoubletsto eliminate alternative apparent time dependences(distancevariation of events;variation of focalmechanism),unlessthere are sourceswhich The observedshear wave effect can be interpreted as are indeedfixed in space[Bokelmann,1997]. A num- beingdue to contributions from this Fresnelvolume. ber of studies have claimed to observe temporal varia- 23,892 BOKELMANN AND HARJES: TEMPORAL a) VELOCITY VARIATION b) Mohr circle before stress drop er•.• foliation cracks c) Shear Wave Velocitiesfor a Numberof Crack Aspect Ratios i o 3.55 i i I i i I _ i S1 _ ._ • 3.5 •3.45 o 03 3.4 3.350 ...... ..j: ;o ;o ., S2 ;o s'o 6'o 90 AnglefromSymmetry Axis(•,•) indegrees Figure 14. (a) Orientationof maximumand xninimumhorizontalcompressive stress(O'H,O'h). Cracksopeningnormal to c3 (= c• if c2 vertical) havesimilar strike as the foliation direction. (b) Increasein cracknormalstressc, - c3 duringa quake,leadingto a flatteningof the cracks (decreasingaspectratio a). (c) Dependenceof S velocitieson crack aspectratio. Decreasing aspect ratio a producesa decreasein 6fl for angleslarger than 30ø. Note that the slower$ velocity fi2, which is polarized in NE-SW direction, is predicted to vary, while the faster fi• is constant. tions,mostlyin the ratio a/fi [seeLukk and Nersesov, upper bound does not preclude temporal variation of 1978]. However,observation of smallvariationsposes the size observedin our study or in that of Poupinet very strongrequirementson eliminating errorsfrom dis- et al. [1984]. In our experience,it is often difficult tance variation and timing, which are very difficult to to unambiguouslydetermine time delaysbetweenfast satisfy with other methods than ones based on wave- and slow shear wave phasesby visual inspectionof a form correlationof doublets. Also for the Anza Gap singlethree-componentseismogram.In fact, initial estidata set, seismic doublets have been used to show that matesof shearwave splitting from our data, which were temporalvariationsare at most5 to 10% [Asteret al., basedon visual analysisalso showedlarge excursions. 1990],which disagreeswith large temporalvariations After allowing only clustersof doubletsand performwhichwereclaimedby otherresearchers [Peacock et al., ing the objective procedure,temporal variationsalmost 1988; Crampinet al., 1990];on the other hand, that vanishedand the stable smaller-scalepattern emerged. BOKELMANN 5. AND HARJES: TEMPORAL VELOCITY VARIATION 23,893 Bokelmann, G.H.R., Azimuth and slownessdeviations from Conclusions the GERESS regional array, Bull. Seismol. Soc. Am., 85, 5, 1456-1463, 1995b. The main result of this study is that shearwave splitting hasbeen observedto vary with time at a depth level Bokelmann, G.H.R., Messung zeitlicher Variationen von Wellengeschwindigkeiten in der Erdkruste, Mitt. Dtsch. of 4 to 9 kin. The analysis procedure is objective in Geophys. Ges., 3, 6-12, 1997. the sensethat subjective influencesare eliminated; im- Bokelmann, G.H.R., A method for resolving small tempoportantly, the procedure is able to determine temporal ral variations of effective elastic properties, SEG Special Volume, in press, 2000. variations of the relative shear wave velocity difference with veryhighaccuracies (• 10-4). The anisotropy itself, as documentedby shear wave splitting, has a size of ~1% and is generally consistentwith previousobservations. Intriguingly, shear wave splitting decreases for ~ 12 hours and is essentially constant afterward. No assumptionis made that the events are colocated. Nevertheless,the analysis showedthat the events actually do occur very closeto each other, confirmingthe hypothesisof similar events. No progressivechangeof sourcelocation is apparent from either the time delays nor the P wave polarizations. It is interesting that the changein medium configuration occurs apparently almost instantaneously, with a lag of at most a few hours. The injected fluid volume cannot explain the temporal changeby itself. On the other hand, the effect of the stressdrop due to induced seismicitymay possibly explain the data if fluid-filled cracksare presentat depth larger than 4 kin. A longertime experiment in a deep borehole as KTB would help to further understand the mechanismsof temporal variation in the Earth's crust. Bokelmann, G.H.R., and S. Baisch, Nature of narrow-band signalsat 2.083Hz, Bull. Seismol.Soc. Am., 89, 156-164, 1999. Crampin, S., and S.V. Zatsepin, Changesof strain before earthquakes;The possibilityof routine monitoringof both long-term and short-term precursors,J. Phys. Earth, •5, 1, 41-66, 1997. Crampin, S., D.C. Booth, R. Evans, S. Peacock,and S.B. Fletcher,Changesin shearwavesplitting at Anza near the time of the North Palm Springsearthquake, J. Geophys. Res., 95, 11,197-11,212, 1990. De Fazio, T.L., K. Aki, and J. Alba, Solid Earth tide and observedchangein the in situ seismicvelocity,J. Geophys. Res., 78, 1319-1322, 1973. Geller, R.J., and C.S. Mueller, Four similar earthquakesin central California, Geophys. Res. Left., 7, 821-824, 1980. Gupta, I.N., Premonitory variationsin S-wavevelocityanisotropy before earthquakesin Nevada, Science, 182, 11291132, 1973. Harjes, H.P., et al., Origin and nature of crustal reflections: resultsfrom integrated seismicmeasurementsat the KTB superdeep drilling site, J. Geophys. Res., 102, 18,26718,288, 1997. Hess, H. H., Seismic anisotropy of the uppermost mantle under oceans, Nature, 203, 629-631, 1964. Hudson, J.A., Wave speedsand attenuation of elastic waves in material containing cracks, Geophys. J. R. Astron. Soc., 6•, 133-150, 1981. Acknowledgments. We wish to thank the KTB team which assistedin performing the injection experiment. Markus Janik, Hartwig Schulte-Theis,Matthias Bahlo, and Thorsten Lukk, A.A., and I.L. Nersesov,Character of temporal changes in the velocities of elastic waves in the Earth's crust of the Bfisselbergprovided valuable help in analyzing the waveGarm region, Izv. Phys. Sol. Earth, 1•, 387-396, 1978. form data. We profired from discussionswith Fritz Rumreel. Reviews by George Helffrich, Peter Shearer, and an L/ischen, E., W. SSllner, A. Hohrath, and W. Rabbel, Inteanonymousreviewer greatly improved the manuscript. grated P- and S-waveboreholeexperimentsat the KTB References Ando, M., Y. Ishikawa, and F. 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