NOTICE CONCERNING COPYRIGHT RESTRICTIONS

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1 NOTICE CONCERNING COPYRIGHT RESTRICTIONS This document my contin copyrighted mterils. These mterils hve been mde vilble for use in reserch, teching, nd privte study, but my not be used for ny commercil purpose. Users my not otherwise copy, reproduce, retrnsmit, distribute, publish, commercilly exploit or otherwise trnsfer ny mteril. The copyright lw of the United Sttes (Title 17, United Sttes Code) governs the mking of photocopies or other reproductions of copyrighted mteril. Under certin conditions specified in the lw, librries nd rchives re uthorized to furnish photocopy or other reproduction. One of these specific conditions is tht the photocopy or reproduction is not to be "used for ny purpose other thn privte study, scholrship, or reserch." If user mkes request for, or lter uses, photocopy or reproduction for purposes in excess of "fir use," tht user my be lible for copyright infringement. This institution reserves the right to refuse to ccept copying order if, in its judgment, fulfillment of the order would involve violtion of copyright lw.

2 TECHNIQUES FOR INTERPRETING AND IMPROVING Vp/Vs MEASUREMENTS WHEN ASSUMING A LAYERED GEOTHERMAL MODEL -- Pul W. - Cton Senturion Sciences, Inc. Tu1 s, Oklhom ABSTRACT If geotherml re is modeled s lyered erth nd elstic constnts vry only with depth, then mesured Vp/Vs rtios will depend on microerthquke positions reltive to the rry s well s focl depths. Vp/Vs rtios obtined from microerthquke dt re reltionships of pprent P nd S phse velocities. An pprent Vp/Vs rtio cn represent medium Vp/Vs vlue if rys to ll sttions re through one medium, or if rrivls re criticl refrctions from lyer t depth. Improved mesurements cn be obtined when fctors contributing to errors in mesuring Vp/Vs re understood. In ddition to P nd S timing precisions, the error in mesuring Vp/Vs depends on epicenter position reltive to n rry with prticulr configurtion, nd the P nd S pprent velocities. INTRODUCTION Mesurements of reltionships between P nd S phse pprent velocities re useful in two respects when evl uti ng mi crosei smi ci ty within geotherml res. First, it is desirble to obtin good loction ccurcies in order to delinete potentil drilling trgets. Computed loctions should stisfy event S-P time intervls; hence, knowledge of the Vp/Vs rtio is required. Second, precise Vp/Vs mesurements my indicte nomlous rock properties within vicinities of geotherml res. Low vlues, Vp/Vs 4.73, would suggest rock voids re not sturted with liquid (Nur nd Simmons, 1969) nd could therefore be stem-filled (Combs, 1974). Frncis (1976) suggests tht by plotting rtio mesurements s function of depth, one might deduce depths to which hydrotherml circu 1 t i on extends. However, one should recognize tht if elstic properties vry only with depth, then observed Vp/ Vs rtios will depend on epicenter positions reltive to the rry. This is even true for events t identicl depths but different epicenter loctions. When plotting S phse rrivl times (or S-P time intervls) versus P onsets, the mesured Vp/Vs reltionships re rtios of pprent P nd S phse velocities nd not precise reltionships of medi velocities. Poisson's rtio cn only be precisely determined when trvel times to ll seismometers re essentilly through medi of one type, or if ll rys hve been criticlly refrcted from lyer t depth. Therefore, discussions of P nd S phse velocity reltionships should be viewed s being those for pprent Vp/Vs rtios. THE APPARENT Vp/Vs RATIOS FOR HYPOTHETICAL EVENTS LOCATED WITHIN A HALF SPACE OVERLAIN BY A LAYER WITH A DIFFERENT POISSON'S RATIO In Figure 1, pprent Vp/Vs rtios re given for hypotheticl events plced 5 km beneth 7 km dimeter, 6-sttion rry which ws deployed during New Mexico geotherml investigtions. From event pprent velocity mesurements, the upper lyer velocity could be represented by Vpl = 4.9 km/sec; the hlf spce velocity ws mesured to be ~6.25 km/sec from events beyond the rry nd to distnces of 5 km. The Poisson's rtio selected for the hlf spce, u2 =.25, is typiclly observed for events refrcted upwrd from the grnitic(?) lyer in western U.S. A Poisson's rtio of ul =.3 is little high for the estimted 3 km of sediments but would be expected for thick section of liquid sturted grvels. P nd S trvel times from hypotheticl events to rry sttions were clculted within.1 msec using exct equtions for rys pssing from points beneth the refrctor to the surfce. Stndrd 1 i ner regression equtions (Drper nd Smi th, 1966) were then used to clculte the pprent Vp/ Vs rtios. Uncertinties t the 95% confidence level were treted s though ll devitions were in the S times. When evluting some S phse devitions from which the curve in Figure 1 ws generted, hypotheticl sttion times were only displced 2-3 msec from regression lines when Vp/Vs determintions were within 2.1 t the 95% confidence level. These S time devitions re significntly smller thn is possible to mesure from field dt. Numerous models could be generted to illustrte vrious effects on mesured velocity nd Poisson's rtio determintions when elstic constnts vry only with depth; however, Figure 1 summrizes most of the results. When n event is in the lower medium nd beyond the rry, P nd S pprent vel oci ti es pproch the vel oci ti es of the lower medi um; consequently, the pprent rtios 71

3 t Sttions t Sme Elevtion -, v) z v).26s l ' ' ' ' ' I l I l, I, t l I I ~ I l L-- 1 ' 5 IO 15 2 DISTANCE FROM ARRAY GEOMETRIC CENTER, KM Fig. 1 Apprent Vp/Vs nd Poisson's rtios which would be mesured if medi Vp/Vs rtios re different t depth, nd hypotheticl foci occur t. identicl depths but t different distnces reltive to 3.5 km rdius pentgonl rry surrounding centrl 6th sttion. Poisson's rtio for the lyer nd hlf spce re ul =.3 nd 2 =.25. Dshed curves re 95% confidence 1 eve1 s obtined from stndrd 1 i ner resression equtions which were used to clculte pprent VP/VS rtios: pproch vlues which re those of the lower medium. This wou1.d lso be true for shllow distnt events which occurred within the upper medium nd were criticlly refrcted. Within the rry, the pprent velocity rtio is strongly dependent on focl position reltive to the rry nd to the refrctor; the results depend on the reltive - mount of trvel time in ech lyer. Medi rtios cn only be pproximtely mesured when significnt percentge of the trvel time is within nersurfce mteril, or if pprent velocities pproch medi velocities. Otherwise, Vp/Vs rtios re pprent reltionships nd should be interpreted in view of event positions reltive to the rry. AN ERROR EQUATION PERTAINING TO Vp/Vs MEASUREMENTS The hypotheticl trvel times used for generting the curve in Figure 1 were known within.1 msec; such precisions re unrelistic to ttin when timing microerthqukes. An impulsive high frequency P onset cn be timed within 1 msec. However n S phse, which rrives within bckground of P phses, cn t best be timed within 2 msec; this ssumes the S onset hs been correctly i denti f i ed. Fctors which contribute to errors in mesuring Vp/Vs cn be nlyzed in terms of n error eqution pertining to plne wve pprent velocity mesurements when using 3-sttion rry. Assume P nd S timing precisions re norml distributions with zero mens nd tht vrinces t the ith sttion re 5& nd S&. Furthermore, ssume P nd S timing vrinces re respectively equl t ll sttions, but tht the two phse sets hve different vlues, Le., stp = s&, nd s& = s& (2) (i = 1, 2, 3). With these ssumptions, n estimte for the stndrd devition of the pprent Vp/Vs rtio is where (3) V i s the P phse plne wve pprent velocity, e is the interior ngle seprting the other two sttions t distnces L, nd i s the pprent Vp/ Vs rtio. The event zimuth $, is mesured from the centrl sttion where e is defined. For cl i brtion purposes, the rrys discussed in this pper hve been dimensioned to mesure (within 5%) P phse pprent velocities of 6.25 km/sec with 2 msec timing precisions when using the sml ler 3-sttion combintions. This requires tht rry rdii be '~4 km. Assume V = 6.25 km/sec, = 1.73, L = 4 km, e = 72, $ = 36 ( worst direction for mesuring s), nd tht P nd S timing precisions re 2 nd 5 msec. With these ssumptions, n pprent Vp/Vs rtio could 72

4 be mesurble within 8% for n impulsive hypotheticl event which occurred 5 km beyond the triprtite rry. Premultipliction of s by 2 indictes P phse timing precisions cour contribute lmost s much to the error in Vp/Vs s do those of S onsets. Thus Vp/Vs should be clculted with errors in both P nd S times tken into considertion. The nonliner regression equtions required to solve these Vp/Vs estimtes hve been compred to results obtined from stndrd liner regression equtions. Provided severl events with impulsive onsets hve been included in the sme Vp/Vs estimte, the results obtined from nonliner nd stndrd regression equtions re ner1.y identicl. However, unless P nd S vrinces re pre-ssigned, the nonliner equtions converge to unresonble solutions where P errors re greter thn those for S phses. For these resons, only stndrd liner regression techniques re used in this pper. An improved Vp/Vs estimte is obtined by trnslting P nd S times from severl events onto single Wdti digrm. However, s ws evident in the previous section, pprent Vp/Vs mesurements depend on the focl position reltive to the rry. Trnslted event times should only include those from microerthqukes which re t the sme position reltive to the rry. Fortuntely, when microerthquke swrms occur, events typiclly hve identicl signtures indicting they re from the sme smll source region. c 1 A3 A Sttion Loctions Fig. 2 A* 5 IO 1 IS I KILOMETERS Microerthqukes Microerthquke epicenters reltive to 6-sttior1, 9 km dimeter Nevd rry. (Dt provided by Erth Power Corp. Tuls, Ok.) INTERPRETATION OF AN APPARENT Vp/Vs RATIO -MEASURED AT A IIEVADA GEOTHERMAL PROSPECT Figure 2 gives epicenter positions for 39 Nevd microerthqukes which were detected with 9 km dimter, 6-sttion rry. The events hd nerly identicl signtures nd ech of the most impulsive events hd P phse pprent velocities of km/sec. The slight pprent velocity vrition for ech event, kl. km/sec nd center sttion S-P intervls, 'L 1.65 seconds, indicte tht 11 km distnce ssignments from the center sttion re resonble. At this distnce reltive to the rry configurtion in Figure 2, 6.5 km/ sec pprent velocity suggests focl depths were s5 km; unique focl depths cnnot be clculted becuse the pprent velocity vrition for ech event is only kl. km/sec. (Focl determintion 1 imittions in view of pprent velocity mesurements re discussed by Cton, 1976.) Trnslting P nd S rrivl times from 7 of the most impulsive swrm events onto the Wdti digrm in Figure 3, the observed pprent Vp/Vs rtio is 1.7 k.5 t the 95% confidence level. From these pprent Vp/Vs results, it is not possible to determine whether the deeper rocks, shllow mterils, or both medi sets hve low Vp/Vs rtios. This mbiguity my be somewht resolved by considering the pprent velocity mesurements from distnt events which hd been criticlly refrcted. Deeper lyer P velocities were typiclly those which the uthor hd mesured in other # RMS of S Residuls: 4msec from 27 rrivls $ -1. I I I I.o tpij - tpj (sec) Fig. 3 Trnslted Wdti digrm for Vp/Vs determintions from 7 events in Figure 2. tpij nd tsi* re P nd S rrivl times t the zth sttion for the jth microerthquke; f nd sj re men rrivl times. (Lit provided by Erth Power Corp., Tuls, Ok.) 73

5 nerby Nevd res. These included lyer P velocities of 5.9, 6.4, nd 7.2 km/sec. If the low pprent Vp/Vs rtio, 1.7, is significnt, nd cn be ttributed to medium P velocity, then the lyer with n nomlous low P velocity would be suspected t shllow depths. This suspected nomlous shllow lyer velocity hs not been confirmed; during the 15 dy microerthquke survey, shllow events did not occur within the rry. CONCLUSIONS In western U.S. geotherml res, microerthqukes hve occurred ner the surfce to ~ 1 km depths. With this rnge of focl depths, pprent Vp/Vs mesurements should be interpreted in terms of lyered erth models. If elstic constnts differ only with depth, then pprent Vp/Vs mesurements require tht the number of sttions nd rry configurtion be dequte to resolve the pprent velocities from which pprent Vp/Vs rtios re obtined. When combining dt from severl events in order to improve Vp/Vs estimte, events should be from the sme smll re in order to retrieve the pprent Vp/Vs rtio for tht position. Direct mesurements of the pprent veloci - ties from other events cn id in resolving mbiguities for n pprent Vp/Vs rtio t prticulr loction reltive to the rry. ACKNOWLEDGMENTS Erth Power Corportion, Tu1 s, Ok., re1 inquished their dt for demonstrting Vp/Vs observtions from one of their Nevd geotherml surveys. Senturion Sciences provided the time, computer fcilities, nd stznogrphic services for this pper. REFERENCES C,ton, P. W., Plne wve pprent velocity vector techniques for evluting nd improving loction ccurcies with dt obtined from smll rrys (7-1 km in dimeter), unpublished mnuscript presented t the 1975 & 1976 AGU Fll Meetings, Senturion Sciences, Tuls, Ok., 71 pp., 1976 Combs, J., Het flow studies, Cos geotherml re, Chin Lke, Cliforni, Technicl Report #2, Advnced Reserch Projects Agency, Contrct NO. ivouz23-74-c-299, 24 pp., 1974 Drper, N. R., nd H. Smith, AppZied Regression Anlysis, John Wiley, New York, Frncis, T. J., The Rtio of Compressionl to Sher Velocity nd Rock Poros,ity on the Axis of the Mid-Atlntic R@e, J. Geophys. Res., 81, , 1976 Nur, A., nd G. Simmons, The effect of Sturtion on Velocity in Lou Porosity Rocks, Erth Plnet, Sci. Lett., 7, ,

A027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data

A027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data A07 Uncertinties in Locl Anisotropy Estimtion from Multi-offset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.