Source Mechanism Study of Quetta Earthquake of May 30, 1935

Abstract:HARSH K. GUPTA and D. D. SINGHThe source mechanism of the major destl-uctive earthquake which occurred in the Quettaregion on May 30, 1935 is determined using the P-wave first motions, S-wave polarization angles andsurface waves spectral data. A thrust faulting is obtained along a plane with strike N 33"E, dip 68"NW,slip angle 124" and a focal depth of 20 km. A unilatersll fault of about 106 km, rupturing with a velocityof 3.1 km/sec is obtained from the differential phase and the directivity function of lG2 - G3 and R2 - R3waves. The source parameters obtained from the surface waves spectra are: seismic moment = 1.75 x 10 28dyne-cm; dislocation = 32.81 meters; fault area = 1778 sq. km; apparent stress = 283 bars; stress25 -4drop = 567 bars; strain energy = 165 x 10 ergs and strain drop = 18.9 x 10 . The high stress dropand apparent stress associated with this went suggest that high tectonic stresses are prevailing in thisregion. A major part of the stresses accumulated before the occurrence of this earthquake had beenreleased thro~ngh the main shoclr.INTRODUCPTIONHimalayan frontal arc, flded by the Chamanfault in the west and Arakanyoma in the east, is seisrni-cally one of the most active region in the entire Alpinebelt. Fig. 1 shows the epicenters of major earthquakessince 1897 of magnitude 3 7.5, that have occurredin the region. Some of these earthquakes were veryu Thr us1 Foul t'C=~ULAIMAN RANGEB=KIRTHAR RANGEA= BALUCHISTAN ARCFig. 1.Map showing major tectonic features of Himalaya and nearby regions. The dots represent epicenters of major earthquakessince 1897. The mechanism solution for the 1950 earthquake has brm taken from Ben-Menahem el at.(1974). Solutions for the 1934 and 1935 earthquakes are also shown (Siugh and Gupta, 1980).Proc. Intern. Commit. Geodynamics, Grp. 6, Mtg. Peshawar, Nov. 23-29, 1979: Spec. Issue, Geol. Bull. Unh.Peshawar, VoZ. 13, 1980.-.

damaging and claimed thousands of human lives. Thefocal mechanism solutions provide better means fordetermining the orientation of regional stress, nature offaulting and sense of motion on the faults. The focalmechanism solutions for a very few large magnitudeearthquakes are available in the Himalayan and nearbyregions. For understanding the regional tectonics of theregion, it is necessary to know the source parametersof these earthquakes. Ben-Menahem et al. (1974) investigatedin detail the Assam earthquake of August 15,1950. The source parameters of the Bihar-Nepal earthquakeof January 15, 1934 have been investigated indetail by Singh and Gupta (1980). Among the remainingearthquakes, the Quetta earthquake of May 30,1935 is of special interest, as sufficient instrumentaldata are available to carry out the detailed source parameterstudies.The area surrounding the Quetta syntaxis formsone of the seismically most active region in the Alpinebelt. Several earthquakes have occurred in the pre-histaricaltimes causing severe damage to both propertyand life. The focal mechanism solution for earthquakesoccuring in this region has been determined by variousinvestigators like Quittmeyer et al. (1979) andChandra (1978 and 1980). A major destructive earthquakeof magnitude M = 7.6 occurred close to (Fig. I)Quetta (epicenter 29.5"N, 66.7"E) on May 30, 1935(origin time 21 h 33 m 0.0. s). It caused a considerableamount of destruction, claimed an estimated30,000 human lives and created numerous fracturesand landslides. Here we present the detailed sourceparameter investigations for this earthquake using theavailable records of merent seismological stationsthroughout the world. The focal mechanism and di•’-ferent seismic source parameters like fault length, rupturevelocity, source time function, seismic moment,dislocation, apparent stress, stress and strain drop areestimated using the body and surface waves data of thisearthquake.FOCAL MECHANISMP and S waves dufu: Seismograms were obtained forthe Quetta earthquake from Merent seismologicalstations throughout the world. The P-wave firstmotion directions are read from the long period verticalcomponent records. These first motions are plotted onthe lower hemisphere of the equal area projection(Fig. 2). S-wave polarization angles are determinedusing the records of a few seismic stations. These areplotted in Fig. 2. The standard deviation and averageerror are calculated by varying the dip and strike ofthe nodal planes within the range, which were permittedfrom the P-wave data. For the best fit model, thestandard deviation and average error are estimated tobe 10.6" and 8.8'. Here the P and S waves data arenot sufficient for defining the nodal planes accuratelyFig. 2., OUETTA MAY 30,1935 ZOKILOMETERSFault plane solution determined using first motionsread from long-period records. Filled and opencircIes represent &st motions compressions anddilatations, respectively. ,P is the pressure axis or axisof maximum compression, T is the tension axis oraxis of minimum compression. X and Y are thepoles of the two nodal planes. S-wave poIarizationdirections are shown by short lines. Small dots indi-Lcate stations for which ody Swave data are used.and, therefore, surface waves spectral data have alsobeen used.Rayleigh/Love wave spechd ratio: Surface wave spectralratio has advantages over the use of absolute surfacewaves spectra, as we do not have to apply thecorrections for the ef•’ect of instrument, path, sourcefiniteness and source time function (Canitez and Toksoz,1971). For the determination of observed spectralratio, the fundamental mode Rayleigh and Love wavesof several minutes duration (Fig. 3 and Table 1) aredigitized at the varying time intervals, depending uponthe wave forms. These data are then interpolated at afixed time interval of 0.3 sec using the Lagerangianinterpolation method. The digitized data are detrendedand the arithmetic mean is removed. Afterwards, thedata are Fourier analysed using the Simpson's methodto get the spectral amplitude and phase. The theoreticalspectral ratios are calculated using the method ofHarkrider (1 970) for different fault orientations consistentwith the P- and S-waves data. The best fit is obtainedby the trial and error comparison of the observedRayleigh/Love wave spectral ratio with the theoreticalones, calculated for focal depths of 10, 20 and 35 kmat five seismic stations. A few such plots are shownin Fig. 4 for the selected best fit model. The fault

TABLE I. The Digitized Signals Recorded at Different Seismic Stations for the Quetta earthquake of Mqy 30, 1935.. - -. .Dis tame Beginning of End of the timeStation Seismograph Component Wave (km) the time window windowName GMT GMThr min sec hr min secUppsalaCopenhagenWiechertWiechert-Galitzin WilipStuttgartGalitzin WillipScoresbysundGalitzin WilipIvigtutWiechertMelbourneWellingtonMilne ShawMilne ShawMAY 30,1935plane orientation for the best fit model are as follows:Strike , 0 = N33"EDip, 8= 68"NWSlip angle, h. = 124"Focal depth, H = 20 kmFautfl length, rupture velocity mtd source time function:Directivity fmction was defined by Ben-Menahem(1961) as the ratio of the spectral amplitude of wavesleaving the source in opposite directions:COP lEWlwherec = phase velocityb = fault lengthv = rupture velocityQ = angle between the fault plane and the great

TABLE 2.. Estimates of the Fault Length for Quettaearthquake of May 30, 1935 from. theDifferential Phases of Love and RayleighwavesFrequency Period STU SCO(Hz) (Sec.) (G2/G3) (R2/R3)We have estimated the fault length and rupturevelocity from the diflexential phases and the direcfivityfunction method (Ben-Menahem and Toksoz, 1962 and1963). For the determination of Uerentid phases ofG2G3 and R2-R3, the Love and Rayleigh waves forQuetta earthquake are digitized (Fig. 3 and Table 1)as described earlier. The digitized data are detrended,corrected for amplitude and instrumental phase shift(Hagiwara, 1958). The amplitude and phase spectrumare obtained using the fast Fourier transform algorithem.The initial phase is obtained using the relation of Ben-Menahem and Toksijz (1 962) :wheret = the time lag of the beginning of the spectralnwindow with respect to the origin time.: a' = Fourier phaseA = epicentral distance of the recording stationM = an integerinst= instrumental phase shiftThe initial phase, @o, is corrected fur the sourcefiniteness effect. Then the Merential phase, 6 4 iscalculated for the pairs of R2-R3 and G2-G3 wavesand is listed in Table 2. The average value ofX'@% ( X' = wave length ) is estimated, which yieldsthe fault length of 106 km.Fig.THEORETICALx = 124'~ 6=-68:SCO- PERIOD (SECONDS) --+4. Comparison of obsdved Rayldgh/Lme wave spectralratio (dots) -&h the theortical ones (continuousline) at a few stations for the best fit model.-.The rupture velocity is calculated using the dire=.tivity functions of G2-G3 and R2-R3 waves. Thedsav-ectiiyit~~ function is obtained from &e spec-tral amplitude ratios of R2-R3 or G2G3 waves,;corrected for the absorption effect. The values of phase /velocity and attenuation coefficients are taken fromMills and Hales (1978). The theoretical directivity iscalculated from the above relation for different combi- ,nations of fault length and rupture velocity. The faultlength is varied in the range of 106 * 30 km andrupture velocity is varied from 2.5 to 3.5 km/sec. 'Fig. 5 shows the directivity functions for the selectedbest fit model. The rupture velocity is estimated to be3.1 km/sec. We have also tried to match the observed ,directivity functions with the theoretical ones which Iwere calculated for different seismic somce models con- :sidered (Ben-Menahem and Toksiiz, 1962). These are lil Ithe exponentially decaying source, and (ii) the bidirec- jtional faulting. The theoretical directivity functions ,obtained for these two seismic source models do not !match satisfactorily with the observed ones. The objer- 'ved directivity function gives a better fit with the 'unilateral horizontal fault movement source model with ,1

MAY 30, 1935and error methods of comparing the observed sourcrtime function with the- synthesized ones. The saurcttime function, which fits the observed data here satisfactorily, is written as:.Ja2G (t) = H (t) € log,, ( 1 + - ) 1t2Here H (t) is the Heaviside unit step function anda is a constant. These results are shown in Fig. 6.a-- THEORE TICAL" 0-dl 2 0.3 0 0 0 Gb? 0-;El- Frequency, Hz -Fig. 6. The observed phase spectra of the source time functionand the reconstructed source" time of the Quettaearthquake.Seismic moment and onbev soslrce parameters:Seismic moment is a measure of the size of an earth.quake source, We have determined it 'using the relationof Udias and Arroyo (1970). For the cddation ofseismic moment, the spectral amplitudes which weredetermined earlier, have been used. We have correctedfor the fmiteness effect of the source by dividing by thefactor Sin X/X,.. .where >Fig- 5.SCO (G2/G3)-3 2 KM/SECObserved and theoretical values of directivity funetions determined at different frequencies for theQuetta earthquake.a constant rupture velocity. Therefore, uailaterd faultpropagation with a constant rupture propgation isinferred for Quetta earthquake.Source time function is obtained using the initialphase of R2 waves. The initial phases of a seismicsource are the phases of Fourier transform of its sotimefunctions. For the synthesis of source time function,several trigonometrical and exponential functions, havebeen considered. The best fit is obtained by the trialThe seismic moment values are fisted in Table 3. Faultarea, A, is determined from magnitude using the relation(Chinnery , 1969) :log A (Sq km) = 0.60 m - 1.31,-.."... ...-- ."*After getting the fault length and fault area, we estimatethe fault width, W, for a rectangular fault model. Theaverage dislocation across the fault plane is estimatedu"sing the relation:wherep = shear modulus (=3x1O1? dyne/cm2)147

TABLE 3. Seismic Moment Estimates for the Quetta earthquake of May 30, 1935.Station Distance Rayleigh Wave Love Wave Average(degree) M M MOdyne-cm) (1028 dyne-cm) O dyne-cm)110 sec 80 sec 65 sec 110 sec 80 sec 65 sec-COP 45.9 4.87 3 -08 1.32 2.76 2.15 2.76 2 -82SCO 61.7 3 -53 1.67 1.32 4.71 1.20 4.72 2.86IVI 75.1 1.57 0.38 0.22 0.59 0.35 0.51 0.60WEL 122.1 0.75 0.19 0.29 1.26 0 -84 0.93 0.71The stress drop, a~; strain energy, E, and straindrop, x; are estimated using the following relations(Eshelby, 1957) :TABLE 4. Estimates of Seismic Source ParametersParameters May 30, 1935x Aa=-EtHere, r = (:)*7and n =--x12Fault length, kmFault width, kmFault area, krn2Rupture velocity, km/secStrain energy, ergs1.65 x lo25Seismic moment, dyne - cm 1.75 x 1028Displacement, metersStress drop, barsApparent stress, bars 283The apparent stress is a measure of the stressesacting in the focal region of the earthquake and is esti- Straitl drop 18.9 xmated by the following relation (Aki, 1966; Brune,1968) : Magnitude, M (Richter, 1958) 7.6Azimuth of strikeDip of Fau1.tSlip angle 124"All these seismic source parametets are listed in Focal depth, km 20Table 4.*. " .a2Source time function, G (t) H(t) { log lo (1 +-) 1t2

The earthquake of May 30, 1935 occurred nearthe Quetta syntaxis. Body and sudace waves studiesindicate thrust faulting along a plane with strikeN 33"E, dip 68"NW and slip angle 124". Isoseismalsof maximum intensity X are aligned in the NNL direction.Chandra (1978) has determined the focal mechanismsolutions for earthquakes near the Quetta region.He has obtained left-lateral strike slip faulting alongthe N-S striking nodal plane for one earthquake, whichoccurred east of Quetta. The focal mechanism solutionsfor earthquakes occurring near the southern part ofthe Sulairnan range, where the structural trend curvestowards the west, shows thrust faulting along eastwestor north-east striking nodal planes. The trend ofthe pressure axis in these mechanism solutions isslightly west of north. Near 30•‹N latitude, the trendof Sulaiman ranges curve around toward west in afestoon-like structure. The focal mechanism solutionsdetermined by Chandra (1980) show predominantlystrike slip faulting in this region. These solutions indicateright lateral movement along west to north-weststriking nodal planes, or left lateral motion alongnorth to north-east striking nodal planes. The seismicitytrend in the epicentral region of these earthquakesfavours a west to north-west striking fault plane (Quittmeyeret al., 1979). Close to the epicentre of 1935earthquake, the Jurassic rocks are overlying the Cretaceousformations and the entire formations are dippingto the north-west side. There are several thrust faultspresent in the region (Fig. 1) where the rocks on thenorthwest side of the fault have been thrusted over therccks on the south-east side (West, 1936).The mountains of Baluchistan consist of simplefolds with axes parallel to the alignment of themountain ranges. In general, the anticlines form theridges and the synclines form the valleys. These foldshave been formed due to relative movements betweenCentral Asia and the Indian subcontinent. The northsouthtrend of the Baluchistan arc is interrupted by asharp re-entrant angle in the neighbourhood of Quetta.At the southern end of Sulaiman range, the mountainsswing sharply towards the west with an east-westtrend and near Quetta, there is again a sharp bendtowards the south (Fig. 1). The north-south trend isresumed along the Kirthar mountains (West, 193 6).The structure of the area consists of a complex patternof fold and thrust with axes changing from eastwestto north-south.The value of stress drop associated with the 1935Quetta earthquake is larger than those reported forcther earthquakes of similar magnitude (Abe, 1972 ;Ben-Menahem, 1977). The high value of stress dropand apparent stress associated with this earthquakesuggests that a major part of the stresses accumulatedbefore the occurrence of this earthquake, have beenreleased though the main shock (Kanamori, 1972).This implies the presence of high tectonic stresses in'the epicentral region of this earthquake. The Quettaregion is seismically quite active.As pointed out by Ben-Menahem and Toksoz(1962), the initial phase at the source consists of twoparts: (i) the phase which is due to strain-release timefunction at a point on the fault, and (ii) the phaseretardation due to fiteness and the motion of thesource. The initial phase for the 1935 earthquake isnot varying much with frequency. This implies thatthe above mentioned two contributions of phases areeither cancelling each other or are constant alongthe entire frequency spectrum. Similar results wereobtained in the case of Alaska earthquake of July 10,1958 (Brune, 1961) and Chillean earthquake of May22, 1960 (Bme et al., 1961), which show a constantinitial phase for the entire period range of 210 to 550sec investigated.CONCLUSIONSThe focal mechanism solution for earthquakesoccurring in the nearby regions of Quetta syntaxisshows strike slip faulting in general. The faultplane solution for the Quetta earthquake of May 30,1935 determined while using the body and surfacewaves spectral data, shows thrust faulting along a planehaving strike N 33"E, dip 68'NW, slip angle 124'and a focal depth of 20 krn. This earthquake is characterizedby high stress drop and apparent stress; indicatingthat high tectonic stresses are prevailing in theepicentral region.Acknowledge?lzents: The authors are grateful to Dr. S.Balakrishna, Director National Geophysical Research Institute,Hyderabad, India for according permission to publish thiswork. 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