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JOURNAL OF PHYSICS OF THE EARTH, Vol. Source 1. Process of Deep from Intermediate-depth and 19, No. Intermediate 1 1, 1971 Earthquakes as Inferred Long-Period P and S Waveforms Earthquakes in the Southwest Pacific Region By Takeshi Disaster Prevention MIKUMO Research Institute, Kyoto University Abstract The source process of four intermediate earthquakes with magnitudes of 6.0-6.8 and focal depths between 100 and 200km has been re-investigated from the analysis of long-period P and S waveforms. The source process times recovered from the times of the first half cycle of recorded P waves or the group delay times derived from the slopes of equalized phase spectrum show an azimuthal dependence with respect to the orientation of a nodal plane and of the null vector. If we assume shear dislocation models for these earthquakes, the dependence yields a solution to the problem of which of two nodal planes corresponds to the slip plane. Various source parameters have also been estimated from the azimuthal dependence by least squares technique. The dimension of the slip plane or the fault length and width range in 25-40km and 8-18 km, respectively, and the rise time of dislocation is found to be about 1sec. The rupture velocity might be as low as 3.2km/sec, if two-dimensional propagation is assumed. The theoretical seismograms of both direct P and S waves appropriate to each recording station have been synthesized on the basis of the estimated source parameters, taking into account the combined effects of wave propagation in the mantle and the crust and of the seismograph response. A good agreement of general features between the observed and synthesized waveforms on the three component seismograms gives support to the above slip dislocation model. Comparison of the amplitudes on the both kinds of seismograms yields of seismic exceed also §1. moment 80-140cm. 170 estimated The bars for in of the stress drop one shock. relation to order at of The the 1.6-3.0×1026 these effective frictional stress Introduction quakes, but also of deep-focus and intermediate-depth earthquakes that occurred between 100 and 600km (TENG and BEN-MENAHEM, 1965; BOLLINGER, 1968; BERCKHEMER and JACOB, 1968; MIKUMO, 1969; FUKAO, 1970). It is expected that if the source of all these earthquakes can be interpreted in terms of shear dislocations, the stress-strain drop at the source, shear stresses causing these earth their variations with depth and that the strength will and and ranges initial Recent seismic observations covering a low frequency range and the introduction of elastic dislocation models have provided a powerful approach to clarify the dynamical process at the source not only of large shallow earth- quakes, and be estimated, dyne・cm earthquakes on stress the slip the from to 50 produce amount of to 90 shear dislocation bars but dislocations might is plane. thermal state of material in the mantle and their implications to the tectonic structure of a deep seismic zone, such as descending slabs of the lithosphere (ISACKS et al., 1968; MCKENZIE, 1969), and the cause of deep and intermediate earthquakes might be brought into the light. It appears that there still remain unsolved problems on the observational side in an application of shear dislocation models to deep earthquakes. The problems are; whether the source is a moving dislocation, or at what velocity dislocations spread out over a slip plane formed in the mantle with increased temperature and pressure; and whether the radiation pattern of S waves including the absolute amplitudes and waveforms can be Takeshi 2 explained by a dislocation source with the same parameters as for P waves. The purpose of the present paper is to elucidate more clearly the source process of intermediate-depth earthquakes, by making direct approach to the problems. The first step is to make an attempt to estimate the source parameters including the dimension, the amount of dislocation and the rupture velocity, from azimuthal variations of recorded P waveforms. The second approach is to synthesize theoretical seismograms of both P and S waves from dislocation sources with the estimated parameters, taking into account the combined effects of wave pro- MIKUMO meters through a linear filter system com- posed of the earth and instrument, and compared with the corresponding records. The comparison has shown that the average waveform on the records is similar to that from a double-couple point source with a ramp function time dependence with τ<3sec, and yielded the seismic moment and probable ranges for some other parameters. Closer examinations reveal, however, some difference in the recorded P waveforms for the first half-period as well as in the slope of the equalized phase spectrum (MIKUMO 1969), depending on the location of recording stations with respect to the source. For this reason, an attempt is made here to evaluate the pospagation in the earth and a recording instrument, and to compare them with their obsible azimuthal dependence of the above two served waveforms on the three-component quantities. Although the waveforms are records, in order to test the appropriateness predominantly controlled by the seismoof the assumed model. The stress drop at graph characteristics, we assume that there the time of these earthquakes and the initial are no serious differences in its frequency stress to produce shear dislocations are disresponse among the stations. This assumption cussed in some detail. may be justified by the fact that the shape of calibration pulses placed on seismograms §2. Data is almost identical at these stations. The earthquakes analyzed here are four (1) The slope of the phase spectrum (or the intermediate shocks that occurred along island group delay time) arcs from New Guinea to the Fuji Islands The equalized source phase spectrum of at depths between 100 and 200km, which direct P waves has been given in Fig. 19 in have been treated in a previous paper (MIKUMO, the previous paper, for all stations in the four earthquakes mentioned. It can be seen 1969). Relevant information is again listed in Table 1. Data used are the long-period that there are appreciable differences in the slope of the spectrum, and a possibility has vertical and two horizontal component seismobeen suggested that the source dimension grams recorded at the WWSSN stations. could in principle be evaluated from the slopes §3. Analysis if the initial phase correction is made for a In the previous study (MIKUMO, 1969), theospherical earth. The correction gives a conretical seismograms of direct P waves have stant term independent on frequency on the been synthesized from moving dislocation standpoint of normal modes (BRUNE, 1964; models with variously assumed source paraSATO, 1969), and hence yields no effects on the Table 1. Information of the earthquakes analyzed. Source slope of source the phase phase faulting spectrum. φ(ω) may Process be in The the written of Deep case and Intermediate (2) unilateral 1969), The τ/2+ω(TL+TW) left-hand and L and slip W are plane, wave the the null phase is group station following ad to slip the to source and the The the the the group azimuth parameters relevant or slope the be determined that evaluated times There of of slip part at from L/υp, W/υp directly from than three more range direction in large be the might in the Crustal to with delay phase be the are station (the first half-periods, spectra and source linear a earthquakes, for; not slopes the 0.15c/s. dependence to The are over and azimuth accounted 15) determined 0.01 some the structures each times scattering. be (earthquake No. between plots rather Figs. 1(a) (earthquake equalized appears the of 1(b) group the of Group delay times, observed (b) No. 23 and frequency for (a) No. 15 upper plotted to delay form, Fig. 1. the from αj and direction respectively. or of be delay 23) No. compressional velocity, the related dislocation, width cosines of to spectrum dφ/4ω then the rupture either vector, of ad υ are and direction relative time length υp and ray the the velocity αk are constant may can (2) indicates stations. In time Eq. τ±L/υ the (1) τ is the side observations. and where 3 corrected of (MIKUMO, φ(ω)=φU(ω)+φS(ω)=ω Earthquakes possible but reason i) The always have process times. with for this assumed appropriate been cor- 4 Takeshi MIKUMO rected for a standard structure of HASKELL (1960).). A difference of 10km in the crustal thickness yields the change of about 1.5sec in the group delay time. ii) The corrected phase spectra do not change monotonously with frequency; and iii) The initial time of digitization might not exactly agree with the arrival time of first P waves when they have a blunt beginning. It would therefore be rather difficult to rely on the group delay times in a precision determination of the source parameters. (b) Source process time Another method is to infer from observed records the apparent time duration of energy release at the source region or the total time of faulting process, which is specified by the source finiteness and the rise time of dislocation. The displacement of P waves ur0(t) at great distances from dislocation sources may be expressed by (MIKUMO, 1969), (3) Fig. 2. Relation between the source process times. first half-periods and The width of the base of the pulse, hereafter termed as the source process time T0, is specified by, (4) (8) where As the a the (5) next time lower times t (7) It is clear the from eqs. deconvolved SW(t) is of a rectangular τ, 2TL convolved form and pulse s(t), so tically that shown that each of with a the such lower a is having time part a as of but schema- to 2. Figs. been 1 (a) solid parallel and half-cycle read circles. alignments on each We 1 (b), of directly at T0 in records.In P the vertical station, notice between t the waves, that and are there dφ/dω, and hence this shows that t can be used as a measure of T0. It is now necessary to find a relationshipbetween t and T0. The procedure emloyed here is similarto that used by BOLMNGER (1968,1970).An empiricalrelation is establishedhere on a number of hypotheticalseismograms, which have been constructedby the convolutionof ur0(t)for variouslyassumed values of T0 with the impulse response h(t) of the earth-instrument quely with Fig. by system. STAUDER, of Δu(t) form a interval and convolution has in width s(t) at the (HIRASAWA this the and SW(t), specified is and respectively. of SL(t) (TL+TW) 1965). ur0(t) (7) pulse 2TW of trapezoid 0〓t〓2 (5) and functions, Δu(t), SL(t), of determine observed seismograms plotted are shall the first have component (6) we from half of which step, domain been Since the form of ur0(t)is not uni- specified depends τ, 2TL made only also and on 2TW, for by the the so various total partition that time of of the computations combinations T0 time have of the Source three parameters Fig. 2 shows station HKC No. 15), an average ble attenuation this each kind the of station, hatched for an relation the above in of in part input has be 2. with conventional of T0. to Table crust, and indicates example for earthquake T/Q=1.5 the and ranges. relation single-layered constants of t of Deep probable of a standard The range their example (Δ〓40°, Φ=314° with instrumental system. within an Process a possiAlthough derived may Source for be ap- process Intermediate Earthquakes 5 plied,as a first approximation,to most of the stations, to recover T0 from t since differences in crustalstructuresand attenuationsdo not yield significantdiscrepanciesin the waveform. Two broken linesB-B and B-S show the relationsderived by BOLLINGER (1970)for an incidentbox-car pulseand half-cosinepulse respectively.However, his relations,do not include the effectsof attenuationsand of the partitionof the total time duration,and are times and direction cosines 6 Takeshi MIKUMO Fig. 3. Source processtimes plottedagainstthe directionsof one nodal planeand of the null vector. (a)No. 12 (b)No. 15 (c)No.6 (d) No. 23 Source Process of Deep and Intermediate not used here. The open circles plotted in the lower part of Figs. 1(a) and 1(b) are the source process times T0 thus estimated from t on the indivisual records. It can be seen that the plotted points show a good consistency with 24φ/dω the with above less scattering. stated reasons, For we this use the and tern of P wave first motions. The next step is to evaluate source parameters do know not gation assume and process times obtained from this time domain analysis, rather than the group delay times from the frequency domain analysis to evaluate the source parameters. the the sionally in at Estimation The a source number are of Source Fig. 4(a). stood as process of stations tabulated to and to the the of surement the between t It zero to sec, and is as 2-3 in local sec only uncertainty, the from a muthal been mine sponds for to each the of Figs. to the the plane is the plane nodal can less the It there T0 as along the linear υk are defined the by the j- source rupture υj=υ/sinφ and dimen- apparent and k-directions, υk=υ/ either of result also null vector. some found can as shown are some linear of Eq. to (9) different be seen between direction of (α1 or α2) the T0 We the and con- nodal directions on radiation 2) In T0∼ slope or moving the υj,k>υp; for the slope should in positive αj,k<1, being this αj,k=υp/υj,k. pat- either positive and In as negative as case be positive positive for direction. with be symmetric intercept be should the stations stations or could opposite for The there to k-axis, to and the null αj,k diagram, moves of but of ∂T0/∂ αj,k rupture the j- direction 3(a)∼3(d).1) υp/υj,k<1, 1), case that of Figs. the slip orientation indicates in υj,k<υp, rupture the the types if the between to does negative vector. the other corre- been direction corresponds the deter- has relevant from which three to that slip azi- planes scatter two inferred are dimen- the directions dependence The Lk υj and the dependence table, nodal two the plane. a 6 possible above and in 0.5- than earthquakes, the rewritten estimated to (α3) to the be almost The considerable of including slip from of T0. that the plane. Fig. 4(a). Geometry for an assumed rupture process. plane. planes from of source two four with direction clude slip the either cosφ, respect the the 3(a)•`3(d), relations and in of be slip interpretation the of given which velocities, rela- order variations with the attenuations the examine tested directions mea- propagation. now rupture along differences in asymmetric dependence has T0 large rupture shall to reaches To take and the Since of we the of may private form, and sions, in been and difference rather and We in 1969). azimuthally sion has structures above the where Lj planes due sometimes average (MIKUMO, crustal of T0 ranges and the make that that 4sec although is which sides (8) 1964; FUKAO, (9) The allowance T0 found about nodal times to eq. under- with respectively. process and case, general be velocities shorter a illustrated (OTSUKA, 1965; in we two-dimenas may different also propa- the azimuth two this travels STAUDER, and We reason, starts from velocity ƒÒ 1970) and this faulting with more with station to In at earthquakes together vector errors 1.0sec. the estimated four 2, normals null uncertainty tion of thus the Table cosines respect for in direction times it unknown υ. rupture assumption communication, longer of bidirectional and of For rupture front four τ and direction This HIRASAWA Parameters W, a constant propagates §4. L, at this stage. here that the point source 7 Earthquakes αj,k< negative with to time values. as υp/υj,k< the can axis of take Takeshi 8 Taking and into tions, we where the jdirection and δT0 From and and shows be the one the slip its width Lk) is of an plane ranges W about 1/2•`1/4 12. the a for earthquake results longer direction Nos. 6 and No. 12, the two the the null 23. In dimension 42 in 15, vector for case has slip it and order of plane in the of earthquake order directions. dimensions Fig. 4(b). were Relation between determined, the apparent the in is and 1970) is for other ranges of the suppose two the rupture is L case (B) the Fig. 4(b) υL,W in velocity the shorter shows the respectively, earthquake of two three slip No. cannot least squares. from It probable ts. in Here case the (A), longer plane(φ=π/2, υw=∞); is direction the 15. uniquely the along rupture cases recorded estimated earthquakes cases: propagated the the The parameters extreme (1969; comparison to estimate two we the has paper of we by however, estimated which earthquake hand, τ and υ possible, in for 140cm be from waves. least computed DLW, previous 70•`100cm the also or amplitudes P reaches On can the double synthesized amount rupture D linear The moment Corrections, the along earthquakes a comparable also direction direction does seismic determine while Lj slip See of earthquake the the but the the for that Lk) km, determined by earthquake. dislocation been and the of being except dimension of to of the value (the each from between L and one show No. Lj 25 20km, length, The has to length Lj amount large around length shorter the of T0. appropriate from (the 6 of two are: as rather estimated the results dimensions velocity The Lj/υ ρ, respectively, with ts=τ ±Lj/υj±Lk/υk for vector source compressional longer the the and squares taken deviation Lk/υp sta- all quantities standard assigning region. Once null situations αj,k for were estimated by source No. the the can above of and k-axes uncertainty to sign three the above, Lk the the determined slip in account re-arranging MIKUMO W relation for assumed the where two give the upper to move (φ=0, υL=∞). between four τ and earthquakes curves from one and lower bounds and the rise time of dislocation. Source Intermediate Earthquakes that come from probable errors in the adopted dimension. If all the four earthquakes occur through the dynamical process with similar the velocity time <24° constants υL,W would by the shows the lowest Case (A), a region earthquake the relation go these for the hatched and measured Plane. If and we the further does but υW cases, from the tan φ=υW/υL, shorter impose not Using we have relations of the a limitation Fig. of 5. φ slip that Fault-plane cannot (MANSINHA, exceed 1964), the their 3.2<υ<υ8〓4.5km/sec shear possible and 13°<φ The stress drop during these earthquakes has also been estimated by using the obtained source parameters. For a dip-slip displacealong (16/3π)μ)D/W long vertical ment, Δ would where side 3.3 bound are 9 respectively. ment except 1.7sec. two we in and earthquake 13°<φ<29° from If lowest region, the a estimated bounded, if τ exceeds for 1/υ2=1/υL2+1/υW2 is last values be The the estimates 3.2<υ<5.1 will No.12. similar range. τ as of 0.7<τ<1.8sec sec through take of velocity values bounded indicates rupture wave 10<υL<14km/sec. wide value <υW<5.5km/sec for and (A) and τ and region Case rather of Deep velocities, hatched curves. of 0.7<τ<1.4sec (B) take rupture fall in the above region Case and Process ) as an (AKI, fault infinitely long 1966), with while fault, Δ for strike-slip σ=(2/π)μD/W=(KNOPOFF, defined by D=(π/4)Dm an displace1958), is the σ= infinitely where average D dis- placement over the entire fault surface. Earthquake No.15 would correspond to the former case, and the latter may be applied to earthquakes Nos. 6, 12 and 23. The above equations assume, however, an infinitely long fault. It may be more appropriate to consider a circular type crack with of dislocation, Δ solutions. a finite radius σ=(7π/16)μD/a a. For (ESHELBY, this Takeshi 10 Table 1957; KEYLIS-BOROK, based on the here as The stress reach All 170bar, the the estimated in for fault-plane lower hemisphere §5. and slip four Comparison thesized in W is the have between of onto net, in the which arrows. Observed P similar 5 illustrates projected by the The reduced take Wulff of 3. been Fig. indicated Seismograms 3. 15 three Table τ and υ solutions direction other parameters shocks. of Table No. the given that the their the L in taken values. source are condition values while drop was earthquake similar earthquakes Estimated stress (a included during show uncertainties on are drop earthquakes The assumption a=√A/π) might four 1959). last 3. and and S SynWaves In the previous study, the synthesized seismograms of P waves have been compared with the vertical component records at 15 stations in each of the four earthquakes analyzed here. There remains, however, an important problem whether observed S waveforms including the absolute amplitudes could also be explained by the dislocation sources derived from P waves. It has long been recognized from observations that predominant periods of S waves are usually longer than those of P waves, but it does not always appear from theoreticalwork (HASKELL, 1964; HIRASAWA and STAUDER, 1965) that moving dislocation models could fully account for the observational results. In this section, theoretical seismograms of S waves, as well as of P waves, are synthesized on the basis MIKUMO source parameters. of the source parameters estimated in the preceding section, taking into account the effects of attenuation, and compared with their recorded waveforms on the three components. The general solutions for the displacement of P and S waves from moving dislocation sources have been given by MARUYAMA (1963), HASKELL (1964),and BURRIDGE and KNOPOFF (1964), and treated in detail for the far field solutions by HIRASAWA and STAUDER (1965) and SAVAGE (1965). It is more convenient for practical purposes here to write the solutions referring to the geographical coordinate at the source. The m-component of the displacement of P and S waves in an infinitehomogeneous medium may be written as, from their solutions, (10) where the suffixes p and s denotes the quantitiesfor P and S waves.The 1- and 2-axes are taken to be perpendicular to the slipplane and parallel to the slipdirection respectively. Using the notations in the previous study (MIKUMO, 1969), (11) where SD(ω)=S1(ω)・S2(ω) and UD(ω)=U(ω)/D. Source Here we nate with X=sinΘ introduce the origin at ・sinΦ, Φ are measured from the from ponents, and 2-, and be (uX, uY, uZ) the 3-axes, Then we geographical coordi- the center of ・cosΦ, the Let the and cosines to the (lm, mm, nm), 11 (14) clockwise comof new Earthquakes (Θ and displacement direction and Intermediate source: Z=cosΘ zenith the relative and of Deep the Y=sinΘ north). Process the where 1-, coordinate respectively. have (5) (12) cp, cSV, the and CSH source relevant The displacements ponents, and SH which waves, for the corresponds (γ, Θ, Φ)-comto those of P, case SV are (13) where in the these components are taken positive directions away from the origin, away M0 as downwards tively. we for Putting θ<π/2, eqs. and (10) clockwise, and (12) respecinto (13), since have been cSV Fig, 6. the of and cSH together seismic (b) No. 15 by of those the in the (MIKUMO, source the from orientation moment from P waves. Figs. of for the first three their Nos. 12 6(a) kinds nodal and nodal the motion P, SV and eqs.(14) of two determined with of evaluated Nodal curves of P, SV and SH waves, (a) No. 12 to source distribution be distribution earthquakes obtain, equal location M0=μDLW. can (15), the is specified the point amplitude, waves pattern constants and double-couple defined The the and station, of 1962). SH are mechanism and and planes first motion 6(b) shows sings of cp, of body waves, curves, in, 15, according two to the Takeshi 12 MIKUMO for the sake of comparison. C(ω) has method of KEYLIS-BOROK (1957). SV waves model emitted downward from the source changes also been computed for the vertical and horicomponents of P and SV waves and the sign during propagation to the station. zontal (HASKELL, This effectis included in the above figures. for SH waves by the matrix method structure approThe above figuresWill be useful forthe syn- 1960, 1962), for the layered thesisof the three components. priate to each station and for the pertinent angle. when the structure is not The body waves radiated from the source incident are sufferedfrom the effectsof propagation known, the unilayered model of HASKELL has to the stations. through the mantle and crust and of the been applied seismograph. The waveforms that would be Now we have the synthesized seismograms components of recorded on seismograms at the earth'ssur- of the Vertical and horizontal face should be derivedfrom the superposition P)and SV waves fPu(t), fPw(t), fSVu(t) and of normal modes in a gravitatingspherical fSVw(t), and of SH waves, fSH(t), through eq. earth (forexample, SATO et al.,1967;USAMI (16). Fig. 7 shows the observed(full line) (broken line) waveforms on et al.,1968). It has been shown (SATO, 1969), and synthesized seismograms for five however, that for direct body waves with the Vertical component periods probably up to about 40sec, the divergence effectfor a limited but ratherwide range of epicentraldistancesmay be approximated With errors less than 5% by the geometrical spreading expected from the ray theory. For this reason,the waveforms may be expressed, to a good approximation, by (MIKUMO, 1969) (16) where and Hp,8(ω)=Pp,8(ω)・Cp,8(ω)・I(ω) P(ω), C(ω), transfer I(ω) mental and respectively. for by spreading models, waves. mainly and For to a Q as KURITA by a constant rate to a Qα/Qβ=9/4 SON relation et al. (1968) (1965), S by of 4/9 and response, waves product profile in the geo- from and the probable case of direct effect, we refer 11) reducing of the suggested to MIKUMO Q at all depths also has of attenuation (Model and mantle instru- system the attenuation model the direct Velocity dissipative are response, total here Jeffreys-Bullen P the P(ω) computed metrical H(ω) crustal response been and function, Values according by their ANDERMM8-Qβ Fig. 7. Observed and syntllesizedseismograms of earthquake No. 23. (vertical component of P and SV waves) Source Process of Deep and Intermediate Earthquakes Fig. 8. Observed and synthesized seismograms (three components of P and S waves) (a) earthquake No. 12. 13 Takeshi 14 Fig. 8. Observed (b) earthquake and synthesized No. 15. MIKUMO seismograms (three components of P and S waves) Source Process of Deep and Intermediate selected stationsin earthquake No. 23. It appears that general features of the waveforms are in good agreement between the two kinds of seismograms. The S waves recorded at MUN and SPA show rather shorterperiods than those predicted. If the short-period oscillations are removed by a proper filtering, the agreement would be much improved. It is more appropriate to make such a comparison on the three component seismograms, since a different kind of information is involved in the horizontal records, particularly of S waves. It is, however, usually difficult to see well-isolated direct S waves on all of the three components at many stations. This is because they are often contaminated by preceding motion of P wave group and later phases such as sS and ScS over a wide range of epicentral distances, and partly because SV waves are sometimes distorted by the crust due to large incident angles. For this reason, the comparison can be made only for a limited number of stations, whereas FUKAO (1970) estimated the fault parameters directly from S waveforms at many stations. Two horizontal components fN(t) and fE(t) on the synthesized seismograms are derived by the rotation of axis, Earthquakes waveforms. An introduction model did instead of make much not amplitudes. It trary assumption tical S-wave than the able is reconcile most the S-wave are sensitive plane the Fig. 5 tudes said that waveforms of amplitudes, 8(a)and and 8(b) depict synthesized stations the of for both line P waves, higher and by longer be seen between tical predictions that the there for most line) may and four 15. All to and the of P observed for the the concluded mainly mantle and times due fault from the the observed S absolute amplitudes dislocation §6. to length and sources above com- waveforms ingive support inferred from P Discussion a this P paper, parameters models. There for deep-focus due agree- 1963; DENNIS theore- 1966; EVISON, and S we source changes is general of be that the the In at 1,500. observations of the process S those width. component normalized of source effects with in the synthesized than accounted attenuations their Figs. waves 12 been magnification ment S be may synthesized Also, the agree may ampliit including longer generally This Although the troughs, and of located (Compare agreement. apparently and are in waves, fault waves. azimuth (full three Nos. have seismograph back epicenter. recorded earthquakes seismograms It may the broken seismograms the to S the 6(b)). or in good periods are and that stations waves recorded P and are predominant waves stations peaks the be two of SV 6(a) that waves However, the the of great SH would some differences specific the and accuracy Figs. also for SV at 15. from possibility discrepancy. since NS- No. from a for plane the comes deviating is also to the nodal are in earthquake amplitudes with there to φ is in larger appreci- in earthquake explanations solutions, near arbi- theore- An discrepancy the acceptable parison cluding station the wave an the however, attenuations could It where COL There combined from at S that makes at BAG incidence partly measured lies, path. different found the significantly waves that here in amplitudes. S and wave circle be also amplitude likely the by respectively, was MM8-Qβ model assumed of Qα=Qβ of 12 It of Qβ difference discrepancy periods. (17) the recorded component No. 15 extentional have for are estimated shear alternative earthquakes, to and transitions WALKER, 1967) dislocation) hypotheses such phase and 1965; tensile models various dislocation as volume (BENIOFF, RANDALL, fracture (SAVAGR, (or 1965; 16 Takeshi MIKUMO BURRIDGE, 1968). It appears, however, that infinite distance could move at a uniform azimuthal dependence of the source process supersonic velocity on a slip or fault plane, with increastimes as well as the radiationpatternsof the if the frictional stress decreases double-coupletype, which were found here, ing displacement velocity across the slip favor the shear dislocationmodels for the plane. four earthquakes analyzed. This does not If we assume bilateral faulting, the total necessarilymean that the source process of process time is the superposition of the width all deep earthquakes can be relatedto shear of two pulses from two unilateral faulting in dislocations.More deep earthquakes in dif- opposite directions. Since a predominant ferent regions need be analyzed to testthe portion with large amplitude usually lies in validityof this model. the first-arrived pulse, the synthesized waveWe have so far assumed bidirectional type form is between those from the two uni(MIKUMO, 1969). It would be of faulting rather than pure unilateraland lateral faulting to discriminate bilateral bilateral,since it may be more realisticto difficult, therefore, from unilateral one on the azimuthal considerthat faultingwould initiate near the faulting of the source process times. center of the stressed region (SAVAGE, 1966) dependence The concept of bidirectional faulting has and proceed rapidlyon the faultsurfacealong been introduced by FUKAO (private communiand across the slip directions,in view of a analysis of a number of evidence that aftershocksof large cation, 1970) in the time domain deep-focus shock in South America. shallow earthquakes occur frequentlyin an multiple It has been demonstrated that this type of area with the main shock at the edge. could account for our results, partiIf we suppose that unilateralfaultingpro- faulting velocity. It appears pagates along the longeraxis of the slipplane cularly for the rupture has propagated at veloci(Case (A)),it would follow that the rupture that the rupture ties between 3.2 and a shear velocity of 4.5 velocitytakes unusuallyhigh values. FUKAO km/sec in the present case, as has been sug(1970)also obtained an extremely high rupby a theoretical work (MANSINHA, ture velocityfor a deep-focus earthquake of gested a number of observations. Banda Sea from the analysisof S waveforms. 1964) and from propagating direction makes a small In these cases,we would have to take the The following interpretations. One would be angle to the shorter axis of the fault plane. are correct, earthsimultaneous faulting; the source process If these interpretations will be such that body waves-are radiated quakes Nos. 6 and 23 with predominant would be approximated almost simultaneously over the entirefault strike slip component while earthquake No. surface within the rise time of dislocation by edge dislocations, 12 having strike-slip with a fraction of dip(FUKAO, 1970). The source process time in earthquake No. 15 characthis case is interpretedas the time difference slip component, and terized by thrust faulting could be associated between the arrivaltime of body waves from with screw dislocations. the nearest point on the faultsurface at the initiationof the rupture process and that We shall next estimate the effective stress slip dislocations from the farthest point at the termination at the initial state to produce sections. (FUKAO, 1970). Another interpretation would from the results in the preceding (1960) has stated that during the be supersonic dislocations, in which the rup- OROWAN ture velocity exceeds elasticwave veloci- fault rupture a frictional stress σf acts and the initial ties. The possibilityhas been suggestedby to resist the fault slippage, ESHELBY (1956)for a part of screw dislocation shear stress σa decreases to σf when the slipon a slipplane in crystals,and by WEERTMAN page will. cease. Since, in this case, an of the energy σfDA will be lost as (1969) for slippage for earthquake faults. amount WEERTMAN (1969)has proved that both screw frictional heating, while an energy 1/2 (σadislocationsand edge dislocationsover an σf)DA will go into the generation of seismic Source waves, the is the stress average 1970). deduced stresses observations, from stress. (AKI, of the leased stress where energy ησmeans stress. E8 and energy release and it follows The have is drop stress to The BRUNE, sphere δ (aver- The σ2), the re- stress of on age stress and of the and deep-focus 1968; 270 with lower were other bars the while at Tonga-Kermadec such apparent it may sider that effective the intermediate than mantle. depths those at These and (1970) stated, the and be not crust high BRUNE, inter150km that in stress. initial the From to shear be and stresses con- stress appreciably the of σf, at a this tional stress tions that is from is the to be should more deep need be analyzed. occur with time derived the regarded slip plane 1969), for be intermediate The the about four 30∼120 relation. above as and fric- dislocations. to that high material dynamic σ1-σf estimated and a the of stress the of BAKER, decrease the relatemperature on and above and 1969). would melting state noted be be litho- (MCKENZIE, stress probably GRIGGS would at could of the increasing partial initial that slabs zones depths 1960: hence It stresses well-lubricated (OROWAN; it esti- temperature-pressure likely produce associated although MCKENZIE's frictional the intermediate or the seismic to It is reach descending low be mater-al, only interpretatentative, earthquakes Acknowledgments I have benefited from stimulate discussions with Drs. Yoshio Fukao and Katsuyuki Abe of the Earthquake Research Institute, and Mr. Kazuo Oike at our Institute. I wish to thank Dr. Michio Otsuka of Kumamoto University for valuable suggestions at an early stage of this study. My thanks are also extended to Mrs. Ritsuko Koizumi for assistance in the present work. Computations were made on a FACOM 230-60 at the Data Processing Center, Kyoto University. obtained characterized reasonable will values shallow however, depths are between for 10 45 average evidence, for (WYSS intermediate these larger those value Trench a high from aver- lies between He their apparent These WYSS mean America. earthquakes for and different shocks with earthquakes South that although 197O). order the magniBRUNE, than the four (MIKUMO, as mediate hand, 1970), that (BERCKHEMER earthquakes WYSS, 1967; of values given than similar tion. bars time as ALLEN, 1970), same the in deep relation we initial low would of for possible in stress to in earthquakes process larger FUKAO, bars are at initial appear effective relations, effective drop slightly ησ for 37 the et al.,1969). the estimates the of earthquakes, and 1968; sum dislocations. considerably methods and average the total faulting earthquakes JACOB, ours. for earthquakes and seismic of σ1, or strength 2.5kb stresses ie. E0=E8+Ef, these shear (BRUNE deep-focus the the σ/2+ησ seems shallow tudes 1968), to (BRUNE intermediate 3, the actual that energies, during estimated Table most of accumulated respectively equal produce four at mate relation energy η are Combing σ1-σf=Δ the and that σ=ησ+σf stress by average and for the further frictional is Δ σ=σ1-σ2<σ1. in strain efficiency a lower bound If we assume seismic 8 stress the not E0; σ=(σ1+σ2)/2=E0/DA=μE0/M0, wave for σ1 and final and does in- 17 values high high be and stress M0, ησ=μE8/M0, in WYss acting high with may Earthquakes both. 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