Title the 1990 Izu-Oshima, Japan, earthqu. Author(s) Fukuyama, Eiichi; Mikumo, Takeshi.

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1 Title Dynamic rupture analysis: Inversin the 1990 Izu-Oshima, Japan, earthqu Authr(s) Fukuyama, Eiichi; Mikum, Takeshi Citatin Jurnal f Gephysical Research: S Issue Date URL RightCpyright 1993 by the American Gep Type Jurnal Article Textversin publisher Kyt University

2 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. B4, PAGES , APRIL 10, 1993 Dynamic Rupture Analysis' Inversin fr the Surce Prcess f the 1990 Izu-Oshima, Japan, Earthquake (M - 6.5) EIICHI FUKUYAMA1 Labratire de Sismlgie, Institut de Physique du Glbe de Paris TAKESHI MIKUMO 2 Disaster Preventin Research Institute, Kyt University, Kyt, Japan A wavefrm inversin has been applied t strng mtin data using a dynamic shear crack mdel. We studied the 1990 Izu-Oshima earthquake (MjM A = 6.5), which has vertical strike-slip faulting with unilateral rupture prpagatin. The inversin has tw steps, a wavefrm inversin and a crack inversin, that are applied iteratively. A wavefrm inversin is used t determine the distributin f rupture starting times and slip dislcatins using the slip functins calculated by the initial crack mdel, r by previus crack inversin. A crack inversin is used t calculate dynamic crack prpagatin that explains the results f the abve inversin. In this step, we use the estimated rupture times as a lcking fracture criterin; the maximum shear stress attained befre a fault segment breaks gives a lwer bund estimate f the peak shear strength at each fault segment. Then the dynamic stress drp distributin is estimated frm the slip distributin btained frm wavefrm inversin assuming a dynamic crack mdel. Frm the results, we determine the rise time distributin and the distributin f a dimensinless stress rati $ defined as (strength excess)/(stress drp). Our analysis gives the fllwing picture f the rupture prcess f the!990 Izu-Oshima earthquake: (1) An asperity-type faulting having large slip and high stress drp was detected in the regin arund the initiatin pint f rupture. (2) Suth f the asperity zne, barrier-type faulting characterized by incherent prpagating rupture, small slip, lng rise time, and high strength excess was detected. This zne crrespnds t the intersectin f the fault with the 1978 earthquake (MjM A = 7.0). INTRODUCTION In the 1980s, a number f detailed earthquake surce mdeling studies have been made using wavefrm inversin techniques [Hartzell and Heatn, 1983; Ruff and Kanamri, 1983; Kikuchi and Fuka, 1985; Fukuyama and lrikura, 1986; Take, 1987; Berza and $pudich, 1988: Kikuchi and Kanam d, 1991]. These studies are all based n "kinematic fault mdels" and d nt invlve "dynamic faulting mechanisms." In kinematic dislcatin mdels, the frm f the slip time functin is prescribed arbitrarily by using a bx-car, a triangle, r a trapezidal shaped functin. These arbitrary assumptins d nt necessarily satisfy the stress-strain cnditins n and arund the fault. Accrdingly, it is pssible that the results btained frm wavefrm inversin based n the kinematic mdels may vilate the stress-strain cnditins and may even be physically unreasnable. T vercme these prblems, we use dynamic shear crack mdel as a basis fr the wavefrm inversin t the bserved recrds. Mikum et al. [1987] attempted t simulate the dynamic rupture prcess f a mderate size earthquake, fitting a kinematic mdel derived by wavefrm inversin by Take and Mikami [1987]. That was dne by applying a threedimensinal spntaneusly fractured shear crack mdel in a hrizntally layered structure under depth-dependent shear stress and laterally hetergeneus stress drp. Similarly, 1Permanently at Natinal Research Institute fr Earth Science and Disaster Preventin, Ibaraki, Japan. 2Nw at Centr Nacinal de Prevencin de Disastres, M6xic. Cpyright 1993 by the American Gephysical Unin. Paper number 92JB /93/92JB $ Quin [1990] als attempted t interpret the surce dynamic rupture histry f the 1979 Imperial Valley earthquake. He tried t fit the surce time functin btained frm the strng mtin recrds by Archuleta [ 1984] t a spntaneus rupture mdel calculated by a bundary integral methd [Das, 1980]. He was successful in determining the general features f the stress-strength distributin ver the fault. Miyatake [1992] presented a simpler methd than that f Quin, which cnverts the distributin f kinematic parameters n a fault int that f dynamic parameters. Hwever, since Quin and Miyatake did nt recalculate the synthetic wavefrms frm the estimated rupture parameters, it is difficult t evaluate the degree f fit f their dynamic mdel t the recrded wavefrms. The main purpse f this paper is t estimate dynamic rupture prperties f a mderate-size earthquake including the distributins f dynamic stress drp and shear strength excess frm near-field seismgrams. We take three steps: (1) calculate initial dynamic rupture f an earthquake assuming hmgeneus distributins f the stress drp and strength excess ver the fault based n the three-dimensinal dynamic crack mdel, (2) perfrm a wavefrm inversin cmbined with the dynamic crack mdeling in rder t get the slip functins as well as the stress drp-strength excess distributins, and (3) estimate the distributins f rise time and dimensinless stress rati S using the abve results. T cnfirm the validity f the abve prcedure, we als calcu- late the synthetic seismgrams at each step and cmpare them with the bserved recrds. THE 1990 Izu-OSHIMA EARTHQUAKE The earthquake we study here is the 1990 Izu-Oshima earthquake (MjMA = 6.5), that ccurred ff the east cast f

3 , 6530 FUKUYAMA AND MIKUMO: DYNAMIC RUPTURE ANALYSIS 35.2N 35.0N 1990 Izu-Oshima earthquake z 5 N 35 N --30 N velcity seismgrams at the nearest statin GJK (Figure 1). We calculate the displacement spectrum f SH waves fr all six statins. The time windw used fr this calculatin is 10 s, which is underlined in Figure 4. The btained $H Furier displacement spectrum fr GJK is shwn in Figure 5. We estimate a seismic mment M0 and a stress drp Art frm the flat level f the displacement spectrum 110 and its crner frequency fc using 4,n'p /:( )p /:(x)13 /:( )13 /:(x)r M = Fs H f (1) 34.8N' 34 GT 34.4N 138.8E J O 1990/02i20 15:53:00-16:54 ': 139.0E 139.: E 139.4E Fig. 1. Lcatins f the strng mtin statins used in this analysis. Lcatins f the main shck epicenter (slid circle) and its aftershck distributin just after the main shck ccurrence are als shwn. The symbls fr the aftershcks are classified by their magnitudes and depths (see Figure 19). [Aki and Richards, 1980], where R is the distance frm the surce t the receiver and F sh is the radiatin pattern f SH waves, x and s are the receiver and the surce lcatins, respectively, and Art = 8.5M[fc/13] 3 (2) [Hanks and Wyss, 1972]. We assume that the density p equals t 2.7 x 103 kg/m 3 fr the surce regin and 2.3 x 103 kg/m 3 fr the bservatin sites. The S wave velcity/3 has been taken as 3.5 km/s fr the surce regin and 1.7 km/s fr the bservatin sites. Table 1 shws the crner frequencies fc, flat levels f/0, mment releases M0, and stress drps/xrr, which have been estimated frm the recrds btained at the six statins. We find that the average mment release is abut 2.4 x 10 8 N m and the average stress drp is abut 1.3 MPa. Althugh these are rugh estimates, they remve a pssible bias (an average f the stress drp) fr the fllwing inversin. the Izu-Oshima island, central Japan. Althugh this is a tectnic earthquake, it seems t be related t the stress changes assciated with the surrunding vlcanic activities ( Izu-Oshima eruptin, 1989 It-Oki submarine vlcan eruptin, etc.). The fault f this earthquake is cnjugate t the fault f the 1978 earthquake (MjM A = 7.0) [Shimazaki and Smerville, 1979; Kikuchi and Sud, 1984]. Figure 1 shws the epicenter f the 1990 Izu-Oshima earthquake (slid circle) and the distributin f its aftershcks that ccurred within 1 hur after the main shck. The hypcenters f the main and aftershcks have been determined by the lcal micrseismic netwrk f the Natinal Research Institute fr Earth Science and Disaster Preven- tin (NIED). The strng mtin bservatin sites we used are als indicated. Statins GJK and ITO belng t NIED, and AJI, MIS, NGT, and OSH belng t the Japan Meterlgical Agency (JMA). The distance t the nearest statin GJK is abut 14 km. Statin GJK recrds grund velcity, while the ther statins recrd grund acceleratins. Figure 2 gives mre details f spatial distributin f aftershcks, indicating that these earthquakes were distributed ver a length f 19 km and at depths between 3 km and 17 km. Fcal mechanism slutin frm P wave first mtins is als shwn indicating left-lateral strike-slip faulting alng a nearly vertical plane. Frm the abve evidence, we assume that the fault rupture initiated at the main shck hypcenter and spread unilaterally ver a nrth-suth striking vertical fault plane, as shwn in Figure 3. We estimate an average stress drp ver the fault frm the spectra f near-field seismgrams. Figure 4 shws an example f three-cmpnent displacement wavefrms derived frm INITIAL DYNAMIC MODEL As a starting mdel fr the wavefrm inversin, we calculate the spatial and tempral patterns f spntaneus dynamic rupture prpagatin n the basis f a threedimensinal dynamic shear crack mdel [Mikum et al., 1987] with a hmgeneus strength under a unifrm shear stress. We incrprate a hrizntally layered structure shwn in Table 2, which has been btained fr this regin frm explsin seismic bservatins [Ikami, 1978; Take, 1988]. We did nt take int accunt the shallwest thin lw-velcity layer f Ikami [1978] and Take [1988] because f the discretized grid spacing f the crack calculatin. This calculatin is made by slving numerically the wave equatins fr a three-dimensinal space; using apprpriate bundary cnditins at the fault plane, at the free surface, and at each f the layer interfaces; and using an apprpriate critical stress fracture criterin [Mikum et al., 1987]. The fracture criterin we use here is apprximately equivalent t the Irwin's [ 1958] criterin. If the critical average stress ver the grid at the crack tip exceeds a certain limit (the static frictinal strength in this case) at any pint n the fault, a fault slip ccurs immediately. This yields successive slips at adjacent segments and spntaneus rupture prpagatin n the fault [e.g., Mikum et al., 1987]. The dynamic mdel thus specifies the frm f the slip time functin, the final slip, and the rupture time at each grid pint. Numerical calculatins have been perfrmed by finite differences. The dimensin f the mdel space is 200 km x 87 km x 80 km. We divide the entire fault surface int 19 x 14 elements with a grid spacing f 1 km. The time increment

4 -- FUKUYAMA AND MIKUMO.' DYNAMIC RUPTURE ANALYSIS /02/20 15:50-16:54 Fcal Mechanism 34.8N 0 ) _( 0 O u O 0km w E ß Cmp Errr = 4/73 S Dil 34.6N 0km 20km -20km Depth E 0km Magnitude Depth _ M< M< < O M<5.0 - C) 5.0 M 20km I I I I ] I I I I -10km 0km 10km Fig. 2. Fcal mechanism slutin f the 1990 Izu-Oshima earthquake n the lwer hemisphere prjectin (left). Aftershck distributin fr 1 hur just after the main shck, which has been determined by the Natinal Research Institute fr Earth Science and Disaster Preventin, Japan (center), and its east-west crss sectin (center lwer) and its nrth-suth crss sectin (fight). The lcatin f the main shck is indicated as the largest circle Izu-Oshima Earthquake 1990 Izu-Oshima Earthquake 1990/O2/20 15: i i i i i i i i I i i i i E E t GJK UD ß : i --. Q. O E < GJK EW Fig. 3. A schematic fault mdel f the 1990 Izu-Oshima earthquake. The initiatin pint f rupture is assumed t be lcated at the hypcenter f the main shck (34.744øN, øE, 7.4 km) '0... 2'0... 3'0 Time(s) Fig. 4. Three-cmpnent displacement wavefrms btained frm the bserved velcity seismgram at GJK. The time windws fr the spectrum analysis are indicated by underlining.

5 6532 FUKUYAMA AND MIKUMO.' DYNAMIC RUPTURE ANALYSIS SH Displacement Spectrum at GJK lo 5 lo 4 5, 102.,- < 101 lo Izu-Oshima earthquake 10-1,,,,, I ,,,,,,,,I,,... I Frequency (Hz) Fig. 5. Furier amplitude spectrum f the 1990 Izu-Oshima earthquake. The nrth-suth cmpnent displacement wavefrms btained at GJK is used fr this calculatin. is 0.05 s. These values satisfy the stability cnditin fr the wave equatin in the three-dimensinal space. In dynamic crack mdels, the patterns f dynamic rupture prpagatin and slip distributin are gverned by the dynamic stress drp tr 0 - tr d and the strength excess % - tr 0, where tr 0, tr s, and tr d are the initial shear stress, the static frictinal strength (r the peak shear stress), and the sliding frictinal stress, respectively. Here we assume these parameters t be 20.0, 20.25, and 18.5 MPa, respectively, which give a unifrm strength excess f 0.25 MPa and a unifrm stress drp f 1.5 MPa. The stress drp f 1.5 MPa is inferred frm the displacement spectrum f SH waves. The stress drp affects the amunt f slip. On the ther hand, the strength excess specifies the pattern f rupture prpagatin. When the strength excess is small, the rupture prpagates with a P wave velcity in the directin parallel t the applied stress and with a S wave velcity in the directin perpendicular t it [see Mikum and Miyatake, 1978; Miyatake, 1980; Mikurn et al., 1987]. When the strength excess is high enugh, the rupture has slwer initial velcities r may nt initiate at all. Figure 6 shws a perspective view f rupture prpagatin and fault slips at every time step. The slightly larger slips in the suthern sectin are due t the unilateral rupture prpagatin. A unilateral rupture causes a cncentratin f seismic energy ahead f the rupture frnt that prduce the large slip; such asymmetrical slip distributin shuld ccur even n a fault with a unifrm strength and subjected t a unifrm stress. Similar numerical calculatin shws that the final slip is symmetrically distributed when the rupture starts at the center f the fault, as expected. Figure 7 shws the distributins f the arrival time f rupture frnt and final amunt f slip n the fault fr the initial mdel. Fr this mdel, the distributins f rupture time and displacement are relatively smth. Figure 8 shws a cmparisn between the bserved wavefrms (slid lines) and the crrespnding synthetic wavefrms (dashed lines). The wavefrms have been nrmalized by the larger f the peak amplitude in bth trace. This nrmalizing factr is shwn at the upper fight f each trace in millimeters. The agreement between these tw sets f wavefrms is nt satisfactry. Ttal mment release frm the initial mdel is 4.6 x 10 8 N m. Althugh this value is abut 2 times larger than that estimated by the spectral analysis, since the peak amplitudes are almst cincides with each ther, we take this mdel as an initial ne. Frm these calculatins, we btain the slip time functins at each grid f the fault surface and use them as a starting mdel fr the fllwing inversin. TABLE 1. Mments and Stress Drps Estimated by Spectral Analysis ITERATIVE INVERSION METHOD The iterative inversin presented here cnsists f a wavefrm inversin and a crack inversin. The wavefrm inver- M0, A fc, Hz fl 0, m s x 1018 N m MPa TABLE 2. Statin GJK Depth, Vp, V$, OSH km km/s km/s ITO AJI NGT MIS Average Velcity Structure fr Dynamic Crack Mdel

6 FUKUYAMA AND MIKUMO.' DYNAMIC RUPTURE ANALYSIS 6533 T= 1 s T= 6 s T = 2 s T= 8 s T= 3 s T= 10 s T = 4 s T= 12 s T= 5 s T= 15 s Dynamic Rupture ( Starting Mdel ) Fig. 6. Displacement histry ver the fault surface calculated frm an initial dynamic rupture mdel with a hmgeneus stress drp and strength excess. sin gives us the distributin f rupture times and slip dislcatins by inverting the bserved wavefrms with a fixed frm f slip functin. The crack inversin is used t invert the kinematic parameters btained in the previus step, giving us the distributin f stress drps and strength excesses as well as the shape f the slip time functin. We repeat these tw inversins by turns until the residual between the bserved and synthetic wavefrms becmes satisfactrily small. Figure 9 shws an example f an imprvement prcess f slip functins at particular pints f the fault. Thrugh the iteratin, the shape f the surce time functin changes gradually as the fit t the data imprves. Wavefrm Inversin We calculate the Green's functins fr all cmbinatins fault segments and statins assuming the hrizntally layered structure shwn in Table 3 (same as the "velcity structure 1" f Take [1988]). The Green's functins are calculated by a discrete wavenumber methd [Buchn, 1981; Ya and Harkrider, 1983]. Dissipative effect are accunted fr by intrducing cmplex wave velcities. Examples f the Green's functins fr sme fault segments at statin NGT are shwn in Figure 10. We calculate synthetic seismgrams by cnvlving these Green's functins with the f

7 6534 FUKUYAMA AND MIKUMO.' DYNAMIC RUPTURE ANALYSIS a) Rupture Time '.'i.i':?:' : :::iiii: :. : 7 -,. :..::.'i.:;¾':':' ' '..:iii'!c"" +:':" : ¾:'!i!i!::?:: : : : : :: '",-' '":" i..:, ::. i:: ;:.::i: ::??':.;. i... ' -: :' :..-..':-"!.. :-' iiil iiii ii::i!iiii!::! :: i ::il ';: ':.:;.i;?::!.iii:. 'i:!!::?::r i ' " ' 0': "; ' -... : i! :; iii :';.-.:...-'...":!!! ß :.-¾;%.:.?: -/ /-, :.,...:...,.,.,. :. g!-..--,.-,.-.-,.,-,,:..... : :.. ============================... _ -.., -g ,....,... ß.'... :'. :::" ::: ;': ' :' ;:::::::'-: ':: :'-::: '... ', ' '"'"-"' ½<'"'" ":'. i! ' ' ":':':' '.:.:.':' ; 7-.?]i:!i'i ::::.::½: :.i:.i::i:.":: ';:'.:::. ::!:: :: :i : : i ;: ::'.:.. '""" "'"' '<½-.- ß '.. ' % Suth Fig. 7. Nrth s b) Slip Dislcatin Suth Nrth Initial parameter distributins f (a) rupture time and (b) dislcatin ver the fault. The parameters are extracted frm the slip time functins calculated frm the hmgeneus dynamic mdel C 60 rn GJK NS NGT EW / _ OSH EW ,-. NGT UD 1( GJK UD,, MIS N ITO NS 14.0 ' AJI EW 2.48 ITO EW 29 AJI UD 5.05 ' MIS UD 4.9 NGT OSH NS.2! \ 10 SECONDS I Fig. 8. A cmparisn between the bserved seismgrams (slid lines) and the synthetic wavefrms (dashed lines) calculated frm the initial mdel. Bth traces are drawn in the same scale in each windw. The numerals attached t each trace indicates the maximum amplitude in millimeters. The same explanatins apply t Figures 16 and 19. I

8 FUKUYAMA AND MIKUMO' DYNAMIC RUPTURE ANALYSIS (055)-1 (108)-1 (137) (055)-2 (108)-2 (137) (055)-3 (108)-3 (137) (055)-4 (108)-4 (137)-4 I 15 SECONDS Prgress f Surce Time Functins Fig. 9. Sme examples f slip time functins during the iterative inversin. Numerals inside the parentheses indicate the lcatin f grid that will appear in Figure 11. Numerals fllwed by a minus sign shw the iteratin steps ("1" indicates the initial mdel). (Left) The largest asperity regin, (center) the barrier regin, and (right) the secnd largest asperity regin. crrespnding slip time functins and by integrating them ver the entire fault surface. The sampling interval f synthetic seismgrams and Green's functins is s. In rder t reduce the number f parameters t be estimated in the wavefrm inversin scheme, we divide the entire fault int 25 subfaults (Figure 11), each f which includes 6 t 12 unit segments with a dimensin f 1 km x 1 km. In each subfault we assume that the deviatin f rupture time and slip dislcatin is the same. This reduces the number f parameters frm 266 x 2 t 25 x 2. T save the cmputatin time, we als assume that all segments belnging t the same subfault have the same the Green's functin. The relatin between the parameters estimated by the wavefrm inversin and thse inverted by the crack inversin is shwn in (3) and (4): TABLE 3. Velcity Structure fr Green's Functin Depth, Vp, Vs, P, km km/s km/s g/cm 3 Qp Qs t ki + 1 t ki r - L t j (3) d/k + l d/k X (1 + Adj) (4) where, tki and d/k represent the rupture time and slip at ith grid in the kth iteratin cycle, respectively. Atj and Adj are parameters f the jth subfault estimated by the wavefrm inversin. Here, i takes n values frm 1 t 266, andj is frm 1 t 25. Fr wavefrm inversin we use the methd by Fukuyama [1991a] which determines the mdel parameters by iteratively minimizing the difference between the bserved and the synthetic wavefrms. Fr the data, we use threecmpnent displacements at six near-field statins (Figure 1) which are cnverted frm the bserved velcity seismgrams r accelergrams by numerical integratin. They are then filtered in the perid range frm 20 t 0.5 s in rder t reduce the high-frequency waves which cannt be prduced by the Green's functin. We d nt use the UD cmpnent recrd at ITO due t a pr quality f the wavefrms caused by an electrical truble during the bservatin. We set the variance f data as 20.0 [ram 2] and the variances f param- eters At, and Ad are changed frm 0.01 t 0.2 [s 2] and frm t 0.1, respectively. These variances f the parameters are chsen in rder t btain the best cnvergence f inversin. Frm all seismgrams the data are extracted in

9 6536 FUKUYAMA AND MIKUMO.' DYNAMIC RUPTURE ANALYSIS O3 NS E W U O ,.._. 23 { i i lo SECONDS Fig. 10. Examples f the calculated Green's functins at NOT fr the subfaults 03, 08, 13, 18, and 23 that will appear in Figure 11. These functins have been calculated by a discrete wavenumber methd s time windws starting abut 5 s preceding the P arrivals. The data include all the near-field bdy waves. The reslutin f the estimated parameters is investigated using synthetic data btained by the final parameters [Fukuyama, 1991 b]. If all parameters are estimated crrectly, the reslutin f parameters is perfect. Otherwise, the difference between the real and simulated inversin results reflects the trade-ff between these parameters. Crack Inversin In this inversin, we estimate the distributin f dynamic stress drp and strength excess ver the fault plane that are cnsistent with the results f the wavefrm inversin. T d this, we recalculate the spntaneus dynamic rupture prcess s as t satisfy the previusly estimated kinematic fault parameters, i.e., the distributin f the fault slip and rupture time. These tw parameters have been estimated fr each f the 25 divided subfaults; befre they are inverted using crack S, 11,,, 9 H Oil Ol Ol[A l, Ol, 1 1' 18 Ol, ) ) ; 1' nan qq n u lnr Z ! I s a lja lqz lq u I lfil lfiq I 18z t vz u z go ; ? 5z ! ?la , N 247 Fig. 11. Fault segmentatin int 25 subfaults frm kmspacing grids. inversin, they are smthed ver the fault plane and spatially interplated at grid pints with a spacing f 1 km. Applying equatins (3) and (4), we btain the distributin f parameters n 266 grid pints. The first step is t fix the rupture time at each grid pint t that btained frm the wavefrm inversin. This is equivalent t intrducing a lcking fracture criterin, under which a fault element des nt break befre the specified rupture time. We assume that the rupture is lcked fr sme time depending n the fault strength lcated ahead f the advancing crack tip. The stress at the lcked segment increases frm the initial level up t the time when it fails. The peak shear strength can then be estimated frm the maximum shear stress just befre the segment breaks. This prcedure fllws that f Miyatake [1992] and is similar in a sense t that adpted by Quin [1990]. Althugh the peak strength estimated in this way depends n the grid spacing used in the numerical calculatins, it shuld be regarded as a lwer bund f the real peak strength. Fr the fixed rupture times, the final slips depend nly n the dynamic stress drp [Quin, 1990]. The secnd step is t estimate the distributin f dynamic stress drp frm the fault slip btained by the wavefrm inversin. The dynamic rupture prpagatin is determined by assigning different stress drps n each f the subfaults and by cmparing the resultant dynamic slip with the slip frm the wavefrm inversin. The initially assigned stress drps are then multiplied by rati between the tw types f the slip averaged within each f the subfaults. This prcedure is repeated until the square sum f the difference between the dynamic and kinematic slips is minimized. Since the abve prcedure invlves nnlinear effects inter-

10 a) Rupture Time Suth FUKUYAMA AND MIKUMO.' DYNAMIC RUPTURE ANALYSIS 6537 :::::':::::'.:::.: :i:?!::';:i:i:::::::::::::::::::::::::::::::::: ::::: :. :::i:::i::: i.'4...<.:?!. i :.:/.. ii ' ;..4 /... ':.-'::':.::'.½:/.." '"... =============================================================================================== 8 :: i?'"' "' '"'"' '" :...- -'-"... '"" "'* '" " '" :;!i :.'... :.. '": 120.::: :.: :::..: ::-:: : ::x:. ::d :.; z '...+. :-::'.:- ' :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::... :2::::::: _ ':'"..:.... ½ar½ '"'"'""'"'"".."' '"-"... ;ii ½ : : : *.?..r--;-:..:;... ' ; :-: -' :. : i::i!i:: ' '"'"'"' ' ' ; '..... )' '"'""'"'"'.. ½½igg:;i::½::::i?:!½-'- ;. : ;a :,...,...,......,,,,,,.:... : ½. : : :;: :!: : :;: :;: : : : : : : : : : :.,.-;:,:.: :... 6 ::::::::."'"'.---'-'. '--'...:. '...'::;! '- : <..'.<..'.:*..a::'.' :M::'. ::'":"'"'"': '......,.:..,.:;.....::.:::: :::i i:i: :.i:i!:;:i:i: :i:..v ,-".... -': 9O!:: iii i..::.- ::... ' '"'"' '"' '": iii:: i i...'.:.i ::':..-:...:...-'iii i;i:: i ::ii!iii!::ii *'"'"'"'"'"'"'"'"'"'"'" "' ::"'":---'"-'------'-'-...'...'..;.? ::. : ii:;:::::!!:...-::?.::::: ii 5... :::::::::::::::::::::::::::::::::::::::::::: Nrth b) Slip Dislcatin :.--.'i :: i::'-""-' ','-': :½ g. '.-'.-:,." j!... ½.. ';-'..-" i... ' ::.-:::: , '-.'½.:......:-' ;:: :::::::.,.: -, :...: : ::...:::::::!::::$::i...:!:i:m: :M:!. : :::: :i :: : :: :::i : :i...::: :!.....:...::!...: :!:;:i:!:i:!...:!:i : i...::::....i:i:i...:i:...:i ::::::!:-;?'''" "":::": : :½,."-d: ::':" '' :';':,- '../ i½;'.:.::::s:;.'.::.::::::-'::::::½:: :::i:i:i:i:i:i: ':,., :i: ::::::::&::i: :! :'.-:i: :!::::-'..: ::::: :::i½i.'.:: &::.:'.'i:i:i:i:i: : :.:::.: :i.'.:: ::.:i: :i:i:m::.: ::.:!: : : : & '...-.½... "'" "'"'" :.;:'..' ::i: ::::::. ::-?':i &':: $?.:': ::::i:-::i:?&': i:i.'::!::.:!:i :i :i: :i : i.':-: ii:'.:?-:::-':';::::: :-':½ ::'.::::'.'- :i :.:.'.::i :.:.'.::i:i: M:!-'.:.'.::!: :;:i::: : ;:i: : : : 30 Suth Nrth Fig. 12. Final crack inversin shixin (mdelc3-_0d, (a) rupture time, and (b) dislcatin. The results are shwn by their abslute values, which are the sum f their initial values and the deviatins btained by the wavefrm inversin C 60 rn acting between dynamic slips at adjacent fault segments, several repeated calculatins are needed t btain a best fit. The slip time functins btained here are then fed back int the subsequent wavefrm inversin in the revised mdel. RESULTS OF ITERATIVE INVERSION After fur iteratin cycles, inverting frm 5 t 20 trials f the wavefrm inversin and the crack inversin, we have reached the preferred slutin named mdel C3-01. The residual reductin is abut 40% with respect t the initial mdel. In Figure 12, we shw the distributins f final parameters ver the fault. The ttal mment release is 4.0 x frm the final dynamic rupture mdel. Several examples f the slip time functins are shwn in Figure 9. Frm these slip functins, we calculate the rise times which are defined as the time until the slip reaches 95% f the final slip. Figure 14 shws the spatial distributin f the estimated rise times. It is nticed that the rise times range frm less than 2 s (at the bttm f the fault) t mre than 10 s (at the zne suth f the hypcenter). The average rise time is abut 7 s. Figure 15 shws a cmparisn between the bserved and synthetic wavefrms calculated fr the final mdel. The agreement between the tw wavefrms has cnsiderably imprved cmpared t the initial mdel, but sme discrep N m. Taking int accunt the reslutin f parameters ancy still remains. The disagreement may be due t the during the wavefrm inversin (Figure 13), the fllwing cmplex crustal structure in the Izu regin, where the Philipfeatures can be seen: (1) The rupture prpagated incher- pine Sea plate cllides againsthe Eurasian plate and subducts ently at the initial stage, and its velcity was slw in the bth eastward and westward. Our crustal mdel des nt take regin abut 5 km suth f the nrthern fault edge. (2) The int accunt such lateral hetergeneity (Tables 2 and 3). largest slip ( cm) was bserved in a narrw regin near Figure 16 shws a time-sliced perspective view f the the initiatin pint, and the secnd largest slip (- 60 cm) at rupture prpagatin f the fault slip ver the fault plane. We the suthern part f the fault. see the incherent prpagatin f rupture and hetergeneus The slip time functin at each grid has been calculated distributin f the fault slips. The rupture initiates with large a) Rupture Time b) lip Dislcatin , :. : 9.0., 0.2,, '*,, Suth Nrth Suth Nrth Fig. 13. E r estimates fr each parameters. The methd fr the estimate fllws Fukuyama [1991b] (see text)

11 ......_.._..._ FUKUYAMA AND MIKUMO: DYNAMIC RUPTURE ANALYSIS a) Initial Mdel b) Mdel #C :: ' '?:?:?:. ::?'"'"" : :. ; :,,,, : : : : :,:-::,:,:,:,: '.::,:: :-.- -.': *.:-: ::..: 12 ::::::::::::::::::::::::::: : :r'"'""" " '"'"'"" '"' '""' '"" ' ' '"""'""' ß "'"'"' ':-'-' -'-..'-.: -.'.: --,--. --, ,...-.:... " ø ': :; :.::'.':.""'""'" '::' -....:..: ½. '-::' "+ -' ::. ":'i:i:i:i: :Ei:i:::i:i.:.... '-...-::i:-":---:-'i:':::'-:. ß... ::::':' ':' :::-..-.:-'.-'...,:½.... :.,, ':.:½. -: :i:: : --.'-,' ;;:... :.. :... :::::::.-:...': ::;::::'- /:;....:.::: ::: ß ' - -'-,-,'-' ::...:.:i: ½ ;. "...,.-:-' '.{.-'[ ":!i:. ':. :::'.. -: --',...--, '?.. ' ' '.-'.- :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: "" ` ` :` ```` `... J :':':"':'::"'"'"½ 10 S ':': "' "' '"""'!; :... -" --' ---'-' -: '"'"'"'" '" ":' :' "'"' -"-: F '" '"' " ':: :'::.i&:... ::?;::r :" : J;i-:... ::::::.::... ½ : - -'-... -" [' :.:.:?'...: '-'-"':- -.g..- i... '"'<;: : flt :-.-'. :. S :::::::::::::::::::: :-:::...;..;;:: 6 ::::::::::::::::::::::::: 4 0 $ut Nrth Suth Nrth Fig. 14. Rise time distributin f the initial mdel and the final mdel (C3-01). 0 slips, spreading slwly in the first 3 s. After this time, it prpagates nearly unilaterally suthward, taking lnger t break the deeper sectin f the fault. The majr rupture prcess lasts abut 10 s. The large slip arund the rupture initiatin zne cntinues t grw up t abut 8 s. DISTRIBUTIONS OF DYNAMIC STRESS DROP AND STRENGTH EXCESS Figure 17 shws the distributin f the dynamic stress drp and strength excess ver the fault plane. The prbable GJK N? NGT EW OSH EW K E 35. NGT UD OSH UD GJK UD '- AJI NS TM '?' ' Nt ---' : / \/, ' _, ITO NS AJI EW 2,48 MIS EW 18.$ ITO EW AJI UD 4. 2 MIS UD NGT NS OSH NS loo SECONDS -01 Fig. 15. A cmparisn between the bserved and synthetic seismgrams fr mdel C3-01. Slid lines are the bservatins and brkens are the synthetics calculated frm the final mdel f the crack inversin

12 FUKUYAMAND MIKUMO: DYNAMIC RUPTURE ANALYSIS 6539 T = 1 s T = 7 s T = 3 s T = 8 s T = 4 s T= 10 s T= 5 s T= 15 s T = 6 s T= 20 s Dynamic Rupture ( Final Mdel ) Fig. 16. Time-sliced perspective view f displacement histry and rupture prpagatin btained by the final dynamic mdel fitting. estimated errrs f these parameters in the crack inversin may be less than 3% in view f the difference between the resultant dynamic slips and fault slips btained frm the wavefrm inversin. The results are summarized as fllws: 1. The lcal dynamic stress drp exceeds 3.5 MPa in the hypcentral zne in the nrthern sectin. It reaches 1.5 MPa in shallw and deep znes in the suthern sectin f the fault. Hwever, it is generally smaller than 0.6 MPa elsewhere. Althugh there is a zne f very small stress drp lcated just suth f the hypcentral zne, n negative stress drp has been detected. 2. The strength excess is fund t be generally small except fr the periphery f the hypcentral zne where it exceeds 1.3 MPa. The high strength zne may be crrelated well t the zne f slw rupture velcity. The abslute values are quite uncertain as will be discussed later. It shuld be mentined, hwever, that the depth dependence f the stress drp and strength excess has nt been identified, and their lateral variatins are mre dminant in the present earthquake. Recent labratry experiments indicate that frictinal behavir f sliding surfaces are temperature dependent, and change frm velcity weakening t velcity strengthening abve C [e.g., Tse and Rice, 1986]. The velcity strengthening leads t negative stress drp, and it has been demnstrated theretically [Mikum, 1992] that the dynamic rupture f a large earthquake riginating in the brittle zne can extend int the semibrittle zne with negative stress drp. Quin [1990] fund a mderate amunt f negative stress drp in the depth range f km at the suthern sectin f the 1979 Imperial Valley earthquake. This culd be real and may be attributed t gethermal envirnments in

13 6540 FUKUYAMA AND MIKUMO: DYNAMIC RUPTURE ANALYSIS a) Stress Drp 5.0 ::::::::::::::::::::::::::: i:.:.: :i.::i:!:?:: b) Strength Excess : ::: i : :! ii : :..'..'.'ii :'::::.. ::..'.: ;. :.. ii!:::. :: ' X:i:!:!:!:!:i:i$ : :' '"'... :':'...:. Z X:i:!:!ii: :i:z:i:!$':-:!::':! i: :X:i::... :':':'":':':*:':':':"*:':'":-:-:':' Z...'..::i:::i:i:i ':':':' :::':::.::!i. '"'"': ',': ' ::i i-': a :::::::::::::::::::: 0.8 a Suth Nrth 0.0 Suth Nrth 0.0 Fig. 17. The distributins f estimated (a) stress drp and (b) strength excess btained by a crack inversin (mdel C3-01). the lwer crust in this regin. Hwever, this type f the negative stress drp has nt been identified in the present case. DISCUSSION The average stress ver the grid immediately utside the tip is inversely prprtinal t the square rt f the grid spacing [Aki and Richards, 1980]. The strength excess estimated here can be crrected taking int accunt the size f the breakdwn zne just ahead f the crack tip. If we assume the size f the breakdwn zne t be abut m fr a mderate-size earthquake [AM, 1992], the maximum stress wuld be times the estimated value fr the grid spacing f 1 km used in the present analysis. Althugh the abslute values f the strength excess are still quite uncertain, we may be able t discuss qualitatively a tpgraphical feature f the fault strength and dynamic stress drp ver the fault thrugh a dimensinless stress rati S, defined as the strength excess r s - r 0 divided by the stress drp r - ' d [Das and Aki, 1977]. It is nticed frm Figure 18 that there are large S znes frm shallw t deep sectins f the fault suth f the hypcentral area, while small S znes may be identified in the hypcentral zne and in the suthern shallw sectin. Large S values cme frm high strength excess and/r small stress drp and hence prvide a strnger resistance t rupture prpagatin. This may be regarded as a barrier-type rupture zne. On the ther hand, small S values imply lw strength excess and/r large stress drp, which may be taken as a break f asperity. It shuld be emphasized here that the tw types f ruptures culd ccur n the fault during a single earthquake. It is fund, hwever, that there was mre than 40 cm f slip displacement in the zne f large S values. The relative intensity f barriers may be defined by this rati. If this rati has much higher values than btained here, rupture wuld nt ccur there and might be arrested. This culd be a strng barrier left unbrken. If, hwever, this rati is nt s high, the rupture ccurs with a small slip as in this case. Small slip results mainly frm lw stress drp there. It has been believed fr lng years and explicitly pinted ut [Heatn, 1990] that the rise times calculated frm Strength Excess / Stress Drp 1.0 '111'i'i.'.'.'.'::P'":4..!!;: " - i i:' " -"..'-' ii??< ::::::" " i!i iiii i : :.: :. -..::'"?-":":':!!i ::::i.?:-- --" :...ji ::... ' '--' -:' ';"'.! :? i.: <?:;?:F-'"'""'""' -.- ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: '... ',,-, 0.8 z:.' "z. -:::::.-.<... ß?: ½i i ii*,:'." ß '.'-'..-::::::*:::' ':,:,*-.-'. :.-... >,':-';:-*"':*:..:.:,:c?:-"*-?:,'- '*"**'" *,: 0.6 i.i.::...;. 111 * i?!':-:: ;,;,:,; ; : iiii ::ii:i;i;i;;;;;11: ; i:;i ":: ::;??,* '*!! :...;:;,; i ;iiii"*-':-...*... f:: ::' :-:½ '?i::.,:?;.:. ;? ii:i:.?; ii!::::-?:i; -'... :;'.;:..'.:::-.'-';...?..: i:;i,,:...i ::; :::::.- :::!::i i ;i :: : :i,::,i ß!:*:* ::::::::::::::::::::::: : :*:*:.::,::,r."---.'.-'.. :'"½*'":* ". ;,i.j -,:**::,::,::,::,::,i,i:::,::** '*'"'* - ---Ji :*: :i:..'. :,:,':: :,: '::... :-,- :,:,>a'.. '-': ::' ' ß ':':.,.,...-.'.,...,.S..,:..:,j:{$.....a,: ,,,..,<c...,.. ;;..*.:-':-'. g!:!$ :.'--':'. :5: :5:.::;!i:i: :i:i:.::i*:5'::..:.- ::!.. ( ' ;::?:: ::' :!:*'::::::::;:::;: ::: : : : : : : : : :.... : i$':'::!: " :*- '.;, ; j.'... ::::::::::::::::::::::::::::::::::::::::::::::::::::::::.... : :,:,: :::,:::::,: ;..:,-'. :::'-. ':,- ::,... ß " J":?: * '... ':i '*... ' - '½ '- * -0.8 Suth Nrth Fig. 18. The distributin f a dimensinless stress rati S, which is btained by the strength excess divided by the dynamic stress drp fr (mdel C3-01). -1.0

14 FUKUYAMA AND MIKUMO' DYNAMIC RUPTURE ANALYSIS O2 2O 34.9 N N 34.7 N /I,'115' 34.6 N 3z.5 N I-]-I E E / E' O. _- A Magn rude M< <M<3.0 O 3. O<_M<Z, a-.o<m< _<M 'T O - Depth (km) <Z< 10 ' _ --' a l O <_Z< 20,-, [] 20 <_Z< 30 I I I I [ I I I I ] I I I I 20. DEPTH (kin) Fig. 19. The distributin f aftershcks fr 1 mnth just after the main shck ccurrence. The hatched area indicates the fault trace f the 1978 Izu-Oshima earthquake estimated frm the aftershck distributin just after the main shck [Tsumura et al., 1978]. dynamic crack mdels are much lnger than that frm the kinematic mdeling f wavefrm data. It has als been pinted ut that the dynamic rupture mdel with the existence f a few barriers culd yield shrter rise time t match the bserved wavefrms. In the present case, hwever, smewhat lng rise times are necessary t explain the bservatin n the basis f the dynamic crack mdel. Althugh the majr slip ccurs in the first few secnds, slw slip with a duratin f several secnds fllws (Figure 9). We cmpare these results with the aftershck activity. Figure 19 shws the epicentral distributin f aftershcks within 1 mnth after the main shck. It is fund that the aftershck activity was very weak at the center f the fault. In this regin the slip displacement is relatively small (Figures 12 and 16). Frm the results f the dynamic rupture analysis, a large S value regin with the high strength excess and lw stress drp has been detected in this regin. These enable us easily t interpret a pssible relatin between the main shck slip and the aftershck activity. This regin seems t act as a barrier during the main shck faulting, crrespnding t the crssing pint f the 1978 Izu-Oshima earthquake [Shimazaki and Smerville, 1979; Kikuchi and Sud, 1984]. It may be suggested that the cause f the barrier during the 1990 Izu-Oshima earthquake culd be the fault trace f the 1978 Izu-Oshima earthquake, that had shifted the preexistent nrth-suth weak line and had made an ffset. CONCLUSIONS We have develped an iterative inversin methd that includes the three-dimensinal dynamic crack calculatin t btain the stress-strength distributin ver the fault. We have applied this methd t the near-field strng mtin array seismgrams f the 1990 Izu-Oshima earthquake. Using the stress drp and strength excess infrmatin, we can identify the faulting type (barrier r asperity). In the 1990 Izu-Oshima earthquake, near the initiatin pint f its rupture, the slip is large (-130 cm) and the rise time is shrt, indicating high stress drp and lw strength excess. Lw S value indicates an asperity-type faulting. While suth f this regin, lw stress drp and high strength excess regin is fund, where the slip dislcatin is small, rupture prpagates slwly and incherently, and rise time is lng (> 10 s). It is recgnized as a barrier-type faulting. It is

15 6542 FUKUYAMA AND MIKUMO: DYNAMIC RUPTURE ANALYSIS interesting that this barrier regin crrespnds t the intersectin with the fault trace f the 1978 Izu-Oshima earth- quake. Acknwledgments. The authrs appreciate the cmments f the assciate editr and tw annymus reviewers which helped t imprve the riginal inversin scheme. They als appreciate Jhn Nabelek fr critical review f the final manuscript. A part f the wavefrm data was prvided by the Japan Meterlgical Agency. The discrete wavenumber synthesis prgram cded by Fumi Yamamizu was used. The calculatin was dne at the Data Prcessing Center, Kyt University. A part f this wrk was dne while ne f the authrs (E. F.) was n leave frm Natinal Research Institute fr Earth Science and Disaster Preventin as a visiting researcher f the Labratire de Sismlgie, Institut de Physique du Glbe de Paris by the schlarship f the Science and Technlgy Agency, Japan. 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(Received Octber 21, 1991; revised September 17, 1992; accepted Octber 12, 1992.)