A TECHNIQUE FOR ESTIMATING DISTINCTIVE STRONG MOTION GENERATION PATCHES AND ITS SLIP VELOCITY FUNCTIONS BY WAVEFORM FITTING

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1 3 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -6, 24 Paper No. 45 A TECHNIQUE FOR ESTIMATING DISTINCTIVE STRONG MOTION GENERATION PATCHES AND ITS SLIP VELOCITY FUNCTIONS BY WAVEFORM FITTING Shinichi MATSUSHIMA, Hiroshi KAWASE 2, and Toshiaki SATO 3 SUMMARY For predicting strong motion with pulse waves that directly lead to seismic damage, it is important to adequately evaluate the heterogeneity of the slip distribution of the source rupture process as well as the effects of the complex subsurface geology. Since the characteristics of velocity pulse waves derived from forward rupture directivity effects are significantly affected by the size and the slip velocity function of the strong motion generation patches (SMGPs), it is necessary to evaluate these parameters accurately. In this study, we developed a technique to resolve multiple SMGPs and applied this technique to resolve the size and slip velocity functions of the SMGPs of actual earthquakes. We used data of the Miyagi-ken Oki, Japan, earthquake of 978 recorded at stations of Public Works Research Institute of Japan. By using the sharp velocity pulses in the data as target, we found that we need relatively small patches and sharp slip velocity functions compared to the asperities derived from previous source inversions to fit the velocity pulse and also the longer period characteristics of the data. INTRODUCTION Seismic damage is strongly influenced by the characteristics of strong motion at the natural period of about second. For predicting broadband strong motion including this period range, it is important to adequately evaluate the heterogeneity of the slip distribution of the source rupture process as well as the effects of the complex subsurface geology. The characteristics of velocity pulse waves, directly leading to seismic damage, derived from forward rupture directivity effects are significantly affected by the size and the slip velocity function of the Strong Motion Generation Patches (SMGPs) (Kawase et al. []). We developed a technique for estimating rupture process assuming a distinctive SMGP by waveform fitting considering the 3-D subsurface geology (Matsushima et al. [2]). If we apply the the recipe for predicting strong ground motion (Irikura et al. [3]) to determine source model for a huge magnitude earthquake, like the ones at the subduction zones in eastern and southern coasts of Japan, we can expect a very large asperity. The corner period for huge magnitude earthquakes Senior Researcher, Ohsaki Research Institute, Inc. 2 Professor, Graduate School of Human Environmental Studies, Kyushu University 3 Research Director, Ohsaki Research Institute, Inc.

2 shifts to longer periods (e.g., for earthquakes of M w 8. the corner period will be about few tens of seconds), so we can expect the long period components to be dominant in observed waveforms. As the corner period shifts to longer periods, the period range of about second becomes relatively short, but the waves in this period range can add up coherently and make forward rupture directivity pulses. In this study, we examined a way to model the source characteristics of large earthquakes that can produce strong motion with wider period range than those by traditional source inversions. HIERARCHICAL STRUCTURED STRONG MOTION GENERATION PATCHES In order to estimate the source characteristics for a wide period range, we need to incorporate a source model that can produce both long and short period strong motions. Since the size of the strong motion generation patch influence the dominant period of the observed velocity pulse, we need to have a concentrated area inside the area where long period strong motions are generated. Here, we propose an idea to incorporate a series of SMGPs that influence the different dominant periods in the strong motion data. These patches should hierarchically exist inside the source region to produce broadband strong motion including velocity pulses. We assume that the amplitude and duration of the slip velocity time function changes as the area of the SMGP changes. TARGET EARTHQUAKE Since the possibility of the reoccurrence of the subduction earthquake in the northeastern coast of Japan is said to be high, we pay attention to the earthquake with the highest possibility which is the Miyagi-ken Oki earthquake. The latest event in the region was the Miyagi-ken Oki earthquake of 978 (M w 7.6). We use strong motion recordings at the stations of Public Works Research Institute of Japan. The data at Kaihoku Bridge contains a velocity pulse with dominant period of to 2 seconds, as well as other stations. By using this sharp velocity pulse as target waveform, we derive the size and slip velocity functions of the SMGPs. Here we incorporate the idea of hierarchical structured SMGPs, in order to simulate the sharp velocity pulse seen in the data together with the longer period characteristics. We focus on the area that includes the source region and the city of Sendai, which is the largest populated area in northeastern Japan. The area we focus on is shown in Fig. with the rectangle. Fig. 2 shows the close-up map inside the rectangle of Fig.. The black rectangle in Fig. 2 shows the location of the source area of the Miyagi-ken Oki earthquake of 978. The blue rectangle shows the SMGP closest to the start of the rupture. We only consider the SMGP close to the start of rupture for this study. The size and location of the source is based on the report by the Headquarters for Earthquake Research Promotion of Japan (HERP) [4]. The source model referenced for this report is results from source inversions (e.g., Yamanaka and Kikuchi [5]). The strike of the fault and the dip is assumed to be 2 degrees and 7.2 degrees respectively (HERP [5]). The red circles in Fig. 2 denotes the observation sites DKHB (Kaihoku Bridge) and DTMD (Tarumizu Dam) we used for estimating the SMGPs. The blue circle is Tohoku University (THUV). METHODOLOGY Outline of the technique We assume a flat-layered velocity model and calculate the Green's functions for desired rake angles by wavenumber integration method by Hisada [5]. The flat-layered structure at DKHB and DTMD is listed in Table and Table 2, respectively. These structures were estimated by HERP [4]. Then the strong motions are calculated by weighting and summing the Green's functions for the desired slip velocity functions. We

3 assume that the fault geometry and location of the start of rupture is a known parameter. Also, it is assumed that the slip is concentrated on the SMGPs and the slip in the rest of the source region is not considered. Formulation In order to compute the simulated waveforms we assume six parameters. The parameters are, size of the SMGP, shape of the slip velocity function (Vd, tr, td, α), and rake (λ). The size of the SMGPs are shown in Fig. 3. We assume that the size of the SMGP with the larger generation of the strong motion is 4km square or 2km square. The background SMGP is 8km by 2km. This is the area shown in Fig. 2 by the blue rectangle. The parameters to describe the shape of the slip velocity function is shown in Fig. 4. Vd is the maximum amplitude, td is the time of the maximum peak, tr is the duration, and α is the decay parameter. We fix the location of the SMGPs in this study. Error estimation To estimate the best combination of the parameters, we use the velocity waveform as target and search for the best fitting case by grid search technique (Sato et al. [7]). The error estimation involves both L and L2 norms. These norms are defined by Eq.(). L: L2 : f ( t) = t2 t f ( t) = t 2 f ( t) f ( t) dt t f ( t) dt () Here, [t, t 2 ] is the time interval, in which the seismogram is used. The L and L2 norms emphasize the high and low frequencies of the data, respectively. The error is defined as, 2 ( f M ) /. e = f M g / g (2) The errors e L and e L2 are defined accordingly. The error ( e ( 2 2 ) ) / L + el2 + el e 2 4. e = + (3) L is defined to be the error estimation for one individual component (Zhao and Helmberger [8]). ESTIMATION OF THE SOURCE PARAMETERS We assume a different range of parameters for the foreground and background SMGP as shown in Table 3. We calculate the error for each set of parameters by Eq.(3) and search for the set of parameters with the least error. We assume that the rake angle is common for the fore- and background patch and the range of the rake angle is to 2 (deg) with 5 deg interval. The rupture velocity (Vr) and shear wave velocity (Vs) is fixed to Vr=3.km/s and Vs=3.93km/s, respectively. For the parameter range of Table 3, the comparison of the velocity waveforms for the best fitting case and the data is shown in Fig. 5. We only use the north-south component of DTMD because the other component may be affected by the Dam. The effective period range of the synthetics is longer than.25 seconds, so the data and synthetics are low-pass filtered at.25 seconds. The synthetics show a fairly good match with the data. The parameters for this best-fit case is listed in Table 4. The slip velocity functions

4 for the best-fit case is shown in Fig. 6. For reference, the slip velocity function by Nakamura and Miyatake [9] derived from parameters in the report by HERP [4] is show in the figure. To check if we can simulate the data with the estimated parameters for longer periods as well as for shorter periods as we described above, we filtered both the data and synthetics for the best-fit case with a low-pass filter at 2 seconds. The period range 2 seconds and longer is the period range used in source inversions for the Miyagi-ken Oki earthquake (e.g. Yamanaka and Kikuchi [5]). The filtered velocity waveforms are shown in Fig. 7. The synthetics show fairly good match with the data also in this period range. Fig. 8 shows the Fourier velocity spectrum of the two. For frequencies lower than few hertz, the Fourier velocity spectrum of the synthetics show good match to those of the data. DISCUSSIONS In the previous section we showed that in order to reproduce the velocity pulse we need a hierarchical structured SMGP at the asperity area. Here, we confirm the effectiveness of the SMGPs. We assume all area of SMGP was uniform with the parameters of the background patch. The velocity waveform for synthetics and data are shown in Fig. 9. As for the waveforms in the period range of.25 seconds and longer, we can see that the synthetics cannot reproduce the velocity pulse of to 2 seconds. But for the longer period range (T > 2 sec) it shows a good match. These results suggest that the hierarchical structure of the SMGP is effective in simulating the relatively short period velocity pulse produced by a large magnitude subduction zone earthquake. CONCLUSIONS We proposed a hierarchical structure of the Strong Motion Generation Patches (SMGPs) in order to estimate the source characteristics for a wide period range. We developed a technique to resolve distinctive SMGPs and applied this technique to resolve the size and slip velocity functions of the SMGPs of a subduction zone earthquake. By assuming a small patch (4km x 4km) that has a sharp slip velocity time function inside a background patch (8km x 2km) that has a smoother slip velocity time function, we were successful to simulate the velocity pulse with a second width observed during the Miyagi-ken Oki earthquake of 978 (Mw7.6). From the results we can conclude that in order to estimate the source characteristics for a wide period range, we need to incorporate a hierarchical structure which the characteristics of SMGPs correspond to the dominant period of the waveforms. ACKNOWLEDGEMENTS We acknowledge Public Works Research Institute of Japan for the use of data of the Off Miyagi earthquake of 978. Some figures were made using GMT (Wessel and Smith []). This study was supported by the project Study on the master model for strong ground motion prediction toward earthquake disaster prevention funded by Special Coordination Funds for Promoting Science and Technology, from MEXT (2-24). REFERENCES. Kawase H, Matsushima S, Graves RW, Somerville PG. Strong Motion Simulation of the Hyogo-ken Nanbu (Kobe) Earthquake Considering Both the Heterogeneous Rupture Process and the 3-D Basin

5 Structure. Proceedings of the 2 th World Conference on Earthquake Engineering, Auckland, New Zealand. Paper no Matsushima S, Kawase H, Sato T. A Technique for Estimating Distinctive Asperity Source Models by Waveform Fitting. EOS Transactions of AGU, 82(47), Fall Meeting Suppl. Abstract S3C Irikura K, Miyake H. Recipe of Strong Ground Motion Prediction for Senario Earthquakes. EOS Transactions of AGU, 84(46), Fall Meeting Suppl. Abstract S42F The Headquarters for Earthquake Research Promotion. On strong ground motion evaluation methods for projected earthquakes in the sea off Miyagi Prefecture Yamanaka K, Kikuchi M. Asperity map along the subduction zone in northeastern Japan inferred from regional seismic data. Journal of Geophysical Research. in print. 6. Hisada Y. An Efficient Method for Computing Green's Functions for a Layered Half-Space with Sources and Receivers at Close Depths (Part 2). Bulletin of Seismological Society of America 995; 85(4): Sato T, Helmberger DV, Somerville PG, Graves RW, Saikia CK. Estimates of Regional and Local Strong Motions During the Great 923 Kanto, Japan Earthquake (Ms 8.2), Part I: Source Estimation of a Calibration Event and Modeling of Wave Propagation Paths. Bulletin of Seismological Society of America 998; 88(): Zhao L, Helmberger DV. Source Estimation from Broadband Regional Seismograms. Bulletin of Seismological Society of America 994; 84(): Nakamura H, Miyatake T. An Appoximate Expression of Slip Velocity Time Function for Simulation of Near-field Strong Ground Motion. Zisin 2 2; 53(): -9. (in Japanese with English abstract). Wessel P, Smith WHF. New, improved version of Generic Mapping Tools released., EOS Transactions of AGU 998; 79 (47): 579.

6 Fig. Map of the Japan islands. The rectangle shows the area of Fig. 2. DKHB THUV DTMD km Fig. 2 Map of the observation site and the source area of the Miyagi-ken Oki earthquake of 978. The black rectangle shows the location of the source area and the blue rectangle shows the asperity closest to the start of the rupture denoted by the star. 42 Table Flat-layered structure at DKHB. Table 2 Flat-layered structure at DTMD. No. Thickness [m] Vp[m/s] Vs[m/s] ρ [g/cm 3 ] Q No. Thickness [m] Vp[m/s] Vs[m/s] ρ [g/cm 3 ] Q

7 Fig. 3 Size of the SMGPs. The SMGP with the larger generation of the strong motion is 4km by 4km or 2km by 2km. The background SMGP is 8km by 2km. This is the area shown in Fig. 2 by the blue rectangle. The unit is in kms. Vd /α t td tr Fig. 4 The parameters to define the shape of the slip velocity function. Vd is the maximum amplitude, td is the time of the maximum peak, tr is the duration, and α is the decay parameter. Table 3 Range of parameters for SMGPs. (a) Foreground min max incre ment size km 2 2x2 4x4 - time to max. vel. td sec duration tr sec 4td 8td 2td coefficient α max. vel. Vd cm/s (b) Background min max incre ment size - km time to max. vel. td sec duration tr sec 8td 2td 2td coefficient α max. vel. Vd cm/s

8 3 OBS NS DKHB OBS EW DKHB SYN EW OBS NS DTMD 2 3 Fig. 5 The comparison of velocity waveforms of the synthetics for the best-fit case and data (T >.25 sec). The red and the blue lines are the data and synthetics, respectively. The black line above each trace is the time window that was used for the grid-search technique. Table 4 Parameters for the best-fit case. Patch Back total HERP (23) size km time to max. vel. sec duration sec coefficient - - max. vel. cm/s rake deg slip m M 9 Nm

9 35 Patch BackG Nakamura&Miyatake(2) Fig. 6 The comparison of the slip velocity function of the fore- and background patches (above). The slip velocity time function of the foreground patch (blue line) has a larger amplitude and shorter duration than the background patch (red line). The slip velocity function by Nakamura and Miyatake [9] is derived from parameters in the report by HERP [4]. 5 OBS NS DKHB OBS EW DKHB SYN EW 2 3 OBS NS DTMD 2 3 Fig. 7 The comparison of velocity waveforms of the synthetics for the best-fit case and data for long periods (T > 2sec). The red and the blue lines are the data and synthetics, respectively. The black line above each trace is the time window that was used for the grid-search technique.

10 DKHB NS DKHB EW DTMD NS. OBS SYN Frequency [Hz] Frequency [Hz] Frequency [Hz] Fig. 8 The comparison of Fourier velocity spectrum of the synthetics for the best-fit case and data for longer periods. From left to right, DKHB NS component, DKHB EW component, DTMD NS component. The red and the blue lines are the data and synthetics, respectively. 35 OBS NS DKHB OBS NS DKHB OBS EW DKHB SYN EW 2 3 OBS NS DTMD 2 3 (a) T >.25 sec OBS EW DKHB SYN EW 2 3 OBS NS DTMD 2 3 (b) T > 2. sec Fig. 9 The comparison of velocity waveforms of the synthetics only by the background patch with paramters for the best-fit case and data. (a) T >.25 sec, (b) T > 2. sec. The red and the blue lines are the data and synthetics, respectively.