Geophysical Journal International

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1 Fast determination of megathrust rupture processes based on teleseismic waveform in a global D velocity structure and tsunami wave estimation with an application to the 0 Tohoku-Oki earthquake Journal: Geophysical Journal International Manuscript ID Draft Manuscript Type: Research Paper Date Submitted by the Author: n/a Complete List of Authors: Baag, So-Young; Seoul National University, School of Earth and Environmental Sciences Rhie, Junkee; Seoul National University, School of Earth and Environmental Sciences; Yoo, Seung-Hoon; Weston Geophysical Corporation, Kim, Seongryong; Seoul National University, School of Earth and Environmental Sciences Kim, Satbyul; Pukyong National University, Department of Earth and Environmental Sciences Kang, Tae-Seob; Pukyong National University, Department of Earth Environmental Sciences Keywords: SEISMOLOGY, Earthquake source observations < SEISMOLOGY, Continental margins: convergent < TECTONOPHYSICS, Subduction zone processes < TECTONOPHYSICS, Tsunamis < GENERAL SUBJECTS

2 Page of Geophysical Journal International Submitted to Geophysical Journal International, Jun., 0 Fast determination of megathrust rupture processes based on teleseismic waveform in a global D velocity structure and tsunami wave estimation with an application to the 0 Tohoku-Oki earthquake So-Young Baag, Junkee Rhie, Seung-Hoon Yoo, Seongryong Kim, Sat-Byul Kim, and Tae-Seob Kang School of Earth and Environmental Sciences, Seoul National University, Seoul, 0, Republic of Korea Weston Geophysical Corporation, Bedford St. #, Lexington, Massachusetts, 0, USA Department of Earth and Environmental Sciences, Pukyong National University, - Daeyeon-dong, Namgu, Busan, Republic of Korea Corresponding author: Junkee Rhie; School of Earth and Environmental Sciences, Seoul National University, Gwanak-ro, Gwanakgu, Seoul, 0, Republic of Korea; Phone) +--0-; Fax) +---; ) rhie@snu.ac.kr Abbreviated title: Fast determination of rupture processes for tsunami forecasting

3 Page of SUMMARY In order to mitigate the tsunami disasters caused by megathrust earthquakes, tsunami forecasting systems utilizing fast and accurate determination of the earthquake s rupture process are essential. In this study, we develop an efficient technique for fast determination of rupture processes on megathrust faults in the Circum-Pacific subduction zones by constructing finite fault models and calculating seismic Green s functions of full waveform in D global velocity structure well before the earthquake. The resulting slip distribution model can be applied to tsunami simulation, enabling the fast prediction of tsunami waves. The large-magnitude tsunamigenic earthquakes occur on subduction zones plate interface where the locations and topographies are already known. Therefore, we constructed megathrust fault models composed of subfaults using the reliable geometries of the plate interfaces in the Circum-Pacific subduction zones. For all available subfault-station pairs of fault models and global broadband seismic networks, teleseismic Green s functions of full waveforms in D global earth structure were computed using the spectral element method. The result forms a Green's function database composed of. millions of Green s functions, such that effects in D wave propagations and complex fault geometries can be accounted in estimated rupture processes promptly after the earthquake. The rupture process along the finite fault models can be computed by the non-negative least-square inversion technique in a short time right after a megathrust earthquake using the Green s function database and broadband teleseismic data set. Regional or global average values can be used for parameters of the rupture process, such as the rupture velocity and subfault source time duration, for fast process. The applicability of this method is tested with the Great 0 Tohoku-Oki, Japan, earthquake. The resulting slip distribution is similar to those of

4 Page of Geophysical Journal International previous studies of the rupture process. The synthetic tsunami waveforms computed based on the slip distribution were reasonably compared with the observations recorded at Deep-ocean Assessment and Reporting of Tsunami (DART) buoys located to the east of Honshu, Japan.

5 Page of INTRODUCTION The tsunamis generated by megathrust earthquakes in subduction zones devastate large areas near and far from the source region across the globe. Recent examples are the Great Sumatra-Andaman earthquake of Mw. occurred on the December 00 off the west coast of the northern Sumatra and the Great Tohoku-Oki earthquake of Mw.0 on March 0 near the east coast of Honshu, Japan (Ammon et al., 00, Lay et al., 00, Simons et al., 0, Tajima et al., 0). In order to mitigate such disasters, it is necessary to get information about the character of the earthquake source and estimate the time and strength of the anticipated tsunami as soon as possible. Traditionally, values of source parameters, such as the centroid, fault orientation and seismic moment, can be obtained from a centroid moment tensor solution within - minutes after a large earthquake (Whitmore, 00). However, it is important to characterize the earthquake source as a realistic finite fault with a slip distribution rather than as a point source type (Hartzell and Heaton,, Lay et al., 00a, Hayes, 0b) in relation with generation of tsunami (Poisson et al., 0, MacInnes et al., 0, Ulutas, 0). The inverted slip distribution using globally distributed seismic data has been used as source input for modeling tsunamis generated by recent large earthquakes (Fritz, 0, Newman et al., 0, MacInnes et al., 0, Wei et al., 0). In the National Ocean and Atmospheric Administration (NOAA) tsunami forecasting system SIFT (Short-term Inundation Forecasting for Tsunamis), an average slip converted from the seismic moment magnitude is uniformly distributed on the pre-defined finite fault model to predict tsunami waves, and then the slip distribution is updated by source inversion as soon as recorded tsunami data is acquired (SIFT Overview, 0, Gica et al., 00).

6 Page of Geophysical Journal International As for the recent large Tohoku earthquake of Mw.0, an early warning of expected tsunami was issued by Japan Meteorological Agency (JMA) in minutes after the earthquake based on a preliminary Mw. (Tsushima et al., 0, Ozaki, 0, Wei et al., 0), which was underestimated. Among recent tsunamis caused by large megathrust earthquakes in subduction zones, the tsunami of the 0 Tohoku earthquake was the first large and only event for which deep-ocean tsunami-meter data were available from multiple stations at distances 00 0 km (Tang et al., 0), which could be used in estimation of the tsunami source. The earliest real-time estimates of tsunami source was done to be used for prediction of tsunamis at. hours from the hypocenter time by NOAA tsunami forecast system using data from two tsunami Deep-ocean Assessment and Reporting of Tsunami (DART) stations # and # at distances 00 km and 00 km from the epicenter, corresponding to tsunami wave arrival times about minutes and hour, respectively (Tang et al., 0, Wei et al., 0). The earliest estimate of the slip distribution using seismic data, useful for tsunami modeling, was provided at approximately. hours after the earthquake origin time by the US Geological Survey (USGS) National Earthquake Information Center (NEIC) (Wei et al., 0). This was a quick finite fault slip model based on Ji et al. (00) using teleseismic body and surface waves, and a planar fault orientation from the USGS NEIC W-phase CMT solution (Duputel et al., 0). Then an updated result was announced at hours after the origin time with a revised rupture velocity and a strike direction based on the Slab.0 plate interface model at subduction zones (Wei et al., 0). In addition to a seismic and/or tsunami wave data, the data from global positioning system can be used as a constraint in the finite fault inversion (Ammon et al., 0, Simons et al., 0, Fujii and Satake, 0, Gusman et al., 0). Each of these data

7 Page of has characteristic features with advantages and disadvantages depending on observational and computational circumstances. At the occurrence of a large megathrust earthquake, one or multiple of these data sets could be utilized depending on availability of real-time or near-real time data. In the current study, we use teleseismic broadband full-waveform records including body waves and surface waves, as one of the components in the finite fault inversion for a megathrust fault slip distribution, but the method can be expandable to a multi-data set. The epicentral distance of the data could be º - 0º which have recording time of minutes, respectively, up to the end points of the surface waves. Teleseismic body waves and surface waves have characteristic features in propagation velocities and frequency contents that can contribute to spatial resolutions of the slip distribution in the waveform inversion. For the given teleseismic full waveform type of data, the main factors that determine the accuracy of finite fault rupture process using teleseismic waveforms are fault geometry and velocity model for Green function. In order to curtail the time in construction of the finite fault geometry based on information after the earthquake occurrence, and consequently the Green s function calculation based on the finite fault geometry, we constructed fault models consisting of subfaults for megathrust fault segments in widely distributed eleven subduction zones of the circum-pacific area, utilizing the D plate interface model Slab.0 of USGS (Hayes et al., 0). We computed Green s functions in D velocity model, SANI (Kustowski et al., 00) using spectral element method (SEM) (Tromp et al., 00) rather than in D velocity model to increase the accuracy. A Green s function database for source-station pairs of all the subfaults in the designed megathrust fault models in the circum-pacific area and

8 Page of Geophysical Journal International hundreds of globally distributed broadband seismic stations is stored so as to be used readily at occurrences of large megathrust earthquakes. The method inverts teleseismic full waveforms based on the non-negative leastsquare technique. The applicability of the method is tested for the 0 Mw.0 Tohoku-Oki earthquake, and the result shows that the scheme of D velocity model and the fault geometry model based on the Slab.0 produces reasonable results of slip distributions for prediction of recorded tsunami observations. The CPU times for computations of the slip distribution and corresponding tsunami waveforms are a few tens of seconds and a few minutes, respectively. Allowing about to minutes of processing time including the CPU time in the inversion for the slip distribution, all computations can be finished within to. hours after the earthquake occurrence, considering minutes of data recording to the end of the surface wave at epicentral distances up to 0. This time is corresponding to about the arrival times of the peak amplitude of the tsunami leading phase approximately at 00 to 00 km distances from the epicenter. Thus the technique could be applicable to the tsunami forecast for at distances greater than these distances, in addition to obtaining a fast and accurate information of the slip distribution on the fault in early times after the earthquake. Even though the method is formulated for the teleseismic waveform inversion, it could be extended to cases of multi-type data including geodetic near-source displacements recorded by GPS with proper relative weighting between data sets. The Green functions of geodetic displacements for sets of subfault-station pairs could be computed and stored as database to be used at the time of an earthquake.

9 Page of MEGATHRUST FAULT MODELS AND GREEN S FUNCTIONS.. Construction of Megathrust Fault Models The slip of megathrust fault is confined to a shallow portion of the plate interface down to about 0 km of depth from the trench in a subduction zone (Lay et al., 0). A large sudden slip along the fault by a megathrust earthquake can generate a disastrous tsunami wave in addition to seismic waves propagating the whole earth (Lay and Bilek, 00, Lay et al., 0). For a reliable result of the full waveform inversion for rupture process of the megathrust fault, a priori of the fault structure is important. We construct large-scale fault geometry models of global megathrust regions based on the information of Slab.0, the three-dimensional numerical model of global subduction geometries (Fig. ) (Hayes et al., 0). The Slab.0 is the first and only model that represents % of the global subduction zones in detail. The global subduction zones in Slab.0 are composed of regions. We chose regions from them for megathrust fault geometry models focusing on the circum-pacific region: Alaska-Aleutians (ALU), Cascadia (CAS), Izu-Bonin (IZU), Kermadec-Tonga (KER), Kamchatka-Kurils-Japan (KUR), Mexico (MEX), Philippines (PHI), Ryuku (RYU), South America (SAM), Solomon Islands (SOL), and Santa Cruz Islands/Vanuatu/Loyalty Islands (VAN) (Fig. ). We divide the regions into multiple fault segments with different sizes based on the curvatures of the trench (Fig. ). In the inversion process for slip distribution of a megathrust earthquake, a fault segment where the hypocenter is located is chosen for a finite fault modeling, and additional nearby segments of megathrust fault model are also chosen depending on the seismic magnitude of the earthquake. The fault model of each segment consists of subfaults with the same strike but with systematically different

10 Page of Geophysical Journal International dips along the dip direction. Thus the model has a single strike direction and piecewise variable dips along the dip direction. The subfault size of megathrust faults for inversion of slip distributions usually varies from smaller size of km km to larger size of 00 km 0 km, depending on the purpose (Ammon et al., 0, Tang et al., 0, MacInnes et al., 0). Tsunami waves are less sensitive to details of localized slip due to intrinsic low frequency contents (Yue et al., 0). Therefore, the subfault size for computation of the tsunami can be a larger size ranging from km km to 00 km 0 km (Fujii et al., 0, Saito et al., 0, Gusman et al., 0, Tang et al., 0, Satake et al., 0, Wei et al., 0). In this study, the size of the subfault was determined to be 0 km x 0 km, considering large magnitudes of the events and the frequency range of the waveform used in the inversion. The procedure of constructing a fault geometry model of a segment is as follows. The locations of the intersection line between the fault surface and the sea floor at a trench is extracted from Slab.0. The extracted location of the curved trench line is approximated to a linear function with length of 0-00 km (smaller in the case of large curvature) using piecewise linear interpolation technique. The linear line corresponds to the near-trench line of a fault segment model. In order to simplify the constructed fault model, the average depth along the trench is used as the depth of the intersection line. Thus, the latitudes, longitudes and the depths of intersecting points between the sea floor and the surface of the fault segment are obtained together with corresponding strike direction. Then to derive the coordinates of the fault segment along the dip direction, coordinates of the plate interface point data from Slab.0 model are projected to a vertical plane perpendicular to the trench direction or the strike direction. Using the plate interface points in the projected coordinates, a piecewise linear function with a few line segments of length 0 km is determined through the least square

11 Page 0 of polynomial approximation and piecewise linear interpolation. These line segments of 0 km in length correspond to traces of planes of subfaults in dip directions. The slope of a line segment corresponds to the dip of the subfault. The fault is subdivided in the strike direction by the length interval 0 km of a subfault. The resulting faults have the maximum depth values up to 00 km, which sufficiently covers shallow, near-trench region of tsunami-generating domain, central region with large slip, low short-period energy domain, and down-dip region with modest-slip, high short-period energy domain. This procedure is done for every megathrust fault segment around the Pacific (Fig.).. Computations for Green s function set In order to get accurate rupture processes of the megathrust from the inversion of recorded full waveform data, the earth model for computation of synthetic seismogram needs to be close to the actual earth structure. The importance of the earth model can be found from the comparisons of recorded broadband full waveform with synthetics computed by SEM using D PREM model and D model for the case of the 0 Mar. Mw. near-east-coast Honshu, Japan, earthquake (A foreshock of the 0 Mar Mw.0 Tohoku-Oki, Japan earthquake) (Fig. ). For the D earth model, we use the D S-wave velocity model SANI (Kustowski et al., 00), associated D P-wave velocity model for the mantle structure, and D CRUST.0 velocity model (Bassin et al., 000) for the crust. This combination of D velocity models for the crust and mantle is also used in all synthetic seismogram computations for D velocity structure in this research. The comparison between the observed and synthetic vertical component seismograms (Fig. ) filtered with passband of 0-00 seconds shows that there are large deviations of waveforms for the synthetics in D model compared to those in D

12 Page of Geophysical Journal International model, as stated in the previous section. In our inversion for slip process of the megathrust fault, the strike and dip of each subfault are given as pre-determined values from design of the fault model. However, the rake and seismic moment at each subfault are variable and to be solved in the inversion process. With the two orthogonal rake angles, and, used as reference rake directions or coordinate axes of slip motions on the subfault, any slip motion on the subfault can be a linear combination of those in the two directions. The assumption of thrust fault mechanism can be realized by the constraint of nonnegative values of the slip components along the two directions. The slip motion on each subfault contributes to displacements at seismic stations. In this study, three-component (EW, NS, and Z) Green s functions at a station are defined as responses of the slip motion in one of the rake directions on a subfault as a point source with a unit seismic moment of 0 0 dyne cm. The Green s functions with an impulse source time function are calculated using SEM in D earth model described above and were convolved with a proper source time function corresponding to the subfault to get Green s functions with a finite source time duration. The results are filtered by a pass-band of 0-00 seconds in order to remove high frequency and very low frequency signals, and then are downsampled to the time interval of 0 seconds (Hereafter, we call it simply Green s functions). The shape of the source time function is an isosceles triangle with duration of 0 s and the covered area by the function in time domain is a non-dimensional unity. In order to be readily used in the inversion for the rupture process right after a megathrust earthquake in a subduction zone, Green s functions for all the subfaultstation pairs are computed and stored before the earthquakes. These pairs include subfaults in all the segments of prescribed subduction zones in the world and seismic stations of worldwide networks of GSN, GEOSCOPE, GEOFON, and MEDNET (Fig.

13 Page of ). With the 0 modeled subfaults, stations, rake directions and components, the total number of Green functions calculated are,,.. INVERSION FOR SLIP DISTRIBUTION.. Methods for the Inversion The synthetic seismogram at a station can be represented by a linear combination of the slip responses of all subfaults on the finite fault surface. For given slips or seismic moments with rake directions on all the subfaults, the synthetic seismogram can be calculated by where N u i (t) = k (r) [M (r) (R) k Gik (t t k ) + M (r) k= k Gik (t t k )] () (t) u i is the i th component amplitude of the three-component displacement seismograms with Nt time points. Indices k represent sequential numbers assigned to subfaults for identifications with k = N k, corresponding to the total number of subfaults. M and M are seismic moment components in reference rake ( r ) k ( r) k directions and, respectively, for k th subfault, presented in terms of the unit ( seismic moment. Functions G r ) ( ) ik ( t) and G r ik ( t) are i th component amplitudes of the Green s functions for the k th subfault with reference slip rake directions and, respectively. These Green s functions have the isosceles triangular source time function and a unit seismic moment of x 0 0 (r) dyne cm as defined above. k is the rake angle of the k th subfault and t k from the hypocenter to the center of the k th subfault. is the time delay due to the rupture propagation

14 Page of Geophysical Journal International For the inversion process using the least-square method, synthetics in the matrix form of the equation () is equated to the observed seismograms in the form of column matrix d, and regularization conditions for minimum moment components and Laplace smoothness are attached to stabilize the inversion numerically, such that G (r), G (r) d [ λ s L ] [ M(r) λ d I M (r)] = [ 0] () 0 Here, G (r) and G (r) are matrices composed of Green s function elements G ( r ) ik ( r) ( t t ) and G ( t t ), respectively, with dimension N N ) (N ). k ik k ( s t k The factors and in the matrix dimension are for components of seismograms and reference rake directions, respectively, and the parameter Ns represents the total number of stations. M (r) and M (r) are column matrices composed of elements (r) (r) M k and Mk, respectively. The column matrix d is for the observed data time series with dimension of N N ). L represents a matrix containing the Laplacian ( s t operator for roughness regularization, and λ s and λ d represent coefficients for smoothing and damping, respectively. The roughness regularization is done separately for the two moment components corresponding to the two reference rakes. The difference between a moment component at a subfault and the average of those values at the surrounding nearest subfaults is used as the Laplacian of the moment component at the subfault, rather than using the nearest subfaults in order to have a stable constraint. In the computation, the technique of non-negative least-square (NNL) method (Lawson and Hanson, ) is used to restrain the seismic moment and (r) (r) corresponding slip values to be positive. The estimated solutions M k and Mk are divided by (r ) (r) to get the slip component and s k, where μ and A sub Asub represent the shear modulus and the area of a subfault, respectively. Since the subfault s k

15 Page of area is fixed, slip amounts are dependent on the shear modulus. The varying shear modulus values with depth are based on SANI s reference earth model, STW0 (Kustowski et al., 00). Then the slip and orientation at each subfault are obtained from the two seismic moment components at each subfault using the equations: (r) (r) (r) s k = [(s k ) + (sk ) ] and λk = cos ( s (r) k ) +. s k In order to check the quality of the inversion, synthetic seismograms are computed based on the estimated distribution of seismic moments and rake angles of subfaults using Eq. () and compared with data. As a criterion of the quality, a variance reduction defined by V R is used, where data ( t i ) and syntt ( i ) represent point values of time series of the observed and synthetic seismograms, respectively, for all components and stations used in the inversion. i [ dat( t a) synt ( t ) ] [ dat( t a) ].. Pre-process for the inversion i i i i A couple of a priori parameters are needed in the linear inversion: rupture velocity and subfault rupture duration time. Both parameters are usually determined through process of multiple experimental inversions in search for the values that yield the largest variance reduction. However, the search for the optimal values of the parameter in the inversion process can be time-consuming and can lead to inefficiency in application to the tsunami prediction. On the other hand, a representative value of the rupture velocity in each of the relatively well-studied subduction regions (i.e. Chile, Tohoku, etc.) can ()

16 Page of Geophysical Journal International be obtained by the weighted average of the values from prior researches. If there is no information on the possible representative value in a subduction zone, the global average of the rupture velocity is assumed to be the representative value of the subduction region and is estimated to be. km/s from sources (Table ) for globally distributed megathrust earthquakes with magnitude greater than Mw.. In the inversion process, either type of rupture velocities can be used depending the availability of information. If a megathrust earthquake occurs in one of the subduction zones with information of representative rupture velocities, then the information can be used in the inversion process, but for cases otherwise, the approximate value of global average is used. Subfault rupture duration time and subfault size used in the inversion for slip distribution are different from one research to another. Ranges of subfault sizes and subfault rupture durations commonly used are 0-0 km and 0- s, respectively. In order to get plausible values of the time duration of the triangular source time function corresponding to the subfault as a point source, an approximate linear relationship between the subfault size and the subfault source time duration for megathrust faults was obtained from those values used or obtained by authors (Ammon et al., 00, Ammon et al., 0, Lay et al., 00b, Lay et al., 0, Lay et al., 0, Suzuki et al., 0, Yue et al., 0) in inversions of slip distributions for megathrust earthquakes (00 Sumatra-Andaman, 00 Mw.0 Tohoku-Oki, 00 Mw. Chile, 00 Mw. Mentawai, 0 Mw. Iquique). The subfault source time duration in seconds increases with the subfault size in km with an approximate slope or ratio of, for an example, 0 seconds of subfault source time duration corresponds to 0 km of subfault subfault size. The subfault rupture duration depends on property of the megathrust earthquake source zone, and usually increases with the size of the subfault. For subfault

17 Page of size about 0 km x 0 km, this study uses subfault rupture duration time of 0 s, which is within the reported range. Right after the occurrence of a large earthquake in one of the megathrust region, the fault segment where the hypocenter is located is determined using the preliminary information of the earthquake. Then the subfault that harbors the hypocenter within the fault segment is located. Usually, the information on the depth of the hypocenter is less accurate compared to the epicenter, and the informed depth does not coincide with a point on the fault plane of the fault model. Thus the hypocenter depth is moved vertically reaching a point on a nearest subfault to get a new hypocenter depth on the fault plane. We assume that the rupture of the fault initiates from this new hypocenter and propagates along the fault surface with circular rupture front, and each subfault surrounding the hypocenter ruptures when the rupture front arrives at the center of it. The distances between the hypocenter and all the subfault s centers along the fault surface were calculated, and divided by the rupture velocity to obtain the delay time relative to the rupture initiation time at the hypocenter. Then the Green s functions mentioned above were delayed in time according to the rupture propagation from the hypocenter point to the center of the subfault. In actual computation, this time-shift process of each Green s function was done in Fourier domain by shifting phases corresponding to the delay time. The rupture velocity during the fault s rupture is assumed to be constant, and there is no repeated activation of ruptures at any part of the fault in this study.

18 Page of Geophysical Journal International Tests and Application.. Test of the Inversion Algorithm using Synthetic Rupture Model Using the inversion process described above, a test of the inversion process was done with an artificial rupture process with a spatiotemporal slip distribution. The hypocenter was put at the center of a subfault near the middle of the megathrust fault model (Fig. ) for the Honshu segment (Fig., marked by KUR *S0) in the Kamchatka-Kuril-Japan subduction region (Fig. ). The hypothetical rupture distribution was constructed by assigning slips corresponding seismic moments and rake angles to all the subfaults on the finite fault. The rupture velocity of. km/s is assumed in calculation of delay times of Green s functions, i.e., the time corresponding to the rupture propagation from the hypocenter to each center of subfault. The three-component synthetic seismograms at GSN stations were computed using the source parameters of subfaults such as slips, rakes, and delay times corresponding to the rupture propagation. They were band-pass filtered between 0~00 seconds and used as a hypothetically observed data set. Then the full waveforms were inverted for slip components of subfaults using Green s functions already stored in the memory system, as described in sections. and.. The slip distribution of the inversion result is exactly the same as the originally designed distribution (Fig. ).. Application to Slip Distribution of 0 Tohoku-Oki Earthquake The Great 0 Mw.0 Tohoku-Oki earthquake occurred on March, 0 at :: GMT. Its hypocenter was located.º N,.º E, and km depth (USGS National Earthquake Information Center PDE: Preliminary Determination of

19 Page of Epicenter). It is reported that the source area of large slip with long-period radiation is located at shallow plate interface and the area of modest slip with high frequency radiation is limited to area of deeper depths (Tajima et al., 0). Using the methods described above, the inversion of full-waveform for the slip process of the Great 0 Tohoku earthquake was performed in this study. In order to perform the waveform inversion for slip distribution of the great 0 Mw.0 Tohoku-Oki earthquake, stations covering the azimuth uniformly are selected from available stations that have relatively low noise signals (Fig. ). The data set of these stations and corresponding Green s functions are pre-processed as described in the section. before the inversion. In the inversion process, this study primarily makes use of global average rupture velocity of. km/s, assuming that there is no information known for the rupture velocity of fault segment prior to the 0 Tohoku-Oki earthquake. Then the result is compared with that computed using the average rupture velocity. km/s of the Tohoku earthquake obtained based on the estimated velocities from previous works of researchers since the event (Table ). Least-square inversions of the waveforms for slip distributions are done in the way described in section. using the D velocity model SANI (Dv) and the fault model based on Slab.0. Synthetic seismograms are also computed for the slip distributions determined by the inversion. Variance reductions are calculated for the waveform similarities between the waveforms of data and synthetics. The inversion result for the scheme (Fig. ) shows a predominant slip distribution on the central upper half of the fault with maximum value of m near the trench, which is close to the average value m obtained from data sources of previous works (Table of Tajima et al. (0)). The overall shape of the slip distribution is similar to those of Yoshida et al. (0) and Hayes, (0a). The width ~ 0 km of

20 Page of Geophysical Journal International the major slip portion on the fault is close to an average value 0 km of those from previous results (Table S). With a given width of the major slip distribution, the extension of it along the strike could be an approximate information for a rapid assessment of the hazard. The total extension of the predominant slip along the strike direction is about 0 km which is a little longer than the average value of 0 km from previous researches listed in Table S. The northeastern extension of the slip distribution up to N is consistent with some of previous works (Lee et al., 0, Koketsu et al., 0, Suzuki et al., 0, Satake et al., 0). Tappin et al. (0) pointed out that the abnormally high tsunami runup heights up to m occurred along the coast of the Sanriku district might have been caused by a large scale submarine landslide. The location is near to the northeastern extension of the slip model based on rupture velocity of. km/s. The southern extension of the significant slip distribution to. N with relatively smaller slips is also consistent with previous works (Koketsu et al., 0, Lay et al., 0, Suzuki et al., 0, Yoshida et al., 0). Maercklin et al. (0) suggested twin ruptures of the Mw.0 Tohoku-Oki earthquake with an additional rupture propagating southwest direction. We identified a south propagation rather than southwest direction in the inversion using rupture velocity of. km/s. Most of the slip directs toward ESE and the moment magnitude is.0. Two examples of waveform comparisons at stations LVZ and CTAO are shown in Fig.. The average variance reduction value for the E, N and Z components of stations is. %. Actually, the global average rupture velocity. km/s used in the computation might not be optimum values for the 0 Tohoku earthquake. We additionally computed the slip distribution using the average rupture velocity. km/s of the Tohoku-Oki earthquake obtained by averaging estimated rupture velocities from previous works.

21 Page 0 of The shape of the overall slip distribution (Fig. ) and resulting parameter values are similar to those obtained using the global rupture velocity. km/s. However, the extension of the significant rupture along the strike is reduced to 0 km which corresponds to the average value of those from previous works (Table S), and the two peaks in the north and south are merged together, and thus it has more slip around the epicenter area than that in Figure. Thus the slip distribution from the rupture velocity. km/s seems to be more similar to those of previous works, but we have no definite confidence on it. The two examples of waveform comparisons at the same stations (LVZ and CTAO) as those in Fig. are shown in Fig.. The average variance reduction value is.0 %... Application to Tsunami Simulation To test the applicability of the results from the finite fault modeling to tsunami simulation, the software Clawpack..0 (Clawpack Development Team, 0) was used to simulate tsunamis using the slip distributions obtained by finite fault inversion described in previous sections. The software calculates initial sea surface deformation due to inclined shear faults using Okada s formulations (Okada, ). And it simulates propagation of tsunami waves caused by the sea surface deformation using finite volume method, with effects of seafloor bathymetry. The tsunami waves are simulated using the fault slip distributions (Figs. and ) from the finite fault inversion of the Great 0 Mw.0 Tohoku-Oki earthquake. For the bathymetry effect, we used NOAA ETOPO -minute Global Relief grid database with -minute grid space model. The results are compared with the observations recorded by four DART buoys located on the east coast of Honshu (Fig. a). The four

22 Page of Geophysical Journal International buoys are DART #, #, #, # in the order of increasing distance from the epicenter of the earthquake. The computed tsunami waveforms using slip distributions from finite fault inversions based on the global rupture velocity. km/s (Fig. ) are shown in Fig., and are compared with observed ones. The misfit of the peak tsunami height amplitude of the leading phase in the simulated tsunami waves at each buoy falls in a range of cm cm from the observation. At the closest buoy, #, the simulated tsunami waveform underestimates the peak amplitude of the observation by cm. At #, # and #, the simulation underestimates the observation by cm, cm, and cm, respectively. The arrival time misfit of the peak tsunami height of the leading phase ranges from 0.-min delay at.-min arrival time distance (DART #) to.-min advance at.-min distance (DART #). Tsunami waveforms using slip distributions from finite fault inversions based on the regional rupture velocity. km/s (Fig. ) are also computed and the results are shown in Fig.. The misfit of the peak tsunami height amplitude of the leading phase in the simulated tsunami waves at each buoy falls in a range of cm 0 cm underestimate from the observation with maximum misfit at DART#. The arrival time misfit of the peak tsunami height of the leading phase ranges from 0.-min delay at.-min arrival-time distance (DART#) to.-min advance at.-min distance (DART#). The results of the tsunami waveforms utilizing the regional rupture velocity are not significantly different from the ones based on the global rupture velocity.

23 Page of DISCUSSIONS As mentioned in sections. and., this study mainly used global average parameters for finite fault inversion of seismic data to simulate the actual application of the tsunami simulation immediately after the occurrence of the earthquake. The results of the tsunami waveforms are not significantly different from the ones using the finite fault inversion utilizing the regional rupture velocity. In comparison of overall performance of results with respect to the observations, we have no preference between the rupture velocities based on the global rupture velocity and the regional one. The seismic waveform inversion for slip distribution of megathrust fault earthquakes can be done with different earth models and fault geometries. In order to test the effect of earth s velocity model and fault geometry models on the results of the finite fault inversion and tsunami simulation, the inversions are done for the four schemes corresponding to combinations of two velocity models and two fault geometry models utilizing the waveform data of the 0 Mw.0 Tohoku-Oki earthquake. The two velocity models are D SANI (Dv) and D PREM (Dv). The two fault geometry models are varying-dip (Vdip) fault model with variable dips based on Slab.0 and constant-dip fault model with a single dip (Cdip) based on CMT solution with strike of 0 and dip of 0 of the Tohoku earthquake (Fig. S). Thus the four combinations of schemes for velocity models and fault geometry models are Dv-Vdip, Dv-Cdip, Dv-Vdip, and Dv-Cdip. The slip distributions obtained using the global rupture velocity. km/s for the three pairs of combination except for the Vd-Vdip case are given in Figs. S S (The result for the Dv-Vdip is given in Fig. ). The overall shapes of the significant slip distributions are similar to that of Dv-Vdip case, but the extensions along the strike direction are reduced, with variable maximum slips from m to m. In order to see

24 Page of Geophysical Journal International the contribution of each of the velocity models and each of the fault geometry models to variance reductions of the waveform fitting, the average variance reduction value is obtained in relation with each of the models. The average variance reduction value. % for Dv-related pairs with Vdip and Cdip (Figs. and S) is larger than. % for Dv-related pairs with Vdip and Cdip (Figs. S and S). Thus the D velocity model results in much higher variance reduction value than the D velocity model. The average variance reduction value. % for Vdip-related pairs with Dv and Dv is slightly larger than. % for Cdip-related pairs with Dv and Dv. Even though the value is only slightly larger, the variable dip model based on Slab.0 plate interface model gives us much advantage in saving computational time of Green s functions by being computed well before the occurrence of the earthquake. The estimated magnitudes for the three cases are Mw., while that for the Dv-Vdip case is Mw.0. The slip distributions obtained using the regional rupture velocity. km/s for the three pairs of combination except for the Vd-Vdip case are given in Figs. S S (The result for the Vd-Vdip is given in Fig. ). Locations and shapes of the significant slip distributions are similar to those obtained using the global rupture velocity. The average variance reduction value. % for Dv-related pairs with Vdip and Cdip (Fig. and Fig. S) is larger than. % for Dv-related pairs with Vdip and Cdip (Fig. S and Fig. S). Thus the D velocity model results in much higher variance reduction value than the D velocity model. The average variance reduction value 0. % for Vdiprelated pairs with Dv and Dv is larger than. % for Cdip-related pairs with Dv and Dv. Thus it is apparent that the performance of the variable dip fault model based on the Slab.0 model is better than that of the constant dip model based on the moment tensor solution in the contribution to the accuracy of waveform inversion, if the regional average rupture velocity is used in the inversion. Thus, from the two cases of using the

25 Page of global and regional rupture velocities, we can conclude that the choice of D velocity model is generally most important, and the choice of the varying-dip fault model is the next in finite fault waveform inversion process for slip distribution. The estimated magnitude for Dv-related schemes is Mw.0, but those values for Dv-Vdip and Dv- Cdip cases are Mw. and., respectively. The slip distributions (Figs. S S) from the three schemes of Dv-Cdip, Dv- Vdip, and Dv-Cdip cases based on the rupture velocities of. km/s and. km/s are also applied to simulations of tsunami waves at the four DART stations. The results are shown in Figures S and S together with the result of Dv-Vdip case. The misfit of the peak tsunami height amplitude of the leading phase in the simulated tsunami waves at each buoy has a large variation among the four schemes. The misfit is up to m, especially at the nearest station DART# for both cases of global and regional rupture velocities. Among the four schemes, the misfits in the simulated tsunami amplitudes based on the scheme of Dv-Vdip have smallest values equal to or less than 0 cm at all DART stations for both the rupture velocities (Figs. S and S). This conclusion demonstrates that -D velocity model and varying-dip slab scheme adequately describe the tsunami, and that this method could be applied to most of the megathrust earthquakes occurring in other subduction zones, even though the conclusion was derived from the inversion process for the great 0 Mw.0 Tohoku- Oki earthquake.. CONCLUSIONS We developed an alternative method for fast determination of a megathrust rupture process (with keeping accuracy) based on most up-to-date plate interface geometry

26 Page of Geophysical Journal International model Slab.0 and SEM for computation of synthetic Green functions in laterally heterogeneous -D mantle model SANI and -D crust velocity model CRUST.0 applicable to forecasting of an intermediate or distant tsunami at distances greater than about 00 km. The fast determination of the rupture process is essential for mitigation of disasters. One of the characteristics of the method presented in this study over the conventional methods with seismic data is that the method does not need priori information on the focal mechanism determined by CMT, because the fault plane and corresponding Green s functions were already computed and stored before the earthquake. This gives an advantage to quickly providing the rupture process of megathrust earthquakes and tsunamis generated by them. Immediately after retrieving recorded data at occurrence of a megathrust earthquake, the rupture process can be computed in a short time by least-square inversion technique using the Green s functions. The inversion method presented in this study can give a solution independent of those based on CMT information There are several subduction zones with megathrusts faults that can cause a large earthquake and consequently large-scale tsunamis in the world (Fig. ). Since the megathrust fault models based on Slab.0 have been constructed for all the subduction zones in the circum-pacific area and corresponding Green s functions in global D velocity model are computed for the world-widely distributed broadband seismic stations, the rupture process can be computed in a short time right after a large earthquake using the waveform inversion method presented in this study. The calculation CPU time for the rupture process inversion was about 0 seconds, and one for the tsunami simulation based on the rupture process was about 0 minutes on personal laptop computer.

27 Page of The megathrust fault models and corresponding Green s functions could be continuously developed and updated. While the currently proposed method utilizes signals in the time range of teleseismic full waveform, the effects of the body waves are diminished greatly relative to the surface waves due to the amplitude and frequency differences. Therefore different weights could be given to body waves and surface waves in the inversion process for slip distribution in order to control the effects of the waves. Furthermore, even if the method is formulated for the teleseismic waveform inversion, it could be extended to a case of multi-data including geodetic near-source displacements recorded by GPS and tsunami waveform data from DART buoy observations, with proper relative weighting between data sets. The Green functions of geodetic displacements for sets of subfault-station pairs could be computed and stored as database to be used at the time of an earthquake. ACKNOWLEDGEMENTS This study was supported by the Research for the Meteorological and Earthquake Observation Technology and Its Application project of the National Institute of Meteorological Research. We also thank the anonymous reviewers for their constructive criticism and their indirect role in significantly improving the article.

28 Page of Geophysical Journal International Figure Caption Figure. Distribution of varying-dip finite fault models constructed based on subduction-zone plate interface geometry model USGS Slab.0. There are subduction zones modeled: Alaska-Aleutian (ALU), Central America (MEX), Cascadia (CAS), Izu-Bonin (IZU), Kermadec-Tonga (KER), Kamchatka/Kurils/Japan (KUR), Philippines (PHI), Ryukyu (RYU), Santa Cruz Islands/Vanuatu/Loyalty Islands (VAN), Solomon Islands (SOL), South America (SAM), and they are assigned with white characters. The location of the modeled finite fault for each fault segment in this study is marked by a rectangle. The segments in each subduction zones are numbered in the order of increasing strike of the fault, in black characters (i.e. S0, S0, ). Each fault segment consists of subfaults defined by depths, strikes and dips at locations in longitudes and latitudes. The depths of the Slab.0 are represented by colored scale in km. The fault segment in which the 0 Tohoku-oki earthquake occurred is marked by an asterisk next to the segment number. Figure. Comparison of observed broadband vertical component waveforms and synthetics by SEM in D PREM and D SANI velocity structures. The waveforms used for comparison are of the 0 March Mw. near-east-coast Honshu, Japan, earthquake (foreshock of the 0 March Mw.0 Tohoku-Oki, Japan earthquake). Stations of seismograms are ARU (.0 ), DGAR (. ) and GRFO (. ). The black traces are the observed seismograms, and the red traces are the synthetics computed in D (a) and D (b) structures using source parameters of GCMT solution. Larger deviations are found for the synthetics in D model compared to D model.

29 Page of Figure. Locations of globally distributed seismic stations, for which the Green functions with sources at all modeled subfaults in subduction zones are calculated and stored in the database. The red squares are GSN, yellow are GEOSCOPE, black are GEOFON, and blue are MEDNET networks. Total number of stations is and corresponding total number of Green's functions is,,. Figure. Synthetic test of the inversion process for a slip distribution on the multidip finite fault model with a constant strike based on Slab.0 in the D SANI velocity model. The fault model corresponds to the eastern Honshu segment (S0) in the KUR region (Table and Fig. ). (a) Artificially designed slip distribution. (b) Inversion result of synthetic seismograms from the slip distribution in (a). The inset shows A-A vertical cross section of the fault with multi-dips in degree. W~W indicate subfaults with numbers counting from the trench. The vertical and horizontal distances are in the same scale. Figure. Global locations of stations used in the exemplary finite fault inversion for 0 Tohoku Earthquake. The stations are located at epicentral distances - 0 and have relatively uniform azimuthal coverage. Figure. Result of the finite fault inversion of the teleseismic full waveforms for the 0 Mw.0 Tohoku earthquake using the D SANI velocity model and the fault model based on Slab.0 with a constant strike (Segment S0 in KUR region). The global average rupture velocity of. km/s and subfault rupture duration time of 0 s were used. The resulting Mw was.0, and variance reduction was. %. Slip distribution with amplitudes and directions is represented by colors and arrows on the

30 Page of Geophysical Journal International left side of the figure. The inset at the top-left corner is for the time variation of the moment rate function. The Inset at the bottom is explained in Fig.. Comparisons between the observation (black) and synthetic waveforms from finite fault modeling (red) at two stations are shown on two columns on the right as examples. The first column is for station LVZ and the second column for station CTAO. Displacement components of the east-west (E), north-south (N) and vertical (Z) directions are shown, from top to bottom. Figure. Result of the finite fault inversion of the teleseismic full waveforms for the 0 Mw.0 Tohoku earthquake using the D SANI velocity model and the fault model based on Slab.0 with a constant strike (Segment S0 in KUR region). The regional representative rupture velocity of. km/s and subfault rupture duration time of 0 s were used. The resulting Mw was.0, and variance reduction was.0 %. Slip distribution with amplitudes and directions is represented by colors and arrows on the left side of the figure. The inset at the top-left corner is for the time variation of the moment rate function. The Inset at the bottom is explained in Fig.. Comparisons between the observation (black) and synthetic waveforms from finite fault modeling (red) at two stations are shown on two columns on the right as examples. The first column is for station LVZ and the second column for station CTAO. Displacement components of the east-west (E), north-south (N) and vertical (Z) directions are shown, from top to bottom. Figure. Results of tsunami simulations using the slip distribution (Fig. ) of the 0 Mw.0 Tohoku-Oki earthquake obtained by the finite fault inversion using rupture velocity of. km/s. Synthetic tsunami waveforms are computed based on the

31 Page of slip distribution estimated from the teleseismic full seismic waveforms using the D global velocity model and the fault model based on the plate interface geometry model Slab.0. The subfault rupture duration time is assumed to be 0 s. (a) Distribution of DART buoy stations (Closed red rectangles with identification numbers) used in comparisons of the recorded tsunami heights with simulated ones. The red star indicates the epicenter of the earthquake. (b)-(e) Comparisons of the observed and synthetic tsunami height wave forms at DART-, -, - and - buoy locations, in the order of increasing distance from the epicenter. (f) Variation of the maximum amplitude misfits as the observed minus the simulated ones, at the four DART buoy stations. The misfits are plotted in the order of increasing distance from the epicenter to each DART buoy station. Stations,, are located in the northeast azimuthal path from the epicenter. Station, enclosed in a box of dotted line, is located in the southeast azimuthal path from the epicenter. Figure. Results of tsunami simulations using the slip distribution (Fig. ) of the 0 Mw.0 Tohoku-Oki earthquake obtained by the finite fault inversion using rupture velocity of. km/s. Explanations on the figure are the same as those given in Fig..

32 Page of Geophysical Journal International REFERENCES Ammon, C.J., Ji, C., Thio, H.K., Robinson, D., Ni, S., Hjorleifsdottir, V., Kanamori, H., Lay, T., Das, S., Helmberger, D., Ichinose, G., Polet, J. & Wald, D., 00. Rupture process of the 00 Sumatra-Andaman earthquake, Science,, -. Ammon, C.J., Lay, T., Kanamori, H. & Cleveland, M., 0. A rupture model of the 0 off the Pacific coast of Tohoku Earthquake, Earth, Planets and Space,, -. Bassin, C., Laske, G. & Masters, G., 000. The Current Limits of Resolution for Surface Wave Tomography in North America, EoS,. Clawpack Development Team, 0. Clawpack software. Duputel, Z., Rivera, L., Kanamori, H., Hayes, G.P., Hirshorn, B. & Weinstein, S., 0. Real-time W phase inversion during the 0 off the Pacific coast of Tohoku Earthquake, Earth, Planets and Space,, -. Fritz, H.M., 0. Insights on the 00 South Pacific tsunami in Samoa and Tonga from field surveys and numerical sumulation, Earth-Science Reviews, 0, -. Fujii, Y. & Satake, K., 0. Slip Distribution and Seismic Moment of the 00 and 0 Chilean Earthquakes Inferred from Tsunami Waveforms and Coastal Geodetic Data, Pure and Applied Geophysics, 0, -0. Fujii, Y., Satake, K., Sakai, S.i., Shinohara, M. & Kanazawa, T., 0. Tsunami source of the 0 off the Pacific coast of Tohoku Earthquake, Earth, Planets and Space,, -0. Gica, E., Spillane, M.C., Titov, V.V., Chamberlin, C.D. & Newman, J.C., 00. Development of the forecast propagation database for NOAA's Short-Term Inundation Forecast for Tsunamis (SIFT). in NOAA Technical Memorandum OAR PMEL.National Oceanic and Atmospheric Administration (NOAA). Gusman, A.R., Murotani, S., Satake, K., Heidarzadeh, M., Gunawan, E., Watada, S. & Schurr, B., 0. Fault slip distribution of the 0 Iquique, Chile, earthquake estimated from ocean-wide tsunami waveforms and GPS data, Geophysical Research Letters,, 0GL00. Gusman, A.R., Tanioka, Y., Sakai, S. & Tsushima, H., 0. Source model of the great 0 Tohoku earthquake estimated from tsunami waveforms and crustal deformation data, Earth and Planetary Science Letters,, -. Hartzell, S. & Heaton, T.,. Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the Imperial Valley, California, earthquake, Bulletin of Seismological Society of America,, -. Hayes, G., 0a. M. - near the east coast of Honshu, Japan: Finite Fault.USGS National Earthquake Information Center. Hayes, G.P., 0b. Rapid source characetrization of the 0 Mw.0 off the Pacific Coast of Tohoku earthquake, Earth Planets Space,, -. Hayes, G.P., Wald, D.J. & Johnson, R.L., 0. Slab.0: A three-dimensional model of global subduction zone geometries, Journal of Geophysical Research,. Ji, C., Wald, D.J. & Helmberger, D.V., 00. Source Description of the Hector Mine, California, Earthquake, Part II: Complexity of Slip History, Bulletin of the Seismological Society of America,, 0-.

33 Page of Koketsu, K., Yokota, Y., Nishimura, N., Yagi, Y., Miyazaki, S.i., Satake, K., Fujii, Y., Miyake, H., Sakai, S.i., Yamanaka, Y. & Okada, T., 0. A unified source model for the 0 Tohoku earthquake, Earth and Planetary Science Letters,, -. Kustowski, B., Ekström, G. & Dziewoński, A.M., 00. Anisotropic shear-wave velocity structure of the Earth's mantle: A global model, Journal of Geophysical Research,. Lay, T., Ammon, C.J., Hutko, A.R. & Kanamori, H., 00a. Effects of Kinematic Constraints on Teleseismic Finite-Source Rupture Inversions: Great Peruvian Earthquakes of June 00 and August 00, Bulletin of the Seismological Society of America, 00, -. Lay, T., Ammon, C.J., Kanamori, H., Koper, K.D., Sufri, O. & Hutko, A.R., 00b. Teleseismic inversion for rupture process of the February 00 Chile (Mw.) earthquake, Geophysical Research Letters,, L0. Lay, T., Ammon, C.J., Kanamori, H., Xue, L. & Kim, M., 0. Possible large neartrench slip during the 0Mw.0 off the Pacific coast of Tohoku Earthquake, Earth, Planets and Space,, -. Lay, T. & Bilek, S., 00. Anomalous Earthquake Ruptures at Shallow Depths on Subduction Zone Megathrusts. in The Seismic Zone of Subduction Thrust Faults, pp. -, eds. Dixon, T. H. & Moore, J. C. 00, New York. Lay, T., Kanamori, H., Ammon, C.J., Koper, K.D., Hutko, A.R., Ye, L., Yue, H. & Rushing, T.M., 0. Depth-varying rupture properties of subduction zone megathrust faults, Journal of Geophysical Research,. Lay, T., Kanamori, H., Ammon, C.J., Nettles, M., Ward, S.N., Aster, R.C., Beck, S.L., Bilek, S.L., Brudzinski, M.R., Butler, R., DeShon, H.R., Ekström, G., Satake, K. & Sipkin, S., 00. The Great Sumatra-Andaman Earthquake of December 00, Science,, -. Lay, T., Yue, H., Brodsky, E.E. & An, C., 0. The April 0 Iquique, Chile,Mw. earthquake rupture sequence, Geophysical Research Letters,, -. Lee, S.-J., Huang, B.-S., Ando, M., Chiu, H.-C. & Wang, J.-H., 0. Evidence of large scale repeating slip during the 0 Tohoku-Oki earthquake, Geophysical Research Letters,, L. MacInnes, B.T., Gusman, A.R., LeVeque, R.J. & Tanioka, Y., 0. Comparison of Earthquake Source Models for the 0 Tohoku Event Using Tsunami Simulations and Near-Field Observations, Bulletin of the Seismological Society of America, 0, -. Maercklin, N., Festa, G., Colombelli, S. & Zollo, A., 0. Twin ruptures grew to build up the giant 0 Tohoku, Japan, earthquake, Sci Rep,, 0. Newman, A.V., Hayes, G.P., Wei, Y. & Convers, J., 0. The October 00 Mentawai tsunami earthquake, from real-time discriminants, finite-fault rupture, and tsunami excitation, Geophysical Research Letters,, L0. Okada, Y.,. Internal deformation due to shear and tensile faults in a half-space, Bulletin of Seismological Society of America,, 0-0. Ozaki, T., 0. JMA s tsunami warning for the 0 great To- hoku earthquake and tsunami warning improvement plan, Journal of Disaster Research,, -. Poisson, B., Oliveros, C. & Pedreros, R., 0. Is there a best source model of the Sumatra 00 earthquake for simulating the consecutive tsunami?, Geophysical Journal International,, -.

34 Page of Geophysical Journal International Saito, T., Ito, Y., Inazu, D. & Hino, R., 0. Tsunami source of the 0 Tohoku- Oki earthquake, Japan: Inversion analysis based on dispersive tsunami simulations, Geophysical Research Letters,, L00G. Satake, K., Fujii, Y., Harada, T. & Namegaya, Y., 0. Time and Space Distribution of Coseismic Slip of the 0 Tohoku Earthquake as Inferred from Tsunami Waveform Data, Bulletin of the Seismological Society of America, 0, -. SIFT Overview, 0. NOAA Tsunami Forecasting System SIFT Overview, pp. - 0National Oceanic and Atmospheric Administration. Simons, M., Minson, S.E., Sladen, A., Ortega, F., Jiang, J., Owen, S.E., Meng, L., Ampuero, J.P., Wei, S., Chu, R., Helmberger, D.V., Kanamori, H., Hetland, E., Moore, A.W. & Webb, F.H., 0. The 0 magnitude.0 Tohoku-Oki earthquake: mosaicking the megathrust from seconds to centuries, Science,, -. Suzuki, W., Aoi, S., Sekiguchi, H. & Kunugi, T., 0. Rupture process of the 0 Tohoku-Oki mega-thrust earthquake (M.0) inverted from strong-motion data, Geophysical Research Letters,, L00G. Tajima, F., Mori, J. & Kennett, B.L.N., 0. A review of the 0 Tohoku-Oki earthquake (Mw.0): Large-scale rupture across heterogeneous plate coupling, Tectonophysics,, -. Tang, L., Titov, V.V., Bernard, E.N., Wei, Y., Chamberlin, C.D., Newman, J.C., Mofjeld, H.O., Arcas, D., Eble, M.C., Moore, C., Uslu, B., Pells, C., Spillane, M., Wright, L. & Gica, E., 0. Direct energy estimation of the 0 Japan tsunami using deep-ocean pressure measurements, Journal of Geophysical Research,. Tappin, D.R., Grilli, S.T., Harris, J.C., Geller, R.J., Masterlark, T., Kirby, J.T., Shi, F., Ma, G., Thingbaijam, K.K.S. & Mai, P.M., 0. Did a submarine landslide contribute to the 0 Tohoku tsunami?, Marine Geology,, -. Tromp, J., Komatitsch, D. & Liu, Q., 00. Spectral-Element and Adjoint Methods in Seismology, Communications in Computational Physics,, -. Tsushima, H., Hirata, K., Hayashi, Y., Tanioka, Y., Kimura, K., Sakai, S.i., Shimohara, M., Kanazawa, T., Hino, R. & Maeda, K., 0. Near-field tsunami forecasting using offshore tsunami data from the 0 off the Pacific coast of Tohoku earthquake, Earth, Palnets, and Space,, -. Ulutas, E., 0. Comparison of the seafloor displacement from uniform and nonuniform slip models on tsunami simulation of the 0 Tohoku Oki earthquake, Journal of Asian Earth Sciences,, -. Wei, Y., Chamberlin, C., Titov, V., Tang, L. & Bernard, E., 0. Modeling of the 0 Japan Tsunami: Lessons for Near-Field Forecast, Pure and Applied Geophysics, 0, -. Wei, Y., Chamberlin, C., Titov, V.V., Tang, L. & Bernard, E.N., 0. Modeling of the 0 Japan Tsunami: Lessons for Near-Field Forecast, Pure and Applied Geophysics. Wei, Y., Newman, A.V., Hayes, G.P., Titov, V.V. & Tang, L., 0. Tsunami Forecast by Joint Inversion of Real-Time Tsunami Waveforms and Seismic or GPS Data: Application to the Tohoku 0 Tsunami, Pure and Applied Geophysics,, -0. Whitmore, P.M., 00. Chapter in The Sea. in Tsunami warning systems, pp. Harvard University Press, Cambridge, MA London, England.

35 Page of Yoshida, Y., Ueno, H., Muto, D. & Aoki, S., 0. Source process of the 0 off the Pacific coast of Tohoku Earthquake with the combination of teleseismic and strong motion data, Earth, Planets and Space,, -. Yue, H., Lay, T., Li, L., Yamazaki, Y., Cheung, K.F., Rivera, L., Hill, E.M., Sieh, K., Kongko, W. & Muhari, A., 0. Validation of linearity assumptions for using tsunami waveforms in joint inversion of kinematic rupture models: Application to the 00 MentawaiMw. tsunami earthquake, Journal of Geophysical Research: Solid Earth, 0, -. Yue, H., Lay, T., Rivera, L., Bai, Y., Yamazaki, Y., Cheung, K.F., Hill, E.M., Sieh, K., Kongko, W. & Muhari, A., 0. Rupture process of the 00 Mw. Mentawai tsunami earthquake from joint inversion of near-field hr-gps and teleseismic body wave recordings constrained by tsunami observations, Journal of Geophysical Research: Solid Earth,, -.

36 Page of Geophysical Journal International 0 0 Table. List of rupture velocities averaged from previous authors for selected megathrust events. For the 0 Tohoku-oki earthquake, the average rupture velocity of each reference was weighted by rupture propagation distances or times. Location Date M w Avg. V rup (km/s) Number of Authors List of Authors Tohoku-Oki, Lay et al. (0), Koper et al. (0), Lee et al. (0), Ammon et al. (0), Meng et al. (0), 0 Mar. Honshu Suzuki et al. (0) NE. Honshu (Tokachi) May.. Nagai et al. (00) Tokachi-Oki, Hokkaido 00 Sep.. Koketsu et al. (00), Yagi et al. (00), Yamanaka and Kikuchi (00), Honda et al. (00) Kuril 00 Nov. Sladen (00) Kuril 00 Jan.. Sladen (00) Michoacan, Mexico Sep.0. Mendoza and Hartzell () Lima-Peru Oct 0.0 Hartzell & Langer () Pisco-Peru 00 Aug. Ji & Zeng (00), Yagi (00), Yamanak (00), Pritchard & Fielding (00), Pritchard & Fielding (00), Lay et al. (00): 0% weight on Lay et al. (00)) Peru Nov.. Spence et al. (), Salichon et al. (00) Canama-Peru 00 Jun.. Kikuch & Yamanaka (00), Giovanni (00), Bileck & Ruff (00), Robinson et al. (00), Pritchard et al. (00), Lay et al. (00) Iquique-Chile 0 Apr 0.. Lay et al. (0), Yagi et al. (0), Gusman et al. (), Illapel-Chile 0 Sep.. Heidarzadeh et al. (0) Chile Mar 0. Mendoza et al. () Maule-Chile 00 Feb.. Lay et al. (00), Vigny et al. (0) Sumatra- Andaman 00 Dec.. Nias-Sumatra 00 Mar.. Ishii et al. (00) Mentawai- Sumatra 00 Oct.. Lay et al. (0), Yue et al. (0) Simple. Average Ammon et al. (00 & 00), Ishii et al. (00), Ji et al. (00), Rhie et al. (00), Yoshimoto et al (0)

37 Page of Figure. Distribution of varying-dip finite fault models constructed based on subduction-zone plate interface geometry model USGS Slab.0. There are subduction zones modeled: Alaska-Aleutian (ALU), Central America (MEX), Cascadia (CAS), Izu-Bonin (IZU), Kermadec-Tonga (KER), Kamchatka/Kurils/Japan (KUR), Philippines (PHI), Ryukyu (RYU), Santa Cruz Islands/Vanuatu/Loyalty Islands (VAN), Solomon Islands (SOL), South America (SAM), and they are assigned with white characters. The location of the modeled finite fault for each fault segment in this study is marked by a rectangle. The segments in each subduction zones are numbered in the order of increasing strike of the fault, in black characters (i.e. S0, S0, ). Each fault segment consists of subfaults defined by depths, strikes and dips at locations in longitudes and latitudes. The depths of the Slab.0 are represented by colored scale in km. The fault segment in which the 0 Tohoku-oki earthquake occurred is marked by an asterisk next to the segment number.

38 Page of Geophysical Journal International Figure. Comparison of observed broadband vertical component waveforms and synthetics by SEM in D PREM and D SANI velocity structures. The waveforms used for comparison are of the 0 March Mw. near-east-coast Honshu, Japan, earthquake (foreshock of the 0 March Mw.0 Tohoku-Oki, Japan earthquake). Stations of seismograms are ARU (.0 ), DGAR (. ) and GRFO (. ). The black traces are the observed seismograms, and the red traces are the synthetics computed in D (a) and D (b) structures using source parameters of GCMT solution (hypocenter of. latitude,. longitude, depth. km, with fault plane of strike, dip, rake ). Larger deviations are found for the synthetics in D model compared to D model.

39 Page of Figure. Locations of globally distributed seismic stations, for which the Green functions with sources at all modeled subfaults in subduction zones are calculated and stored in the database. The red squares are GSN, yellow are GEOSCOPE, black are GEOFON, and blue are MEDNET networks. Total number of stations is and corresponding total number of Green's functions is,,.

40 Page of Geophysical Journal International Figure. Synthetic test of the inversion process for a slip distribution on the varying-dip finite fault model with a constant strike based on Slab.0 in the D SANI velocity model. The fault model corresponds to the eastern Honshu segment (S0) in the KUR region (Fig. ). (a) Artificially designed slip distribution. (b) Inversion result of synthetic seismograms from the slip distribution in (a). The inset shows A-A vertical cross section of the fault with varyingdips in degree. W0~W0 indicate subfaults with numbers counting from the trench. The vertical and horizontal distances are in the same scale.

41 Page of Figure. Global locations of stations used in the exemplary finite fault inversion for 0 Tohoku Earthquake. The stations are located at epicentral distances - 0 and have relatively uniform azimuthal coverage.

42 Page of Geophysical Journal International Figure. Result of the finite fault inversion of the teleseismic full waveforms for the 0 Mw.0 Tohoku earthquake using the D SANI velocity model and the fault model based on Slab.0 with a constant strike (Segment S0 in KUR region). The global average rupture velocity of. km/s and subfault rupture duration time of 0 s were used. The resulting Mw was.0, and variance reduction was. %. Slip distribution with amplitudes and directions is represented by colors and arrows on the left side of the figure. The inset at the top-left corner is for the time variation of the moment rate function. The Inset at the bottom is explained in Fig.. Comparisons between the observation (black) and synthetic waveforms from finite fault modeling (red) at two stations are shown on two columns on the right as examples. The first column is for station LVZ and the second column for station CTAO. Displacement components of the east-west (E), north-south (N) and vertical (Z) directions are shown, from top to bottom.

43 Page of Figure. Result of the finite fault inversion of the teleseismic full waveforms for the 0 Mw.0 Tohoku earthquake using the D SANI velocity model and the fault model based on Slab.0 with a constant strike (Segment S0 in KUR region). The regional representative rupture velocity of. km/s and subfault rupture duration time of 0 s were used. The resulting Mw was.0, and variance reduction was.0 %. Slip distribution with amplitudes and directions is represented by colors and arrows on the left side of the figure. The inset at the top-left corner is for the time variation of the moment rate function. The Inset at the bottom is explained in Fig.. Comparisons between the observation (black) and synthetic waveforms from finite fault modeling (red) at two stations are shown on two columns on the right as examples. The first column is for station LVZ and the second column for station CTAO. Displacement components of the east-west (E), north-south (N) and vertical (Z) directions are shown, from top to bottom.

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45 Page of Figure. Results of tsunami simulations using the slip distribution (Fig. ) of the 0 Mw.0 Tohoku-Oki earthquake obtained by the finite fault inversion using rupture velocity of. km/s. Synthetic tsunami waveforms are computed based on the slip distribution estimated from the teleseismic full seismic waveforms using the D global velocity model and the fault model based on the plate interface geometry model Slab.0. The subfault rupture duration time is assumed to be 0 s. (a) Distribution of DART buoy stations (Closed red recatangles with identification numbers) used in comparisons of the recorded tsunami heights with simulated ones. The red star indicates the epicenter of the earthquake. (b)-(e) Comparisons of the observed and synthetic tsunami height wave forms at DART-, -, - and - buoy locations, in the order of increasing distance from the epicenter. (f) Variation of the maximum amplitude misfits as the observed minus the simulated ones, at the four DART buoy stations. The misfits are plotted in the order of increasing distance from the epicenter to each DART buoy station. Stations,, are located in the northeast azimuthal path from the epicenter. Station, enclosed in a box of dotted line, is located in the southeast azimuthal path from the epicenter.

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47 Page of Figure. Results of tsunami simulations using the slip distribution (Fig. ) of the 0 Mw.0 Tohoku-Oki earthquake obtained by the finite fault inversion using rupture velocity of. km/s. Explanations on the figure are the same as those given in Fig..

48 Page of Geophysical Journal International Supplementary Material Slip Distribution Results and Application to Tsunami Comparison of Slip Distribution with Finite Fault Modeling using Different Earth and Slab Models Finite fault modeling and inversion can be done with many different earth models and fault geometries. The most conventional methods of finite fault modeling make use of D earth model with single-dip fault model based on CMT solution. To test the effect of earth and fault geometry models on the finite fault inversion and tsunami simulation, the inversions are done for the four schemes corresponding to combinations of two velocity models and two fault geometry models. The two velocity models are D SANI (Dv) and D PREM (Dv). The two fault geometry models are varying-dip (Vdip) fault model with variable dips based on Slab.0 and single-dip fault model with a constant dip (Cdip) based on CMT solution (Fig. S). The constant-dip fault model based on the CMT is designed to be a simple rectangular plane with strike of 0 and dip of 0. Thus the four combinations of schemes for velocity models and fault geometry models are Dv-Vdip, Dv-Cdip, Dv-Vdip, and Dv-Cdip. Dv-Vdip scheme is shown in the main body of the article. The same global rupture rupture velocity of. km/s and smoothing of 0 % was applied to all four schemes. Characteristic features of the inversion results for the scheme of Dv-Vdip are described above, and the other three cases are as follows: () In the case for Dv-Vdip scheme, larger slips are distributed in the central upper part of the fault, but the area is a little narrower in strike direction and deeper than the case for Dv-Vdip (Fig. S). The maximum slip is m and the horizontal direction of subfault slips converge towards ESE direction. Moment magnitude is., smaller than the case of the Dv-Vdip.

49 Page of Two examples of waveform comparisons at stations LVZ and CTAO are shown in Fig. S. The variance reduction value is. %. () In the scheme of Dv-Cdip, most of subfault slip directs toward the east with maximum slip of m (Fig. S). The moment magnitude is.00 comparable to the case of Dv-Vdip. The waveform comparisons at stations LVZ and CTAO are shown also in Fig.. The variance reduction value is. %. () The slip distribution for the case of Dv-Cdip is confined to a relatively small area with elongated shape along the dipdirection (Fig. S). Slip directions are towards the east, which is similar to the case of Dv- Cdip. Maximum slip is m and the moment magnitude is., smaller than the case of Dv- Vdip. Two examples of waveform comparisons at stations LVZ and CTAO are shown along with the slip distribution in Fig. S. The variance reduction value is. %. The results of finite fault inversions for the four schemes show that the cases for D velocity model have much higher variance reduction values (. % of Dv-Vdip and. % of Dv- Cdip) compared to those of D velocity model (. % of Dv-Vdip and. % of Dv- Cdip). For the D velocity model it is not easy to choose the better one between the Dv-Vdip and Dv-Cdip schemes, since the difference (. %) of variance reduction values between them is not significant. However, for D velocity model, Dv-Vdip scheme of varying-dip case has significantly higher value than that of Dv-Cdip scheme of single-dip case. Thus we can conclude that the choice of D velocity model is generally most important, and the choice of the varying-dipfault model is the next in finite fault waveform inversion process for slip distribution. Application to Tsunami Simulation (Dv-Cdip, Dv-Vdip, Dv-Cdip Cases) The applicability tests of the each of the finite fault scheme s inversion results (Dv-Vdip, Dv-Cdip, Dv-Cdip in addition to Dv-Vdip) to tsunami simulations were done using the Clawpack..0 software. Each of the finite fault scheme used the same global rupture velocity

50 Page of Geophysical Journal International of. km/s, subfault rupture duration time of 0 s, and smoothing of 0 %. In the case for Dv- Vdip, the maximum amplitudes of simulated tsunami waves deviated from the observation in the range of 0. m 0. m. It underestimated the amplitudes at buoy # by 0. m, buoy # by 0. m, # by 0. m, and # by 0. m. For Dv-Cdip case, the simulated waves underestimated observation recorded at buoy # by 0. m, # by 0. m, # by 0. m, and overestimates the observation recorded at buoy # by 0. m. The maximum amplitudes of simulated tsunami waves for Dv-Cdip showed the largest deviation from the ones of observation. They underestimated the observation recorded at buoy # by m, # by 0. m, # by 0. m. However, the simulated tsunami wave at buoy # fit the amplitude of the observation. The deviation range of tsunami heights obtained from simulations using the finite fault inversion result for the scheme Dv-Vdip was the smallest among the four combination schemes of the velocity and fault models. Even though it was not easy to choose the best scheme in the seismic waveform inversion due to comparable variance reduction values for Dv-Vdip and Dv-Cdip cases, we found that the tsunami simulation based on the scheme Dv-Vdip predicts the observed tsunami in the best way. This may be due to Vdip slab model more accurately reflects the actual fault geometry than the Cdip. The applicability tests of the four finite fault inversion schemes using the regional rupture velocity of. km/s to tsunami simulations were also done (Fig. S). The results showed similar trend as the tests using the global rupture velocity. The maximum tsunami amplitudes of Dv-Vdip scheme deviated from the observation in the range of -0. m to -0.0 m. Dv- Cdip showed the deviation range of -0. m to 0. m. The Dv-Cdip s deviation range was - m ~ -0.0 m, and the Dv-Vdip scheme showed the deviation range of -0. m ~ -0. m, as mentioned in the main text. As in the tsunami application for the four finite fault inversion

51 Page 0 of schemes using the global rupture velocity of. km/s, the scheme Dv-Vdip showed the smallest deviation, and the Dv-Cdip showed the largest deviation from the observation. Magnitude Range for Application Since the current method proposed for a fast determination of slip distribution of megathrust earthquake in this study uses the fixed subfault size of 0 km x 0 km, the rupture area need to be larger than this size. In order to check minimum Mw magnitude applicable to the current method, the sizes of isolated slip patch of megathrust earthquakes with Mw magnitude range.~. were checked from published literatures: 00 Oct. Mw. Mentawai EQ; 0 Apr.0 Mw. Iquique EQ; 00 Apr.0 Mw. Solomon Island EQ; 00 Jun. Mw. Peruvian EQ; 0 Sept. Mw. Illapel EQ; 00 Nov. Central Kuril Island EQ. All of them have isolated slip patch size larger than 00 km x 0 km. However, the rupture area of the Mw. foreshock ( March 0) of the Mw.0 Tohoku mainshock ( March 0) is expected to be 0 km x 0 km (Koketsu et al., 00). Thus, the size of concentrated slip is expected to converge to a single subfault size of 0 km x 0 km at some Mw values between.0 and.. Therefore, it is recommended to apply the current inversion technique to earthquakes of Mw equal to or greater than about. in order to have characteristic spatial shapes of concentrated slip distributions with areas covering at least a few subfaults.

52 Page of Geophysical Journal International Reference Ammon, C.J., Ji, C., Thio, H.K., Robinson, D., Ni, S., Hjorleifsdottir, V., Kanamori, H., Lay, T., Das, S., Helmberger, D., Ichinose, G., Polet, J. & Wald, D., 00. Rupture process of the 00 Sumatra-Andaman earthquake, Science,, -. Ammon, C.J., Kanamori, H., Lay, T. & Velasco, A.A., 00a. The July 00 Java tsunami earthquake, Geophysical Research Letters,, L. Ammon, C.J., Lay, T., Kanamori, H. & Cleveland, M., 0. A rupture model of the 0 off the Pacific coast of Tohoku Earthquake, Earth, Planets and Space,, -. Ammon, C.J., Velasco, A.A. & Lay, T., 00b. Rapid estimation of first-order rupture characteristics for large earthquakes using surface waves: 00 Sumatra-Andaman earthquake, Geophysical Research Letters,. Avouac, J.-P., Meng, L., Wei, S., Wang, T. & Ampuero, J.-P., 0. Lower edge of locked Main Himalayan Thrust unzipped by the 0 Gorkha earthquake, Nature Geoscience. Banerjee, P., Pollitz, F., Nagarajan, B. & Burgmann, R., 00. Coseismic Slip Distributions of the December 00 Sumatra-Andaman and March 00 Nias Earthquakes from GPS Static Offsets, Bulletin of the Seismological Society of America,, S-S0. Banerjee, P., Pollitz, F.F. & Burgmann, R., 00. The Size and Duration of the Sumatra- Andaman Earthquake from Far-Field Static Offsets, Science,, -. Benavente, R. & Cummins, P.R., 0. Simple and reliable finite fault solutions for large earthquakes using the W-phase: The Maule (Mw=.) and Tohoku (Mw=.0) earthquakes, Geophysical Research Letters,, -. Chlieh, M., Avouac, J.P., Hjorleifsdottir, V., Song, T.R.A., Ji, C., Sieh, K., Sladen, A., Hebert, H., Prawirodirdjo, L., Bock, Y. & Galetzka, J., 00. Coseismic Slip and Afterslip of the Great Mw. Sumatra-Andaman Earthquake of 00, Bulletin of the Seismological Society of America,, S-S. Duputel, Z., Rivera, L., Kanamori, H., Hayes, G.P., Hirshorn, B. & Weinstein, S., 0. Realtime W phase inversion during the 0 off the Pacific coast of Tohoku Earthquake, Earth, Planets and Space,, -. Dziewonski, A.M. & Anderson, D.L.,. Preliminary reference Earth model, Physics of the Earth and Planetary Interiors,, -. Fritz, H.M., 0. Insights on the 00 South Pacific tsunami in Samoa and Tonga from field surveys and numerical sumulation, Earth-Science Reviews, 0, -. Fujii, Y. & Satake, K., 00. Tsunami Source of the 00 Sumatra-Andaman Earthquake Inferred from Tide Gauge and Satellite Data, Bulletin of the Seismological Society of America,, S-S0. Fujii, Y. & Satake, K., 0. Slip Distribution and Seismic Moment of the 00 and 0 Chilean Earthquakes Inferred from Tsunami Waveforms and Coastal Geodetic Data, Pure and Applied Geophysics, 0, -0. Fujimoto, H., 0. Seafloor Geodetic Approaches to Subduction Thrust Earthquakes, Monographs on Environment, Earth and Planets,, -. Gusman, A.R., Murotani, S., Satake, K., Heidarzadeh, M., Gunawan, E., Watada, S. & Schurr, B., 0. Fault slip distribution of the 0 Iquique, Chile, earthquake estimated from ocean-wide tsunami waveforms and GPS data, Geophysical Research Letters,, 0GL00. Hayes, G.P., Wald, D.J. & Johnson, R.L., 0. Slab.0: A three-dimensional model of global subduction zone geometries, Journal of Geophysical Research,. Ishii, M., Shearer, P.M., Houston, H. & Vidale, J.E., 00. Extent, duration and speed of the 00 Sumatra-Andaman earthquake imaged by the Hi-Net array, Nature,, -.

53 Page of Ji, C., Wald, D.J. & Helmberger, D.V., 00. Source Description of the Hector Mine, California, Earthquake, Part II: Complexity of Slip History, Bulletin of the Seismological Society of America,, 0-. Kanamori, H. & Rivera, L., 00. Source inversion of W phase: speeding up seismic tsunami warning, Geophysical Journal International,, -. Koketsu, K., Hikima, K., Miyazaki, S.i. & Ide, S., 00. Joint inversion strong motion and geodetic data for the source process of the 00 Tokachi-oki, Hokkaido, earthquake, Earth, Planets and Space,, -. Lay, T., Ammon, C.J., Hutko, A.R. & Kanamori, H., 00a. Effects of Kinematic Constraints on Teleseismic Finite-Source Rupture Inversions: Great Peruvian Earthquakes of June 00 and August 00, Bulletin of the Seismological Society of America, 00, -. Lay, T., Ammon, C.J., Kanamori, H., Koper, K.D., Sufri, O. & Hutko, A.R., 00b. Teleseismic inversion for rupture process of the February 00 Chile (Mw.) earthquake, Geophysical Research Letters,, L0. Lay, T., Ammon, C.J., Kanamori, H., Xue, L. & Kim, M., 0. Possible large near-trench slip during the 0Mw.0 off the Pacific coast of Tohoku Earthquake, Earth, Planets and Space,, -. Lay, T., Yue, H., Brodsky, E.E. & An, C., 0. The April 0 Iquique, Chile,Mw. earthquake rupture sequence, Geophysical Research Letters,, -. MacInnes, B.T., Gusman, A.R., LeVeque, R.J. & Tanioka, Y., 0. Comparison of Earthquake Source Models for the 0 Tohoku Event Using Tsunami Simulations and Near-Field Observations, Bulletin of the Seismological Society of America, 0, -. Newman, A.V., Hayes, G.P., Wei, Y. & Convers, J., 0. The October 00 Mentawai tsunami earthquake, from real-time discriminants, finite-fault rupture, and tsunami excitation, Geophysical Research Letters,, L0. Ozaki, T., 0. JMA s tsunami warning for the 0 great To- hoku earthquake and tsunami warning improvement plan, Journal of Disaster Research,, -. Piatanesi, A. & Lorito, S., 00. Rupture Process of the 00 Sumatra-Andaman Earthquake from Tsunami Waveform Inversion, Bulletin of the Seismological Society of America,, S-S. Poisson, B., Oliveros, C. & Pedreros, R., 0. Is there a best source model of the Sumatra 00 earthquake for simulating the consecutive tsunami?, Geophysical Journal International,, -. Rhie, J., Dreger, D., Burgmann, R. & Romanowicz, B., 00. Slip of the 00 Sumatra- Andaman Earthquake from Joint Inversion of Long-Period Global Seismic Waveforms and GPS Static Offsets, Bulletin of the Seismological Society of America,, S- S. Satake, K.,. Inversion of Tsunami Waveforms for the Estimation of a Fault Heterogeneity: Method and Numerical Experiments, Journal of Physics of the Earth,, -. Simons, M., Minson, S.E., Sladen, A., Ortega, F., Jiang, J., Owen, S.E., Meng, L., Ampuero, J.P., Wei, S., Chu, R., Helmberger, D.V., Kanamori, H., Hetland, E., Moore, A.W. & Webb, F.H., 0. The 0 magnitude.0 Tohoku-Oki earthquake: mosaicking the megathrust from seconds to centuries, Science,, -. Spillane, M.C., Gica, E., Titov, V.V. & Mofjeld, H.O., 00. Tsunameter network design for the U.S. DART arrays in the Pacific and Atlantic Oceans, ed Administration, U. S. D. o. C. N. O. a. A., Pacific Marine Environmental Laboratory, Seattle, WA.

54 Page of Geophysical Journal International Tang, L., Titov, V.V., Bernard, E.N., Wei, Y., Chamberlin, C.D., Newman, J.C., Mofjeld, H.O., Arcas, D., Eble, M.C., Moore, C., Uslu, B., Pells, C., Spillane, M., Wright, L. & Gica, E., 0. Direct energy estimation of the 0 Japan tsunami using deep-ocean pressure measurements, Journal of Geophysical Research,. Tromp, J., Komatitsch, D. & Liu, Q., 00. Spectral-Element and Adjoint Methods in Seismology, Communications in Computational Physics,, -. Tsushima, H., Hirata, K., Hayashi, Y., Tanioka, Y., Kimura, K., Sakai, S.i., Shimohara, M., Kanazawa, T., Hino, R. & Maeda, K., 0. Near-field tsunami forecasting using offshore tsunami data from the 0 off the Pacific coast of Tohoku earthquake, Earth, Palnets, and Space,, -. Wei, Y., Chamberlin, C., Titov, V., Tang, L. & Bernard, E., 0. Modeling of the 0 Japan Tsunami: Lessons for Near-Field Forecast, Pure and Applied Geophysics, 0, -. Wei, Y., Chamberlin, C., Titov, V.V., Tang, L. & Bernard, E.N., 0. Modeling of the 0 Japan Tsunami: Lessons for Near-Field Forecast, Pure and Applied Geophysics. Wei, Y., Newman, A.V., Hayes, G.P., Titov, V.V. & Tang, L., 0. Tsunami Forecast by Joint Inversion of Real-Time Tsunami Waveforms and Seismic or GPS Data: Application to the Tohoku 0 Tsunami, Pure and Applied Geophysics,, - 0. Yue, H., Lay, T., Rivera, L., Bai, Y., Yamazaki, Y., Cheung, K.F., Hill, E.M., Sieh, K., Kongko, W. & Muhari, A., 0. Rupture process of the 00 Mw. Mentawai tsunami earthquake from joint inversion of near-field hr-gps and teleseismic body wave recordings constrained by tsunami observations, Journal of Geophysical Research: Solid Earth,, -.

55 Page of Table S List of Previous Studies and Slip Dimension Author Year Slip Distribution Dimension Length (km) Width (km) Ammon et al Ide et al Fujii et al Koketsu et al. 0 0 Koper et al. 0 0 Lay et al Lee et al Lin et al Saito et al. 0 0 Shao et al. 0 0 Simons et al Suzuki et al Wei, S. et al. 0 0 Yoshida et al. 0 0 Yue and Lay USGS (Hayes, G) 0 00 Gusman et al Romano et al Yue and Lay Satake et al Bletery et al Satake and Fuji 0 0 Wei et al. 0 0? Average 0

56 Page of Geophysical Journal International Figure S. Comparison of two finite fault models with constant strikes in the eastern Honshu segment. The rectangular frame of solid line in black color represents the multi-dip finite fault

57 Page of model based on Slab.0 (S in KUR). The other rectangular frame with dots in orange color as subfault center points represents the single-dip fault model based on the CMT solution of the 0 Mw.0 Tohoku earthquake. The red star is for the epicenter location of the 0 Tohoku- Oki earthquake reported by USGS, and the black star is for the centroid location reported by global CMT. The inset shows the comparison of the two model s depth profiles. The piecewiselinear curved line in black color is for the fault plane trace of the multi-dip fault model, and the straight line in red color is for the fault plane of the single-dip fault model. The vertical and horizontal distances are in the same scale.

58 Page of Geophysical Journal International Figure S. Result of the finite fault inversion of the teleseismic full waveforms for the 0 Mw.0 Tohoku earthquake using the D velocity model (PREM) and the fault model based on Slab.0 with a constant strike (Segment S in KUR region). The global average rupture velocity of. km/s and subfault rupture duration time of 0 s were used. The resulting Mw was., and variance reduction was. %. Slip distribution with amplitudes and directions are represented by colors and arrows on the left side of the figure. The Inset at the top-left corner is for the time variation of the moment rate function. The inset at the bottom is explained in Fig.. Comparisons between the observation (black) and synthetic waveforms from finite fault modeling (red) are shown on two columns on the right as examples. The first column is for station LVZ and the second column for station CTAO. Displacement components of the eastwest (E), north-south (N) and vertical (Z) directions are shown, from top to bottom.

59 Page of Figure S. Result of the finite fault inversion of the teleseismic full waveforms for the 0 Mw.0 Tohoku earthquake using the D velocity model (SANI) and the single-dip fault model based on CMT solution. The global average rupture velocity of. km/s and subfault rupture duration time of 0 s were used. The resulting Mw was., and variance reduction was. %. Slip distribution with amplitudes and directions are represented by colors and arrows on the left side of the figure. The Inset at the top-left corner is for the time variation of the moment rate function. The inset at the bottom is explained in Fig.. Comparisons between the observation (black) and synthetic waveforms from finite fault modeling (red) are shown on two columns on the right as examples. The first column is for station LVZ and the second column for station CTAO. Displacement components of the east-west (E), north-south (N) and vertical (Z) directions are shown, from top to bottom.

60 Page of Geophysical Journal International Figure S. Result of the finite fault inversion of the teleseismic full waveforms for the 0 Mw.0 Tohoku earthquake using the D velocity model (PREM) and the single-dip fault model based on CMT solution. The global average rupture velocity of. km/s and subfault rupture duration time of 0 s were used. The resulting Mw was., and variance reduction was. %. Slip distribution with amplitudes and directions are represented by colors and arrows on the left side of the figure. The Inset at the top-left corner is for the time variation of the moment rate function. The inset at the bottom is explained in Fig.. Comparisons between the observation (black) and synthetic waveforms from finite fault modeling (red) are shown on two columns on the right as examples. The first column is for station LVZ and the second column for station CTAO. Displacement components of the east-west (E), north-south (N) and vertical (Z) directions are shown, from top to bottom.

61 Page 0 of Figure S. Result of the finite fault inversion of the teleseismic full waveforms for the 0 Mw.0 Tohoku earthquake using the D velocity model (PREM) and the fault model based on Slab.0 with a constant strike (Segment S in KUR region). The regional average rupture velocity of. km/s and subfault rupture duration time of 0 s were used. The resulting Mw was.0, and variance reduction was. %. Slip distribution with amplitudes and directions are represented by colors and arrows on the left side of the figure. The Inset at the top-left corner is for the time variation of the moment rate function. The inset at the bottom is explained in Fig.. Comparisons between the observation (black) and synthetic waveforms from finite fault modeling (red) are shown on two columns on the right as examples. The first column is for station LVZ and the second column for station CTAO. Displacement components of the east-west (E), north-south (N) and vertical (Z) directions are shown, from top to bottom.

62 Page of Geophysical Journal International Figure S. Result of the finite fault inversion of the teleseismic full waveforms for the 0 Mw.0 Tohoku earthquake using the D velocity model (SANI) and the single-dip fault model based on CMT solution. The regional average rupture velocity of. km/s and subfault rupture duration time of 0 s were used. The resulting Mw was., and variance reduction was. %. Slip distribution with amplitudes and directions are represented by colors and arrows on the left side of the figure. The Inset at the top-left corner is for the time variation of the moment rate function. The inset at the bottom is explained in Fig.. Comparisons between the observation (black) and synthetic waveforms from finite fault modeling (red) are shown on two columns on the right as examples. The first column is for station LVZ and the second column for station CTAO. Displacement components of the east-west (E), north-south (N) and vertical (Z) directions are shown, from top to bottom.

63 Page of Figure S. Result of the finite fault inversion of the teleseismic full waveforms for the 0 Mw.0 Tohoku earthquake using the D velocity model (PREM) and the single-dip fault model based on CMT solution. The regional average rupture velocity of. km/s and subfault rupture duration time of 0 s were used. The resulting Mw was., and variance reduction was. %. Slip distribution with amplitudes and directions are represented by colors and arrows on the left side of the figure. The Inset at the top-left corner is for the time variation of the moment rate function. The inset at the bottom is explained in Fig.. Comparisons between the observation (black) and synthetic waveforms from finite fault modeling (red) are shown on two columns on the right as examples. The first column is for station LVZ and the second column for station CTAO. Displacement components of the east-west (E), north-south (N) and vertical (Z) directions are shown, from top to bottom.

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65 Page of Figure S. Results of tsunami simulations using the slip distributions (Fig. S, S, S, ) of the 0 Mw.0 Tohoku-Oki earthquake obtained by the finite fault inversions using rupture velocity of. km/s. Synthetic tsunami waveforms are computed based on the slip distribution estimated from the teleseismic full seismic waveforms using the D (PREM) global velocity model and the fault model based on the plate interface geometry model Slab.0 (Dv-Vdip), D global velocity model and the single-dip fault model based on CMT solution (Dv-Cdip), D (SANI) global velocity model and the single-dip fault model based on CMT solution (Dv-Cdip), and D global velocity model and the fault model based on the plate interface geometry model Slab.0 (Dv-Vdip). The subfault rupture duration time is assumed to be 0 s. (a) Distribution of DART buoy stations (Closed red rectangles with identification numbers) used in comparisons of the recorded tsunami heights with simulated ones. The red star indicates the epicenter of the earthquake. (b)-(e) Comparisons of the observed and synthetic tsunami height wave forms at DART-, -, - and - buoy locations, in the order of increasing distance from the epicenter. (f) Variation of the maximum amplitude misfits as the observed minus the simulated ones, at the four DART buoy stations. The misfits are plotted in the order of increasing distance from the epicenter to each DART buoy station. Stations,, are located in the northeast azimuthal path from the epicenter. Station, enclosed in a rectangle of dotted line, is located in the southeast azimuthal path from the epicenter.

66 Page of Geophysical Journal International