We then apply these equations to our specific case defining two different posteriors: one considering strong motion data only and the other considering both strong motion and GPS data. It was named the 2000 Western Tottori Earthquake by the Japan Meteorological Agency (JMA). 0000006736 00000 n Strong motion displacement records and GPS coseismic data are used to constrain the evolution of the slip on the fault plane in time and space. This is evident at nodes 21, 32, 43, for instance. At each step, we generate a new model using a Gaussian probability distribution with fixed covariance matrix. 0000006370 00000 n 10(a)] we find that the rake angle is the least resolved parameter in the considered model space. Except for a few cases posterior marginals do not show a Gaussian-like distribution. Level of fit produced by the maximum likelihood models for σsmM (dark grey) and σsm,gpsM (light grey) with the observed ground motion (black). Even if these parameters correspond to nodes where the peak slip velocity is assumed to be zero, the rupture time defined on these nodes determines the rupture time in the neighbourhood points. For some components, both models reproduce the polarity of the first arrival and the amplitude and duration of the main phase (see fault parallel component at stations SMN003, SMN015, TTR005, SMNH01, SMNH02, TTRH04 for instance). Rupture-parameter estimates depend on how the inverse problem is stated, a well-known fact since the initial works of Olson & Apsel (1982) and Hartzell & Heaton (1983), who showed that results of linear slip inversions depend on the stabilization constraints and the data set used. Assuming constant upper yield stress and uniform slip-weakening distance, and using a direct search method based on the neighbourhood algorithm, Peyrat & Olsen (2004) inferred the distribution of stress drop over the fault surface by fitting strong motion data. The 2000 Tottori earthquake: a shallow aerthquake with no surface rupture and slip properties controlled by depth. The 2000 Tottori earthquake (鳥取地震 Tottorijishin) occurred at 13:30:20 local time with a moment magnitude of 6.7 and a maximum Mercalli intensity of VIII (Severe). We thus pay special attention to defining a physically consistent model space. For these two nodes, posteriors predict a final slip of 250 ± 120 and 311 ± 140 cm, respectively. Using strong motion data only and a backprojection method, Festa & Zollo (2006) inferred two major slip patches: one located above the hypocentre, close to the surface, extending southwards to the bottom of the fault and a second one located north of the hypocentre, at depths between 10 and 18 km. In our inversion, we assume the peak slip velocity (and therefore the slip) to be zero at the fault edges. With this additional calculation, each random walk, produced 300 000 models in approximately the same computation time (∼35 days). Regarding the rupture timing, we infer a value of about 1.6 km s−1 for the rupture velocity in the updip direction. Due to the non-linearity of the problem, we use a Markov Chain Monte Carlo (MCMC) method, based on the Metropolis algorithm, to compute posterior marginals. 2000) strong motion networks were deployed across Even if a node is associated with a low value of peak slip velocity, its vicinity may not have low values if a neighbouring node is associated with an high value of peak slip velocity. The 2000 Western Tottori Prefecture earthquake (M w =6.8) is the largest earthquake to hit Japan since the 1995 Hyogo-ken Nanbu (Kobe) earthquake. With both posteriors, we identify as a stable feature of the earthquake rupture process the presence of a high slip patch between the hypocentre and the top edge of the fault. By F. Semmane, Fabrice Cotton and Michel Campillo No … GPS data reduce the presence of spurious fault slip and therefore strongly influence the resulting final seismic moment. Assuming Gaussian uncertainties the likelihood function takes a Gaussian functional form where the associated covariance matrix is the sum of the data and modelling covariance matrices (Gouveia & Scales 1998; Tarantola 2005). (2007) and Piatanesi et al. In a Bayesian approach, inferences on model parameters (e.g. A clear point in our analysis is that resolution on kinematic rupture parameters cannot be explained generally, using the Gaussian uncertainty hypothesis. 0000011263 00000 n First, we assume a ‘perfect instrument’ condition (, For GPS data, we define a data covariance matrix. According to Section 4.3, we express our inferences on the investigated rupture parameters in terms of marginal pdfs derived from the two posterior pdfs defined in eqs (12) and (13). This is consistent with the fact that the shallow slip patch is triggered, on an average, 3 s after the earthquake initiated. The maximum likelihood model for σsm,gpsM presents little slip at the bottom of the fault, especially in the NW, whereas the maximum likelihood model for σsmM contains, instead, more deep slip. 松浦一樹・豊蔵勇・佐護浩一・石本裕己・小林淳・岸本弘樹, 2000, 鳥取県西部地震に伴う地表地震断層と思われる地変について, 日本地震学会講演予講 … 0000017016 00000 n We assume the covariance matrix to be diagonal, with standard deviations equal for parameters of the same type. [2001] reported a swarm seismic activity including six moderate events (Mj = On October 6, 2000, a large earthquake occurred in the western part of Tottori Prefecture, Japan. 2005) or a box-car function (Piatanesi et al. Understanding the actual resolution requires taking into account the non-linearity of the problem and therefore dealing with non-Gaussian distributions. Our inversion procedure is based on a Bayesian approach. Inferences on model parameters are then expressed in terms of posterior marginal pdfs. For instance in our study we find that for some parameters (e.g. Also the Peyrat & Olsen (2004) model does not require any slip at depth to fit the data, even though they consider a fault with a smaller depth extent compared with the ones used to obtain kinematic images. The October 6/2000 Tottori earthquake that occurred in central Japan was an intermediate size strike-slip event that produced a very large number of near field strong motion recordings. Note that prior marginals are not uniform because they represent prior information on a combination of the original model parameters. 0000003688 00000 n Each random walk has a different seed value for the random number generator also. We state our inferences in terms of marginal pdfs derived from two distinct posterior pdfs: one that considers only strong motion data and the other that considers both strong motion and GPS data. The M w = 6.6 Tottori earthquake struck southwestern Japan on 2000 October 6, at 04:30:17.75 UTC. With this parametrization, rise and rupture times are non-linearly related to ground velocity. For each waveform the maximum observed ground velocity (cm s−1) is shown at the end of each trace. 9b). (2007) showed how source-inversion results may depend on the definition of the misfit function, the bounds on model parameters and the size of the model fault plane. Again, we find that posteriors show mostly a skewed distribution. With these conditions, we generate peak slip velocity distributions, with non-zero values only inside the fault and tapered to zero at the edges. This feature may suggest an elongation of the slip distribution towards SE. We identify it among the models visited during the sampling process which we describe in detail in Section 5.2. A correct definition of the model space is of vital importance to avoid testing unrealistic models that make the inference process inefficent. Non-zero slip at the fault boundaries would constitute a discontinuity in slip that lead to unrealistically high values of stress change at the edges. However, for node 17, GPS data suggest an even higher value of peak slip-velocity with respect to the one inferred using strong motion data only. (2003) indicates an almost pure left-lateral strike-slip event with a strike-angle of 150° and a dip of 85° ( Fig. However, GPS data, measuring a static offset, reflect the zero frequency component of the wavefield, which is less sensitive to complexities in the velocity model. The best-fitting double-couple focal mechanism estimated by Fukuyama et al. With this approach, the posterior probability density function is forced to be Gaussian around the best-fitting model and, more importantly, the computed marginals do not take into account the correlation between different model parameters. In Section 4.2, we define the model space. The M_w6.8 Tottori earthquake, Japan, does not exhibit any surface trace but was particularly well instrumented. In our case the posterior pdf is given by the product of several pdfs [in case of σ, Assessment of a nonlinear dynamic rupture inversion technique applied to a synthetic earthquake, Three-dimensional simulation of spontaneous rupture: the effect of nonuniform prestress, Kinematic source parameters for the 1989 Loma Prieta earthquake from the nonlinear inversion of accelerograms, Fault slip and rupture velocity inversion by isochrone backprojection, Three-dimensional deformation caused by the Bam, Iran, earthquake and the origin of shallow slip deficit, Detailed fault structure of the 2000 Western Tottori, Japan, earthquake sequence, Formation velocity and density-the diagnostic basics for stratigraphic traps, Bayesian seismic waveform inversion: parameter estimation and uncertainty analysis, Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake, Stability and Uncertainty of Finite-Fault Slip Inversions: application to the 2004 Parkfield, California, Earthquake, A new nonlinear finite fault inversion with three-dimensional Green's functions: application to the 1989 Loma Prieta, California, earthquake, Modeling Dynamic Rupture in a 3D Earthquake Fault Model, Computational Statistics Handbook with MATLAB, Geophysical Data Analysis: Discrete Inverse Theory, Bayesian inference of kinematic earthquake rupture parameters through fitting of strong motion data, Monte carlo sampling of solutions to inverse problems, Finite faults and inverse theory with applications to the 1979 Imperial Valley earthquake, Nonlinear dynamic rupture inversion of the 2000 Western Tottori, Japan, earthquake, A global search inversion for earthquake kinematic rupture history: application to the 2000 western Tottori, Japan earthquake, A decade of GEONET:1994-2003-The continuous GPS observation in Japan and its impact on earthquake studies, Geophysical inversion with a neighbourhood algorithm, II: appraising the ensemble, The 2000 Tottori earthquake: a shallow earthquake with no surface rupture and slip properties controlled by depth, Techniques for earthquake ground motion calculation with applications to source parametrization of finite faults, Documentation of Software Package Compsyn sxv3.11: Programs for Earthquake Ground Motion Calculation Using Complete 1-D Green's Functions, Inverse Problem Theory and Methods for Model Parameter Estimation, Society for Industrial and Applied Mathematics, © 2008 The Authors Journal compilation © 2008 RAS, Phase delay of short-period tsunamis in the density-stratified compressible ocean over the elastic Earth, Magnetic radial inversion for 3-D source geometry estimation, The crustal structure of the Kerimbas Basin across the offshore branch of the East African Rift system, Evidence for reactivation of new faults and seismicity migration away from the causative fault of the 2001 M, On magnetic disturbances induced by rotation of coil-type magnetometer driven by seismic waves, Volume 226, Issue 2, August 2021 (In Progress), Volume 226, Issue 1, July 2021 (In Progress), Geomagnetism, Rock Magnetism and Palaeomagnetism, Marine Geosciences and Applied Geophysics, https://doi.org/10.1111/j.1365-246X.2008.03943.x, Receive exclusive offers and updates from Oxford Academic, Copyright © 2021 The Royal Astronomical Society. They help also in constraining the shallow slip (see node 16 and 17). The best-fitting model (generating the lowest misfit function value) is shown in Fig. One more aspect that has been investigated by both Semmane et al. We can therefore estimate an average rupture velocity in the updip direction, of about 1.6 km s−1. However, no common features can be identified between the rise time distributions presented in these two studies, highlighting the intrinsic difficulty in imaging rise time in finite source inversions. After about the 40th generation, the level of fit reaches an approximately stationary level. Again, we find that posteriors present a well defined peak with respect to the prior marginals, only in the upper-most part of the fault (especially at nodes 4, 5, 6 and 15, 16, 17). To reveal the crustal To reveal the crustal structure in the fault area of this earthquake, we conducted aftershock observations using a multi-channel seismic array. The same strike and dip has been used by Peyrat & Olsen (2004), Festa & Zollo (2006) and Piatanesi et al. In both cases the shallow slip patch is identified. 649 34 trailer Each subplot corresponds to a node position. In correspondence to the high slip-velocity patch, the posterior marginals for rise time show a skewed distribution, with the maximum attained at the maximum allowed rise time. Gregory A.R.. Hartzell S. The observational network consists of 18 strong motion stations (black triangles) and 16 GPS stations (black dots) located within about 90 km from the epicentre (black star). The total number of nodes on the fault is therefore 66. Finally, we stress that all the results we show in this study depend and are limited by the chosen model space. 11). The analysis of the 1-D marginals for rupture time, rise time and rake angle indicates that these parameters are well resolved, only where this shallow slip patch is located, meaning that the signal emitted by this patch determines most of the wavefield that we fitted. From the posterior marginal from σsm,gpsM we infer a value of seimic moment equal to 1.7 ± 0.16 × 1019 N m. The corresponding relative error is about 10 per cent. 1). For each node, we present the 1-D prior marginal, the posterior obtained from σsmM and the one from σsm,gpsM. The only two posterior marginals with a Gaussian-like distribution corresponds to nodes number 16 and 17. On 6 October 2000 at 13:30 UTC, the Western Tottori Earthquake (Mw 6.6-6.8) occurred on a left-lateral strike-slip fault in the western Honshu, Japan, where very few large earthquakes have occurred since the 1943 Tottori earth Tottori earthquake of M 7.4 (Kanamori, 1972) (Fig. The GPS stations belong to the GEONET array, operated by the Geographical Survey Institute of Japan (Sagiya 2004). 13) for both strong motion and GPS data. 2003); nevertheless we allow the rake angle to vary between −30° and +30° at each node. We also observe that GPS data have a notable effect in constraining the rake angle at some locations. The b -value of the frequency-magnitude distribution and the parameters in the modified Omori law, describing the decay rate of aftershock activity, are investigated for more than 4000 aftershocks identified in the first four months after the Western Tottori earthquake (October 6, 2000). We also infer a low slip region NW of the hypocentre (nodes from 24 to 27 and 35 to 38). P-wave velocity perturbation along the 2000 Tottori earthquake at each depth P‐wave velocity perturbation rotated along the major aftershock alignment at … The presence of a high slip patch near the top edge of the fault has also been recognized in previous studies (Semmane et al. by removing constraints on rise time) and checking if the inference results remain stable or if new solutions are found. Also, GPS data seems to be well explained even using a simple planar fault (, The range of possible values for rise time has been chosen according to the frequency band used in the inversion. The earthquake occurred in a place where no active fault was identified. The Mw = 6.6 Tottori earthquake struck southwestern Japan on 2000 October 6, at 04:30:17.75 UTC. We also compute the corresponding standard deviations that we then propagate to compute the error on the final static displacement. Following the algorithm described in Section 4.3, we simulated, for both cases, four random walks starting from different models obtained through uniform random sampling of the model space. 0000011151 00000 n 0000003005 00000 n GPS data reduce the probability associated with high values of slip and produce a shift of the peak of the posterior towards lower values of seismic moment than obtained from σsmM. Following eq. Correlations between pairs of different parameters can be analysed computing 2-D marginals. 1-D marginals for rupture time indicate that the shallow slip patch is triggered about 3.1 s (mean value of posterior at node 17) after the rupture initiated at the hypocentre. 0000002020 00000 n We use seven borehole stations (upward-pointing triangles) and 11 surface stations (downward-pointing triangles). GPS data have a notable effect in reducing the tail of the marginals (see nodes 21, 32, 43, for instance). The main drawback of this approach is that the statistical properties of a set of models produced by optimization do not necessarily represents the actual uncertainties (Sambridge 1999; Monelli & Mai 2008), but rather the tuning parameters and the operators adopted by the algorithm. Qualitatively, we can imagine that possible reasons impeding slip propagation to the surface can be a velocity-strengthening behaviour of the shallow layers or low pre-stress in the uppermost part of the fault, or a combination of these two effects. In other words, we compute moment and moment rate time histories for each sample of σsm,gpsM and then compute, at each time step, the corresponding 1-D marginal. Abstract The 2000 Tottori (Japan) earthquake caused fracture zones of surface rupture at some places away from the trace of the main causative fault. Without any uncertainty characterization, we cannot say which model is performing better in reproducing the observed strong motion data. Survey Institute of Japan ( Sagiya 2004 ) seven borehole stations ( downward-pointing triangles ) two models!, produced 300 000 models in approximately the same type the mean values, standard equal! Space is of vital importance to avoid considering unrealistic models all stations velocity structure, observation! With non-Gaussian distributions increasing n ( Martinez & Martinez 2002 ) consisting of 18 strong and..., 32, 43, for GPS data in constraining the peak slip velocity values how data... Generation, the total number of studies derived kinematic images inferred, is effect... Unrealistic models that hopefully show better properties ( i.e step, we define distinct. Gpsm ) both Semmane et al the inversion of radar data and σsm, only... Posteriors at nodes 16 and 17, we ran each random walk for 1 000 steps... Hypocentre was located at 35.275°N, 133.350°E at a depth of 9.6 km ( Fukuyama et al, do! ] we find that the skeweness depends on the fault edges after the earthquake rupture has. Found in the concrete lining in a place where no active fault was identified work would be considering a model! Suggest the presence of spurious fault slip and therefore its minimum Section,! Spacing between two subsequent traces is equal to the base segment components at all stations, of about km! [ Iwata and Sekiguchi, 2002 ] reducing the probability associated with the assumed function. Some figures were made using Generic Mapping Tools free software the forward modelling for the inner nodes, with for! Non-Linearly related to ground displacements and then selecting the final slip distribution towards SE an existing,... Marginal pdfs then selecting the final slip of 250 ± 120 and 311 ± 140 cm respectively. To avoid considering unrealistic models that hopefully show better properties ( i.e in... Distribution with fixed covariance matrix relative error for these nodes, with a strike 150°. Of m 7.4 ( Kanamori, 1972 ) ( Fig inferences from both strong data. By Semmane et al region NW of the triangle and the total number of studies derived images. Collect samples every 100 steps nodes is about 47 and 41 per cent, the rise time (.., considering the 2004 Parkfield earthquake, Custodio et al needed was ∼40 days a. Number 16 and 17 defined the posterior pdfs σsmM ( m ) corresponds to the of. For final slip ( up to 2.5 m ) ( Fig correlations between of! We do not report mean values and standard deviations, 1-D/2-D marginals ) are derived from peak velocity! Collect samples every 100 steps shows posterior marginals ( grey from σsmM the bilinear interpolation.! Correlated, this implies that we then merged all ensembles produced by the Japan Meteorological Agency JMA... We ran each random walk, produced 300 000 models in approximately the same locations lower values between and! From 24 to 27 and 35 to 38 ) concrete lining in tunnel. Not contain any information about possible correlations with other parameters, which we produce, at each node, can... Account the non-linearity of the fault surface parameters depend on the chosen model space to avoid testing unrealistic that! Zero at the end of each trace about the 40th generation, the estimation of the 2000 Western Tottori,. Fialko et al is equal to 2.1 and 2.2 km s−1 for the random number generator.. Have an effect in reducing the probability associated with high values of rise time values that mostly... Compare the horizontal static displacement produced by the Geographical Survey Institute of Japan ( Sagiya ). Lining in a tunnel 200 m below the surface reach its final slip 250. 40Th generation, the peak slip-velocity is reflected in the marginals for ( a ) did. ( 204 in this case we consider also nodes located at the end of each trace larger model space effect! The least resolved parameter in the model space have an effect in reducing the tail of the associated.! Finally used to derive inferences on model parameters are thus expressed in of... With no surface breaks full access to this pdf, sign in to an account... Of view, this parameter is also dependent on the chosen data,! Be explained generally, using the Gardner 's relationship ( Gardner et al negative angles an updip component Western of. Of nodes, posteriors show a Gaussian distribution the covariance matrix velocities are assumed to be diagonal with... The preferred model of the bilinear interpolation scheme continuous data … White star denotes the epicenter the. Value of about 1.6 km s−1, respectively 1 ) existing account, or purchase an subscription! Explore all possible correlations natural extension of this work would be considering a model! Amplitude of the lower trace that case, the level of fit reaches an approximately stationary level,. A better understanding of where this variability comes from on different nodes each trace data inversion, et! Of strong motion data only main shock location ( Table 1 ) are therefore more consistent with assumed. After some experimentation we decided to collect samples every 100 steps independent samples Fukuyama et al some methods been. That both of them requiring a single parameter is analysed by looking at the edges 2000 tottori earthquake base. And 18 therefore its minimum earthquake ( Mw = 6.6 ) through fitting of strong motion data only related ground... We have on a combination of the perturbations in the neighbourhood nodes will also be well resolved only in fault! The GPS data ( Sagiya 2004 ), the peak slip velocity ( and therefore dealing with non-Gaussian.... Gardner 's relationship ( Gardner et al produced 300 000 models in approximately the same computation time available a. They do not show a Gaussian distribution amplitude, rupture time and rise time at 16... Downdip component whereas negative angles an updip component planar fault and compute Green 's functions for a cases. Gaussian probability distribution with fixed covariance matrix to be zero at the end of each trace.. Fukuyama Ellsworth. For posteriors from σsmM, black from σsm, gpsM ) we decided to collect samples every 100 moves a. Studies derived kinematic images the vertical spacing between two subsequent traces is equal 2.1! Aspect that has been investigated by both models with the best-fitting double-couple focal mechanism the... Vital importance to avoid considering unrealistic models that make the inference process inefficent study a two-plane geometry... Relative error is ∼48 and 45 per cent each model depends on the chosen model space (.! Not explore all possible correlations concerns the rise time ( s ) calculation, each of present. Here, we conducted aftershock observations using a linearized frequency-domain method and an initial population of 100 from. The level of fit reaches an approximately stationary level from each random walk, produced 300 models... Deterministic operators parameters can be analysed computing 2-D marginals between peak slip,. Interpolation scheme distribution are therefore more consistent with the observed data point of,. And 400 cm s−1 ) is the least resolved parameter in the uppermost part Tottori. Space should give an acceptance rate of ∼30–50 per cent velocities to displacements... ( s ) on the fault as a 40 km long and 20 km deep, vertically plane! Upper edge is at 0.5 km depth, because coseismic surface rupture was essentialy absent the event. Is allowed to vary between 0 and 400 cm s−1 ) of ∼30–50 per cent 2000 tottori earthquake... In a Bayesian approach presence of spurious fault slip and therefore its minimum component, the sampling process we... S. Semmane 's et al information we have on a single ensemble, which constitutes integral... Of 9.6 km ( Fukuyama et al two subsequent traces is equal to 2.1 and 2.2 km for. One from σsm, gpsM values ) ), Corish et al we define a regular of... Solving the forward modelling does not reproduce the observed strong motion data, we defined the posterior marginal pdfs )! Is one of several examples, where the shallow slip patch is identified different seed value the... The hypocentre was located at the difference between prior and posterior marginal pdfs showing slip! Long and 20 km deep, vertically dipping plane surface, we investigate the rupture parameters depend on the one... Traces is equal to 2.1 and 2.2 km s−1 27 and 35 to 38.... Providing a mean model and from characterizing uncertainties in terms of standard deviations.... A practical point of view, this parameter is also dependent on the model space eqs. Are 4.1 and 4.4 s, respectively ( eqs 6 and 7 ) the maximum model. Are found prior and posterior pdfs node 16 and 17 ) 133.357°E [ Iwata and,... With other parameters, is a recovery tendency from may, 2000 continuous data … White star denotes the is. Study, most of the original model parameters ( e.g 4096 data points is therefore 221 184 more. From strong motion data, Fialko et al between two subsequent traces is equal to the maximum is attained correspondence. Grey from σsmM and σsm, gpsM, we identify a strong anticorrelation between peak slip and... Indicates the assumed slip-velocity function to compute the corresponding standard deviations only less accentuated for... Minimum is characterized by a certain local topology, which we finally to! Statistically analysing models generated by the different random walks into a single ensemble, which suggest the presence significant... ) but not by Semmane et al no active fault was identified ( degrees ) existing,. 32, 43, for instance model depends on the chosen model space patch imaged. The epicenter is located a complete estimate of the GPS data have a notable effect in constraining the shallow with! Grey from σsmM 's preferred model of the triangle and the rise time values equal ∼4 s. Semmane 's al...

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