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[SCG55-P10] A finite mixture model for inferring a fault network from hypocentral locations and focal mechanisms
Keywords:finite mixture model, fault configuration, fault geometry, fault network, 2016 Kumamoto earthquake
A large number of hypocenters and focal mechanism solutions (FMSs) are now determined from a vast amount of data from dense seismic networks. The hypocenters and FMSs play an important role in revealing configuration and geometries of subsurface faults (fault network) of a large earthquake. The fault network is usually determined by visual inspections using many depth cross sections, which is rather subjective. In this study, we newly developed a finite mixture model (FMM) in order to infer the fault network as objectively as possible. For simplicity, the faults of interest are assumed to be planes with a characteristic length of about 10 km, which is intended to use the resultant fault network for analysis of rupture processes or prediction of strong ground motion.
In our FMM, the density of earthquakes related to each fault is described with the Gaussian distributions along both strike and dip directions while the power-law distribution proposed by Powers and Jordan (2010, JGR; PJ10) is introduced for the fault-normal direction. In addition, a uniform distribution is used as one mixing component for uncorreltaed events, which are unlikely to be related to the fault network of interest. As input data, not only hypocentral locations but also FMMs are used. The choice of the number of mixture components (i.e., faults) is an important problem, and the slope heuristic method (Birge and Massart, 2007, Probab. Theory Relat. Fields; Maugis and Michel, 2011, ESAIM: Probability and Statistics) is utilized.
Gaussian mixture models have already been used by Ouillon et al. (2012, JGR; O12) and Meyer et al. (2019, J. Appl. Geophys.; M19) for delineating a fault network. In these previous studies, the FMSs were not fully used in the course of the inference. Specifically, O12 did not use the FMSs as input data. M19 used the FMSs to evaluate the inferred model but not to improve the solutions. In these studies, uncorrelated events were excluded before inferring a fault network. However, it should be noted that the problem of inferring the fault network can be regarded as a classification problem in which each earthquake is categorized into one of the mixing components. Hence, as done in our study, it is reasonable that uncorrelated events constitutes one of the categories of the classification problem to be considered. In these previous studies, the Gaussian distribution has been assumed for the fault normal direction, but PJ10 have shown that the power-law distibution explained the hypocentral distribution along the direction better than the Gaussian distribution. That is why we adopt the power-law distribution as mentioned above.
We apply the developed method to the aftershock data of the 2016 Kumamoto earthquake (Shito et al., 2020, Zisin). The appropriate number of faults is estimated to be six with the slope heuristic method, and the total number of the mxiture components is seven. The resultant model is compared with a fault model derived from geodetic (InSAR and GNSS) data (Yarai et al., 2016, J. Geospatial Inf. Auth. Jpn.). The comparison with the geodetic fault model is intended to perform a cross-check of fault models inferred from different kinds of data. We verify that our model generally agrees with the geodetic fault model, and find that a region with slip during the mainshock but few aftershocks are recognized as outside of the faults. Such overlooking should be resolved in future works.
Acknowledgement: This study is supported by MEXT through the project of Seismology toward Research Innovation with Data of Earthquake (STAR-E) [grant number JPJ010217].
In our FMM, the density of earthquakes related to each fault is described with the Gaussian distributions along both strike and dip directions while the power-law distribution proposed by Powers and Jordan (2010, JGR; PJ10) is introduced for the fault-normal direction. In addition, a uniform distribution is used as one mixing component for uncorreltaed events, which are unlikely to be related to the fault network of interest. As input data, not only hypocentral locations but also FMMs are used. The choice of the number of mixture components (i.e., faults) is an important problem, and the slope heuristic method (Birge and Massart, 2007, Probab. Theory Relat. Fields; Maugis and Michel, 2011, ESAIM: Probability and Statistics) is utilized.
Gaussian mixture models have already been used by Ouillon et al. (2012, JGR; O12) and Meyer et al. (2019, J. Appl. Geophys.; M19) for delineating a fault network. In these previous studies, the FMSs were not fully used in the course of the inference. Specifically, O12 did not use the FMSs as input data. M19 used the FMSs to evaluate the inferred model but not to improve the solutions. In these studies, uncorrelated events were excluded before inferring a fault network. However, it should be noted that the problem of inferring the fault network can be regarded as a classification problem in which each earthquake is categorized into one of the mixing components. Hence, as done in our study, it is reasonable that uncorrelated events constitutes one of the categories of the classification problem to be considered. In these previous studies, the Gaussian distribution has been assumed for the fault normal direction, but PJ10 have shown that the power-law distibution explained the hypocentral distribution along the direction better than the Gaussian distribution. That is why we adopt the power-law distribution as mentioned above.
We apply the developed method to the aftershock data of the 2016 Kumamoto earthquake (Shito et al., 2020, Zisin). The appropriate number of faults is estimated to be six with the slope heuristic method, and the total number of the mxiture components is seven. The resultant model is compared with a fault model derived from geodetic (InSAR and GNSS) data (Yarai et al., 2016, J. Geospatial Inf. Auth. Jpn.). The comparison with the geodetic fault model is intended to perform a cross-check of fault models inferred from different kinds of data. We verify that our model generally agrees with the geodetic fault model, and find that a region with slip during the mainshock but few aftershocks are recognized as outside of the faults. Such overlooking should be resolved in future works.
Acknowledgement: This study is supported by MEXT through the project of Seismology toward Research Innovation with Data of Earthquake (STAR-E) [grant number JPJ010217].