9:45 AM - 10:00 AM
[SSS11-10] Spatial complexity characteristics of faut parameters based on self-similar models -Comparison of earthquake slip of Japan and all over the world-
Keywords:self-similar, spatial complexity, fault slip, wavenumber domain
1. Introduction
Earthquake source parameters such as slip and stress drop on fault planes have spatially variable distributions. One of the models considered the complexity of the fault parameters is the self-similar model in which the spatially inhomogeneous distribution is characterized in the wavenumber domain (Hanks, 1979). As for the self-similar model, it was shown theoretically and numerically that the far field displacements follow the ω-2 decay assuming the “k-square” model in which the slip spectrum decays as k-2 beyond the corner wavenumber (Andrews, 1980, 1981; Herrero and Bernard, 1994). The slip complexities of past earthquakes around the world were characterized using the wavenumber spectra (Somerville et al. 1999; Mai and Beroza, 2002). The characterized complexities were utilized for strong motion simulations and validated by comparison with observation records of earthquakes around the world, such as in the SCEC BBP project. However, only four earthquakes in Japan were used for their evaluations, and validations of the complexities on Japan earthquakes are insufficient. In this study, the slip complexities are evaluated using the self-similar model for many earthquakes in Japan.
2. Methods
Targets are 38 earthquakes in Japan occurred from 1923 to 2016, and we used 61 fault slip models published on SRCMOD (http://equake-rc.info/srcmod/). One-segment fault models are used, since our targets are two-dimensional spatial distributions. In this study, 23 crustal earthquakes, 13 interplate earthquakes, and 2 intraplate earthquakes are used respectively.
The complexity evaluation method is similar to Mai and Beroza (2002). 2-D Fourier transform are applied to the fault slips to obtain 2-D wavenumber spectra. Then their spectra are fitted to the von Karman autocorrelation functions using grid-search, and the correlation distances and the Hurst exponents are estimated. Specifically, the correlation distances ar and the Hurst exponents H are estimated from circular-averaged spectra. Next, the correlation distances ax and ay are estimated from along-strike spectra and downdip spectra respectively under conditions where H estimated from the circular-averaged spectra are fixed. These H, ax, and ay of earthquakes in Japan are compared with previous studies of earthquakes around the world. Differences between source types are also examined.
3. Results
Figure 1 shows the wavenumber spectra of all models.
Hurst exponents H estimated by circular-averaged spectra are independent of moment magnitude MW, and differences between source types are small. The median of H is 0.77 and close to H = 0.75 by Mai and Beroza (2002). Next, Correlation distances ax estimated by along-strike spectra have positive correlation with MW, and differences between source types are small. Linear regression results of log(ax) on MW for all earthquakes, crustal earthquakes, and interplate earthquakes respectively are almost the same as those of Mai and Beroza (2002). Therefore, the difference of H and ax characteristics between Japan and the world tends to be small.
Correlation distances ay estimated by downdip spectra have positive correlation with MW like ax. On the other hand, there are differences between source types, and the ay of interplate earthquakes are larger than that of crustal earthquakes. In addition, ay tends to be constant for MW 6 class or higher crustal earthquakes. The same tendency is also acknowledged for MW 8 class or higher interplate earthquakes. These may indicate the saturation of the fault width due to the thickness of the seismogenic layer. Based on these trends, ay are regressed for each source types with two segments of the following equation,
log(ay) = bMW + c (MW <= MWC)
log(ay) = bMWC + c (MW > MWC).
As a result, MWC, which is a break point, is 6.6 for crustal earthquakes and 8.4 for interplate earthquakes. These are consistent with the boundary between the 1st stage and the 2nd stage of 3-stage scaling relations by Irikura and Miyake (2001) and Tajima et al. (2013).
Earthquake source parameters such as slip and stress drop on fault planes have spatially variable distributions. One of the models considered the complexity of the fault parameters is the self-similar model in which the spatially inhomogeneous distribution is characterized in the wavenumber domain (Hanks, 1979). As for the self-similar model, it was shown theoretically and numerically that the far field displacements follow the ω-2 decay assuming the “k-square” model in which the slip spectrum decays as k-2 beyond the corner wavenumber (Andrews, 1980, 1981; Herrero and Bernard, 1994). The slip complexities of past earthquakes around the world were characterized using the wavenumber spectra (Somerville et al. 1999; Mai and Beroza, 2002). The characterized complexities were utilized for strong motion simulations and validated by comparison with observation records of earthquakes around the world, such as in the SCEC BBP project. However, only four earthquakes in Japan were used for their evaluations, and validations of the complexities on Japan earthquakes are insufficient. In this study, the slip complexities are evaluated using the self-similar model for many earthquakes in Japan.
2. Methods
Targets are 38 earthquakes in Japan occurred from 1923 to 2016, and we used 61 fault slip models published on SRCMOD (http://equake-rc.info/srcmod/). One-segment fault models are used, since our targets are two-dimensional spatial distributions. In this study, 23 crustal earthquakes, 13 interplate earthquakes, and 2 intraplate earthquakes are used respectively.
The complexity evaluation method is similar to Mai and Beroza (2002). 2-D Fourier transform are applied to the fault slips to obtain 2-D wavenumber spectra. Then their spectra are fitted to the von Karman autocorrelation functions using grid-search, and the correlation distances and the Hurst exponents are estimated. Specifically, the correlation distances ar and the Hurst exponents H are estimated from circular-averaged spectra. Next, the correlation distances ax and ay are estimated from along-strike spectra and downdip spectra respectively under conditions where H estimated from the circular-averaged spectra are fixed. These H, ax, and ay of earthquakes in Japan are compared with previous studies of earthquakes around the world. Differences between source types are also examined.
3. Results
Figure 1 shows the wavenumber spectra of all models.
Hurst exponents H estimated by circular-averaged spectra are independent of moment magnitude MW, and differences between source types are small. The median of H is 0.77 and close to H = 0.75 by Mai and Beroza (2002). Next, Correlation distances ax estimated by along-strike spectra have positive correlation with MW, and differences between source types are small. Linear regression results of log(ax) on MW for all earthquakes, crustal earthquakes, and interplate earthquakes respectively are almost the same as those of Mai and Beroza (2002). Therefore, the difference of H and ax characteristics between Japan and the world tends to be small.
Correlation distances ay estimated by downdip spectra have positive correlation with MW like ax. On the other hand, there are differences between source types, and the ay of interplate earthquakes are larger than that of crustal earthquakes. In addition, ay tends to be constant for MW 6 class or higher crustal earthquakes. The same tendency is also acknowledged for MW 8 class or higher interplate earthquakes. These may indicate the saturation of the fault width due to the thickness of the seismogenic layer. Based on these trends, ay are regressed for each source types with two segments of the following equation,
log(ay) = bMW + c (MW <= MWC)
log(ay) = bMWC + c (MW > MWC).
As a result, MWC, which is a break point, is 6.6 for crustal earthquakes and 8.4 for interplate earthquakes. These are consistent with the boundary between the 1st stage and the 2nd stage of 3-stage scaling relations by Irikura and Miyake (2001) and Tajima et al. (2013).