11:15 AM - 11:30 AM
[SSS06-09] Radiation-corrected empirical Green's function in slip inversion
Keywords:empirical Green's function, slip inversion, source process
Slip inversion is one of the useful methods to analyze source processes, which have the advantage of being able to estimate the detailed spatial and temporal slip distribution. In this method, the least square problem is solved for the slip amount at each time step and each spatial step to minimize the waveform misfit between the observed waveforms and the synthetic waveforms which are generated by convolving the Green’s functions and the source time functions. Therefore, we need to estimate the accurate Green’s functions for the slip inversion and there have been numerous efforts to accurately estimate Green’s functions. In the case of theoretical Green’s function that is calculated from a given velocity structure, detailed a priori information on seismic velocity structure is required (e.g. Bouchon, 1981; Takeo, 1985). In contrast, empirical Green’s function (EGF), which is obtained by utilizing the seismograms of nearby small earthquakes with similar focal mechanisms, requires the occurrence of such appropriate events nearby the target event (e.g. Hartzell, 1978). To release these strict constraints partially, we proposed “radiation-corrected EGF” by correcting the radiation patterns of the EGF seismograms (Fig. 1). In particular, based on the ray theory, we can calculate the theoretical radiation patterns of the target event and the EGF event. Then, using the ratio of the radiation patterns in each component at each station, we correct the amplitude of the EGF seismogram for each of P, SV, and SH waves.
The effectiveness of the radiation correction was confirmed by the simplest synthetic tests with a triangular source time function in our previous study. Therefore, in this study, we investigate the applicability of the radiation-corrected EGF to the multi-time-window method (Olson and Apsel, 1982; Hartzell and Heaton, 1983). As a first step in applying the radiation-corrected EGF to the multi-time window method, we solve inversion problems in a setting that the fault finiteness is negligible. Therefore, we consider only time steps for the inversion.
At first, we applied this radiation-corrected EGF and the conventional EGF to the real data to confirm the superiority of the radiation pattern correction. We investigated the reproductivity of the synthetic waveforms and the estimated moment using the observed waveforms of three Mw~5 class earthquakes: the 2007 Mw 5.0 Mie earthquake, the 2011 Mw 5.2 Hiroshima earthquake, and the 2016 Mw 4.8 Kumamoto earthquake. We used the underground KiK-net stations of the National Research Institute for Earth Science and Disaster Resilience (NIED) within the epicentral distance of 50 km from each of the target event. To calculate the radiation pattern, we estimated the take-off and incident angles by ray tracing in a horizontally-layered structure of the JMA2001 (Ueno et al., 2002) using the TauP package (Crotwell et al., 1999). As a result of the real data application, we confirmed that the better moment estimations with better waveform fittings can be obtained by the radiation-corrected EGF compared to the conventional method for the three cases.
Next, to investigate the validity of the results obtained in the real data application, we performed recovery tests of the source time functions. In these recovery tests, we verified the reproductivity of the estimated source time functions using theoretical waveforms calculated from given source time functions which were determined randomly under the same station distribution, focal mechanisms, and hypocenter location as three analyzed earthquakes in the real data application. The theoretical waveforms are calculated using the FK application (Zhu and Rivera, 2002) in the velocity structure of JMA2001. We made 1,000 randomly determined source time functions and solved the inversion problems with the radiation-corrected EGF and the conventional EGF for each given source time function. As a result of the recovery tests, for all samples, the results with the radiation-corrected EGF have better waveform fittings, better moment estimations, and better reproductivity of the source time functions than those with the conventional EGF for three earthquakes. In addition, we confirm that the inversion results are fairly stable regardless of the shape of the source time functions.
The effectiveness of the radiation correction was confirmed by the simplest synthetic tests with a triangular source time function in our previous study. Therefore, in this study, we investigate the applicability of the radiation-corrected EGF to the multi-time-window method (Olson and Apsel, 1982; Hartzell and Heaton, 1983). As a first step in applying the radiation-corrected EGF to the multi-time window method, we solve inversion problems in a setting that the fault finiteness is negligible. Therefore, we consider only time steps for the inversion.
At first, we applied this radiation-corrected EGF and the conventional EGF to the real data to confirm the superiority of the radiation pattern correction. We investigated the reproductivity of the synthetic waveforms and the estimated moment using the observed waveforms of three Mw~5 class earthquakes: the 2007 Mw 5.0 Mie earthquake, the 2011 Mw 5.2 Hiroshima earthquake, and the 2016 Mw 4.8 Kumamoto earthquake. We used the underground KiK-net stations of the National Research Institute for Earth Science and Disaster Resilience (NIED) within the epicentral distance of 50 km from each of the target event. To calculate the radiation pattern, we estimated the take-off and incident angles by ray tracing in a horizontally-layered structure of the JMA2001 (Ueno et al., 2002) using the TauP package (Crotwell et al., 1999). As a result of the real data application, we confirmed that the better moment estimations with better waveform fittings can be obtained by the radiation-corrected EGF compared to the conventional method for the three cases.
Next, to investigate the validity of the results obtained in the real data application, we performed recovery tests of the source time functions. In these recovery tests, we verified the reproductivity of the estimated source time functions using theoretical waveforms calculated from given source time functions which were determined randomly under the same station distribution, focal mechanisms, and hypocenter location as three analyzed earthquakes in the real data application. The theoretical waveforms are calculated using the FK application (Zhu and Rivera, 2002) in the velocity structure of JMA2001. We made 1,000 randomly determined source time functions and solved the inversion problems with the radiation-corrected EGF and the conventional EGF for each given source time function. As a result of the recovery tests, for all samples, the results with the radiation-corrected EGF have better waveform fittings, better moment estimations, and better reproductivity of the source time functions than those with the conventional EGF for three earthquakes. In addition, we confirm that the inversion results are fairly stable regardless of the shape of the source time functions.