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[SSS11-29] Distribution of Aftershock Hypocenters Relative to Fault Plane for Probabilistic Seismic Hazard Analysis Based on Fourier Spectru
Keywords:probabilistic seismic hazard analysis, aftershock, strong ground motions
1.Introduction
Probabilistic seismic hazard analysis based on the Fourier spectrum was theoretically developed and its specific calculation method was proposed by Nagao et al. (Journal of JSCE, 2005) and Yamada (Doctoral dissertation from Tottori University, 2011). Compared to the general probabilistic seismic hazard analysis using distance attenuation relationships, which are used worldwide and focus only on the response acceleration/velocity of a single-degree-of-freedom system corresponding to a specific period or the peak motions, the analysis based on the Fourier spectrum enables rigorous consideration of the frequency characteristics, duration, and total energy of strong motions. Therefore, the analysis based on the Fourier spectrum is advantageous for discussing impact on structures.
However, the existing method of the probabilistic seismic hazard analysis based on the Fourier spectrum still has several problems. One of these problems is that hazard of aftershocks caused by great earthquakes has not been considered. The hazard curve of each frequency is calculated as accumulation of the annual exceedance probabilities of the Fourier amplitude of each earthquake. Therefore, whether aftershocks are included in the target events directly affects the level of calculated seismic hazard.
In order to conduct an appropriate analysis considering aftershocks, the spatial and magnitude distributions and the number of aftershocks are necessary. In probabilistic seismic hazard analysis based on the Fourier spectrum, rectangular faults are assumed for large earthquakes which are identifiable before the analysis. Therefore, it is convenient to simulate the spatial distribution of aftershock hypocenters relative to the assumed rectangular fault plane.
In this study, we evaluated the empirical distribution of aftershock hypocenters of the 2011 Tohoku earthquake as an example. Distributions were evaluated along-strike and -dip directions and the direction perpendicular to them. The number of aftershocks were evaluated by comparing the distributions of before and after the mainshock. Then the method to generate aftershocks for probabilistic seismic hazard analyses will be discussed.
2.Distribution after shock hypocenters of the 2011 Tohoku earthquake around the fault plane
First, we extracted seismic source data with Japan Meteorological Agency Magnitude MJ = 5.0 or larger which are meaningful for the hazard analysis, occurred near the source region of the 2011 Tohoku earthquake during the two periods: (1) From the date of the mainshock, March 11, 2011, to the end of December 2021, and (2) From March 11, 1998, to the end of December 2009 (Both periods are approximately 11 years and 10 months). The empirical spatial distribution relative to the assumed fault plane was evaluated in a Cartesian coordinate system, of which x-y plane includes the fault plane. The rectangular fault planes proposed by Geospatial Information Authority of Japan (composed of two planes) were used here. The spatial distributions are shown in the figure ((a) the upper panel: the dip direction, (b) the middle panel: rake direction, (c) the bottom panel: direction perpendicular to the fault plane). The coordinates were normalized so that the fault width (in dip direction) was 1. The distributions for the three directions differ from each other and have unique characteristics.
Pseudo Aftershock hypocenter locations can be generated based on the empirical spatial distribution in the dip direction and the direction perpendicular to the fault plane, while the locations in the rake direction are randomly set within a specified range for probabilistic seismic hazard analyses. Distribution of the number of aftershocks by magnitude range can be given by the actual distribution evaluated as the difference between before and after the 2011 Tohoku earthquake.
Probabilistic seismic hazard analysis based on the Fourier spectrum was theoretically developed and its specific calculation method was proposed by Nagao et al. (Journal of JSCE, 2005) and Yamada (Doctoral dissertation from Tottori University, 2011). Compared to the general probabilistic seismic hazard analysis using distance attenuation relationships, which are used worldwide and focus only on the response acceleration/velocity of a single-degree-of-freedom system corresponding to a specific period or the peak motions, the analysis based on the Fourier spectrum enables rigorous consideration of the frequency characteristics, duration, and total energy of strong motions. Therefore, the analysis based on the Fourier spectrum is advantageous for discussing impact on structures.
However, the existing method of the probabilistic seismic hazard analysis based on the Fourier spectrum still has several problems. One of these problems is that hazard of aftershocks caused by great earthquakes has not been considered. The hazard curve of each frequency is calculated as accumulation of the annual exceedance probabilities of the Fourier amplitude of each earthquake. Therefore, whether aftershocks are included in the target events directly affects the level of calculated seismic hazard.
In order to conduct an appropriate analysis considering aftershocks, the spatial and magnitude distributions and the number of aftershocks are necessary. In probabilistic seismic hazard analysis based on the Fourier spectrum, rectangular faults are assumed for large earthquakes which are identifiable before the analysis. Therefore, it is convenient to simulate the spatial distribution of aftershock hypocenters relative to the assumed rectangular fault plane.
In this study, we evaluated the empirical distribution of aftershock hypocenters of the 2011 Tohoku earthquake as an example. Distributions were evaluated along-strike and -dip directions and the direction perpendicular to them. The number of aftershocks were evaluated by comparing the distributions of before and after the mainshock. Then the method to generate aftershocks for probabilistic seismic hazard analyses will be discussed.
2.Distribution after shock hypocenters of the 2011 Tohoku earthquake around the fault plane
First, we extracted seismic source data with Japan Meteorological Agency Magnitude MJ = 5.0 or larger which are meaningful for the hazard analysis, occurred near the source region of the 2011 Tohoku earthquake during the two periods: (1) From the date of the mainshock, March 11, 2011, to the end of December 2021, and (2) From March 11, 1998, to the end of December 2009 (Both periods are approximately 11 years and 10 months). The empirical spatial distribution relative to the assumed fault plane was evaluated in a Cartesian coordinate system, of which x-y plane includes the fault plane. The rectangular fault planes proposed by Geospatial Information Authority of Japan (composed of two planes) were used here. The spatial distributions are shown in the figure ((a) the upper panel: the dip direction, (b) the middle panel: rake direction, (c) the bottom panel: direction perpendicular to the fault plane). The coordinates were normalized so that the fault width (in dip direction) was 1. The distributions for the three directions differ from each other and have unique characteristics.
Pseudo Aftershock hypocenter locations can be generated based on the empirical spatial distribution in the dip direction and the direction perpendicular to the fault plane, while the locations in the rake direction are randomly set within a specified range for probabilistic seismic hazard analyses. Distribution of the number of aftershocks by magnitude range can be given by the actual distribution evaluated as the difference between before and after the 2011 Tohoku earthquake.