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[SCG60-P02] Characterization of Rake Angle Variation of Heterogeneous Source Models
Keywords:heterogeneous source model, rake angle, strong motion prediction
For scenario-based strong motion prediction, various source parameters such as fault length, width, strike, dip, rake, and rupture propagation velocity must be assumed in advance, in addition to the location of the target source fault. The Earthquake Research Committee of the Headquarters for the Earthquake Research Promotion (2017) has compiled a procedure for strong ground motion prediction method for earthquakes with specified source faults (strong motion prediction recipe). This procedure incorporates knowledge obtained by collecting and analyzing the results of source analyses of past earthquakes. For example, many studies have been published on the scaling of fault area, asperity area, and short-period level with respect to seismic moment. From these previous studies, the mean values of each source parameter and their variations have been obtained, and the effects of uncertainties in the source parameters on strong motion prediction have been discussed [e.g., Yamada et al. (2007), Hikita et al. (2015)]. Furthermore, in addition to spatial heterogeneity in the amount of slip, slip rate, and stress drop, spatial heterogeneities in rupture velocity and rake angle also affect the predicted strong ground motions [e.g., Iwaki et al. (2016)].
This study focuses on the heterogeneity of rake angle. The average rake angle to be set in the source fault model for strong motion prediction should be appropriately given based on information such as active fault evaluation, plate subduction direction, stress field, and so on. On the other hand, information for providing heterogeneity of rake angle as aleatory uncertainty is not necessarily well known. The Earthquake Research Committee (2017) also adds the caution that "if the rake angle is made constant across the fault, the directivity effect tends to be too pronounced in the strong motion prediction results," but does not mention any specific guidelines for providing spatial heterogeneity in rake angle. Graves and Pitarka (2010), one of the broadband strong motion prediction methods developed in the United States, suggests that the standard deviation of the rake angle be set to 15 degrees, but the basis for setting the standard deviation of the rake angle to 15 degrees is unclear.
We analyzed the standard deviation of the rake angle by collecting the results of source inversion analysis for earthquakes in Japan. The digital data of source models used in this study were collected from the publicly available databases of SRCMOD [Mai and Thingbaijam (2014)] and the National Research Institute for Earth Science and Disaster Prevention (NIED). As of the end of January 2023, we have collected 36 source models for 28 earthquakes. They include 23 models for 16 inland earthquakes, 12 models for 11 plate-boundary earthquakes, and 1 model for 1 intraslab earthquake. The moment magnitudes of these earthquakes range from 5.6 to 9.1.
The rake angles are distributed in a bounded interval of [-180°, 180°) and are cyclic. To obtain the sample mean and sample standard deviation of such angular data, it is necessary to use the method of circular statistics among directional statistics [e.g., Shimizu (2006, 2018), Arai (2011)]. First, the rake angle of each sub-fault is considered as a vector and weighted averaged by the slip amount to obtain a mean resultant vector. From the mean resultant length R, the standard deviation is given by (-2 log R)^0.5. For source models consisting of multiple fault segments with different rake angles, the mean and standard deviation of the slip angle are estimated for each fault segment. For example, in the case of the source model of the 2016 Kumamoto earthquake by Asano and Iwata (2016), the segment corresponding to the Hinagu fault had a mean slip angle of -164° with a standard deviation of 14°, and the segment corresponding to the Futagawa fault had a mean slip angle of -141° with a standard deviation of 19°.
The mean standard deviation of the rake angle for all earthquakes was 20° ± 5°, with no clear difference between the two earthquake types: 21° ± 5° for inland earthquakes and 18° ± 5° for plate-boundary earthquakes. Since the number of models included in the dataset is not very large, it is considered appropriate to give the mean value of 20°, which is the mean of the standard deviations of all the earthquakes, as the degree of heterogeneity of the slip angle at this time.
Acknowledgements: We used the digital data of the source models released from SRCMOD and NIED K-NET databases. We appreciated all of authors who made their source models available in those database.
This study focuses on the heterogeneity of rake angle. The average rake angle to be set in the source fault model for strong motion prediction should be appropriately given based on information such as active fault evaluation, plate subduction direction, stress field, and so on. On the other hand, information for providing heterogeneity of rake angle as aleatory uncertainty is not necessarily well known. The Earthquake Research Committee (2017) also adds the caution that "if the rake angle is made constant across the fault, the directivity effect tends to be too pronounced in the strong motion prediction results," but does not mention any specific guidelines for providing spatial heterogeneity in rake angle. Graves and Pitarka (2010), one of the broadband strong motion prediction methods developed in the United States, suggests that the standard deviation of the rake angle be set to 15 degrees, but the basis for setting the standard deviation of the rake angle to 15 degrees is unclear.
We analyzed the standard deviation of the rake angle by collecting the results of source inversion analysis for earthquakes in Japan. The digital data of source models used in this study were collected from the publicly available databases of SRCMOD [Mai and Thingbaijam (2014)] and the National Research Institute for Earth Science and Disaster Prevention (NIED). As of the end of January 2023, we have collected 36 source models for 28 earthquakes. They include 23 models for 16 inland earthquakes, 12 models for 11 plate-boundary earthquakes, and 1 model for 1 intraslab earthquake. The moment magnitudes of these earthquakes range from 5.6 to 9.1.
The rake angles are distributed in a bounded interval of [-180°, 180°) and are cyclic. To obtain the sample mean and sample standard deviation of such angular data, it is necessary to use the method of circular statistics among directional statistics [e.g., Shimizu (2006, 2018), Arai (2011)]. First, the rake angle of each sub-fault is considered as a vector and weighted averaged by the slip amount to obtain a mean resultant vector. From the mean resultant length R, the standard deviation is given by (-2 log R)^0.5. For source models consisting of multiple fault segments with different rake angles, the mean and standard deviation of the slip angle are estimated for each fault segment. For example, in the case of the source model of the 2016 Kumamoto earthquake by Asano and Iwata (2016), the segment corresponding to the Hinagu fault had a mean slip angle of -164° with a standard deviation of 14°, and the segment corresponding to the Futagawa fault had a mean slip angle of -141° with a standard deviation of 19°.
The mean standard deviation of the rake angle for all earthquakes was 20° ± 5°, with no clear difference between the two earthquake types: 21° ± 5° for inland earthquakes and 18° ± 5° for plate-boundary earthquakes. Since the number of models included in the dataset is not very large, it is considered appropriate to give the mean value of 20°, which is the mean of the standard deviations of all the earthquakes, as the degree of heterogeneity of the slip angle at this time.
Acknowledgements: We used the digital data of the source models released from SRCMOD and NIED K-NET databases. We appreciated all of authors who made their source models available in those database.