Investigation of Scaling Relations by Using Database Composed of Inversion Models of Inland Crustal Earthquakes in Foreign Countries

We examined the scaling relations proposed in the previous studies (the 3-stage model; Leonard, 2014; Hanks and Bakun, 2008; Thingbaijam et al., 2017) by using the database composed of the source models of the inland crustal earthquakes (Mw4.5-8.0) which occurred in the foreign countries. At first, we trimmed the periphery of the source inversion models with the small slip, which would not affect the seismic moment. Then, we validated the scaling relations between length, width, fault area, average slip, and the seismic moment. The 3-stage (HERP, 2020) and 2-stage (Hanks and Bakun, 2008) scaling relations assuming the saturation of fault width and the 1-stage (Leonard, 2014; Thingbaijan et al., 2017) scaling relations assuming with self-similarity show more or less similar levels of agreements to the source parameters. We extracted asperities from the trimmed fault models, and we found the combined area of asperities was 23% of the trimmed fault area on average. We found that 22% (HERP, 2020) of the 3-stage scaling relation of the fault area shows best agreement to the combined area of asperities in the wide range of the seismic moment. The natural logarithmic residuals between the source parameters and the scaling relations of fault area and asperity area have a tendency to be smaller in the larger seismic moment (M0 > 1019 Nm), and the average and the standard deviation of the residuals of the 3-stage scaling relation and the one of Thingbaijam et al. (2017) are smaller than others. Furthermore, we selected the source models inverted from strong motions, and we validated the scaling relations by using the source parameters extracted from the selected source models. The natural logarithmic residuals of the selected models were not significantly different from those of the whole source models including models inverted from not only strong motions but also teleseismic data, InSAR data, and so on. Taking into account the correspondence of the dataset and the different schemes of the methods to estimate the scaling relations, we validated the scaling relations without Thingbaijam et al. (2017). It is found that the 3-stage scaling relation provided the smaller average and standard deviation of residuals at all stages in terms of both fault and asperity areas, and that the simple scaling relations of Leonard (2014) also provide similarly small residuals within the wide Mw range.