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Examination of Averaged Stress Drop Equations Connecting Outer and Inner Fault Parameters for Strong Motion Prediction

Averaged stress drop equations are important in fault modeling for predicting strong ground motions, because they relate the outer and inner fault parameters in an asperity model. We examined several equations, including an equation of a circular crack by using the seismic moment, the area of the asperities, and the stress drop on the asperities. We compared the relationships between the seismic moment and the seismic fault area calculated by each equation with the existing empirical relationships, and concluded that the equation of a circular crack can be applied to small crustal and subduction plate-boundary earthquakes without surface breakings such as the May 1997 Kagoshima-ken-hokuseibu earthquake ( M W 6.1) and the 2003 Tokachi-oki earthquake ( M W 8.1). Most of the results showed that the equation of a circular crack can not be applied to large crustal or subduction plate-boundary earthquakes with surface breakings such as the 2016 Kumamoto earthquake ( M W 7.1) and the 2011 Tohoku earthquakes ( M W 9.0). This is because the equation of a circular crack was derived from the fault model without surface breakings. Our examinations showed that the stress drop equation by Fujii and Matsu’ura (2000) and the dynamic stress drop equation by Irie et al . (2011) for vertical strike-slip faults can be applied to the Kumamoto earthquake and that the dynamic stress drop equation by Dorjpalam et al . (2015) for thrust faults can be applied to the Tohoku earthquake.