Relationships between moment magnitude and fault parameters: theoretical and semi-empirical relationships

Fault parameters are important in earthquake hazard analysis. In this paper, theoretical relationships between moment magnitude and fault parameters including subsurface rupture length, downdip rupture width, rupture area, and average slip over the fault surface are deduced based on seismological theory. These theoretical relationships are further simplified by applying similarity conditions and an unique form is established. Then, combining the simplified theoretical relationships between moment magnitude and fault parameters with seismic source data selected in this study, a practical semi-empirical relationship is established. The seismic source data selected is also to used to derive empirical relationships between moment magnitude and fault parameters by the ordinary least square regression method. Comparisons between semi-empirical relationships and empirical relationships show that the former depict distribution trends of data better than the latter. It is also observed that downdip rupture widths of strike slip faults are saturated when moment magnitude is more than 7.0, but downdip rupture widths of dip slip faults are not saturated in the moment magnitude ranges of this study.