Statistical estimation of coefficients of Matsuda's formula connecting seismogenic fault-length with earthquake magnitude

Abstract

Matsuda's formula consists of the linear combination of log L and M, where L is the seismogenic fault-length and M the earthquake magnitude. The coefficients of this formula are determined in most cases by the least squares method applied to coseismically generated L and M data. In the present paper, however, we propose another method of calculating coefficients by using mutually independent L and M data, for example, L determined by geological surveys and M by historical documents of seismic damages. Such a method is available under the assumption that the statistical distribution of M of historical events is equal to that of M calculated from L through Matsuda's fomula.
The method proposed here is applied to Kumamoto's L and M data, and then we determine the coefficients regarding the whole land, the northeast (east of 138°E longitude) and the southwest (west of 138°E longitude) of Japan. We find as a result a statistically significant difference in coefficients between the northeast and the southwest of Japan. The difference may possibly imply the geological contrast that reverse faults are predominant in the northeast but lateral faults in the southwest.