Coefficients of Matsuda's formula dependent on the locality and type of seismogenic fault

Abstract

Matsuda's formula connecting the seismogenic fault-length L with the earthquake magnitude M is expressed in the form of log L: -α +β M with the two coefficients α= 2.9 and β =0.6. In the previous volume of this journal, we proposed a new method for statistically estimating these coefficients on the assumption that the statistical distribution of log L can be transformed to that of M through the above formula with unknown values of α and β. In this study, the proposed method is applied to Kumamoto's data of the maximum and the segmented seismogenic fault-length, and then we estimate the respective values α MAX, β MAX, α SEG andβ SEG. The actual seismogenic fault rupture is possibly realized within the ranges of αSEG< α<αMAX andβ SEG< β < β MAX. Kumamoto's data file includes the type of fault such as reverse or lateral. The coefficient β is related to the seismic energy contribution to increasing fault length, so that its value is presumed to be larger for lateral-type faults than for reverse-type ones. Using Kumamoto's data file, we examine its fault-type dependency, and prove as a result our presumption is right.