A statistic model for segmented lengths of seismogenic fault system

Abstract

Gamma distribution is used to fit Kumamoto's data of fault lengths by proper choice of two parameters a and β for“ Maxlen model” and a and b for“ Segment model”. The parameter α (or b) serves as a scale parameter but a change inα (or a) depends on the shape of the distribution curve. When a Maxlen model is segmented into k parts, approximate Maxlen-Segment relations α ∼ ka and β ∼ b hold good; this implies both the mean and variance are approximately proportional to k. Assuming that the fault movement is seismogenic, the earthquake magnitude can be converted from the fault length. Such converted magnitude is governed by a distribution law similar to the modified Gutenberg-Richter law proposed by Utsu.