Choosing the Magnitude Range for Estimating the b-Value

Abstract

Modern seismological practice makes a wide use of the Gutenberg–Richter relation to describe the magnitude distribution. One of its parameters is the b-value (the slope of the earthquake recurrence curve in a log scale). This study proposes some new approaches to the problem of adequate and efficient statistical estimation of the parameter. We discuss the correct choice of the magnitude range over which the Gutenberg–Richter relation is a straight line to an acceptable degree of accuracy, and which should be used to estimate the b-value. We propose an efficient technique for incorporating discreteness and the grouping of magnitudes in earthquake catalogs (the method of maximum likelihood for discrete distributions). We discuss the problem of time-dependent variation for the lower threshold of complete earthquake reporting and propose a statistical approach to this variation.