Analysis of Gutenberg-Richter b-value and mmax

Part II: Estimators for b-value

Abstract

This report is the second of a series of three which have the main goal to achieve a method to estimate the parameters b and mmax that are essential when Gutenberg-Richter law is used for seismic hazard assessment. This paper is devoted to analyze the estimators of b-value.

We give an estimator for the expected value of M( N ) and an exact and numerically stable variance

for it; M( N ) represents the ordered values (by size) of magnitude catalogue.

We go on the development of the theory of Kijko-Sellevoll functions, applying them to calculate generalized b estimators of the seismic catalogue.