Minimum sample size for detection of Gutenberg-Richter's b-value

Abstract

In this study we address the question of the minimum sample size needed for distinguishing between Gutenberg-Richter distributions with varying b-values at different resolutions. In order to account for both the complete and incomplete parts of a catalog we use the recently introduced angular frequency magnitude distribution (FMD). Unlike the gradually curved FMD, the angular FMD is fully compatible with Aki's maximum likelihood method for b-value estimation. To obtain generic results we conduct our analysis on synthetic catalogs with Monte Carlo methods. Our results indicate that the minimum sample size used in many studies is strictly below the value required for detecting significant variations.