Gutenberg–Richter B-Value Time Series Forecasting: A Weighted Likelihood Approach

Abstract

We introduce a novel approach to estimate the temporal variation of the b-value parameter of the Gutenberg–Richter law, based on the weighted likelihood approach. This methodology allows estimating the b-value based on the full history of the available data, within a data-driven setting. We test this methodology against the classical “rolling window” approach using a high-definition Italian seismic catalogue as well as a global catalogue of high magnitudes. The weighted likelihood approach outperforms competing methods, and measures the optimal amount of past information relevant to the estimation.