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.
Highlights
The Gutenberg–Richter law [1] represents the building block of modern seismology, widely adopted by seismologists to describe the relationship between the magnitude and frequency of seismic events [2]
Aki [8] and Utsu [16] show that the Gutenberg–Richter law corresponds to an exponential distribution, and the b-value can be estimated by the maximum likelihood (ML)
Four out of the six rolling windows we significantly outperformed by the weighted likelihood (WL) method, and in only one case the Bayes Factor considered were significantly outperformed by the WL method, and in only one case the provided weak evidence in favor of the competing benchmark
Summary
The Gutenberg–Richter law [1] represents the building block of modern seismology, widely adopted by seismologists to describe the relationship between the magnitude and frequency of seismic events [2]. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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