A New Model for the Distribution of Observable Earthquake Magnitudes and Applications to $b$-value Estimation

TL;DR

This paper introduces a comprehensive model for earthquake magnitude distribution that improves $b$-value estimation by utilizing all available data and accounting for sensor network limitations and environmental variations.

Contribution

A novel, flexible model for observable earthquake magnitudes that enhances $b$-value estimation accuracy over traditional methods.

Findings

Model captures spatio-temporal variations in seismic data.

Significantly improves $b$-value estimates.

Accounts for sensor network coverage and limitations.

Abstract

The $b$-value in the Gutenberg-Richter (GR) law contains information that is essential for evaluating earthquake hazard and predicting the occurrence of large earthquakes. Estimates of $b$ are often based on seismic events whose magnitude exceed a certain threshold, the so called magnitude of completeness. Such estimates are sensitive to the choice of threshold and often ignore a substantial portion of available data. We present a general model for the distribution of observable earthquake magnitudes and an estimation procedure that takes all measurements into account. The model is obtained by generalizing previous probabilistic descriptions of sensor network limitations and by using a generalization of the GR law. We show that our model is flexible enough to handle spatio-temporal variations in the seismic environment and captures valuable information about sensor network coverage. We also show that the model leads to significantly improved $b$-value estimates compared with established methods relying on the magnitude of completeness.