A Poisson model for earthquake frequency uncertainties in seismic hazard analysis

TL;DR

This paper proposes using Poisson models to better estimate uncertainties in earthquake frequency data, addressing limitations of Gaussian assumptions in seismic hazard analysis.

Contribution

It introduces a Poisson-based approach for modeling earthquake count uncertainties, improving the accuracy of seismic hazard assessments.

Findings

Poisson models fit earthquake count data better than Gaussian assumptions.

The method provides a straightforward way to estimate total event uncertainties.

Application to multiple catalogs demonstrates robustness and practicality.

Abstract

Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete and of unequal variance. In general, the observed number in any given magnitude range is described by a binomial distribution which, given a large total number of events of all magnitudes, approximates to a Poisson distribution for a sufficiently small probability associated with that range. In this paper, we examine four earthquake catalogues: New Zealand (Institute of Geological and Nuclear Sciences), Southern California (Southern California Earthquake Center), the Preliminary Determination of Epicentres and the Harvard Centroid Moment Tensor (both held by the United States Geological Survey). Using independent Poisson distributions to model the observations, we demonstrate a simple way of estimating the uncertainty on the total number of events occurring in a fixed time period.