Embracing Uncertainty in "Small Data" Problems: Estimating Earthquakes from Historical Anecdotes

TL;DR

This paper introduces a Bayesian framework to estimate the location and magnitude of historical earthquakes from sparse anecdotal data, improving seismic risk assessment for pre-instrumental events.

Contribution

It presents a novel Bayesian inference method tailored for small, anecdotal datasets to estimate earthquake parameters and uncertainties.

Findings

The 1852 Banda Sea earthquake is well-characterized with this method.

The 1820 south Sulawesi event may involve a dual fault rupture.

The framework effectively quantifies uncertainties in historical seismic estimates.

Abstract

Seismic risk estimates will be vastly improved with an increased understanding of historical (and pre-historical) seismic events. However the only existing data for these events is anecdotal and sparse. To address this we developed a framework based on Bayesian inference to estimate the location and magnitude of pre-instrumental earthquakes. We present a careful analysis of results obtained from this procedure which justifies the sampling algorithm, its convergence to the resultant posterior distribution, and yields estimates on uncertainties in the relevant quantities. Using a priori estimates on the posterior and numerical approximations of the Hessian, we demonstrate that the 1852 Banda Sea earthquake and tsunami is indeed well-understood given certain explicit hypotheses. Using the same techniques we also find that the 1820 south Sulawesi event may best be explained by a dual fault rupture, best attributed to the Kalatoa fault potentially conjoining the Flores thrust and Walanae/Selayar fault.