Embracing Uncertainty in "Small Data" Problems: Estimating Earthquakes from Historical Anecdotes
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.
Cite
@article{arxiv.2106.07797,
title = {Embracing Uncertainty in "Small Data" Problems: Estimating Earthquakes from Historical Anecdotes},
author = {Nathan E. Glatt-Holtz and Ronald A. Harris and Andrew J. Holbrook and Justin A. Krometis and Yonatan Kurniawan and Hayden Ringer and Jared P. Whitehead},
journal= {arXiv preprint arXiv:2106.07797},
year = {2025}
}