arXiv subjects

Hayden Ringer

Publications and source records attributed to Hayden Ringer.

3 recordsLinked to original sources

arXiv2021

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

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.

stat.AP↗

arXiv2021

Analysis of Normal-Form Algorithms for Solving Systems of Polynomial Equations

We examine several of the normal-form multivariate polynomial rootfinding methods of Telen, Mourrain, and Van Barel and some variants of those methods. We analyze the performance of these variants in terms of their asymptotic temporal complexity as well as speed and accuracy on a wide range of numerical experiments. All variants of the algorithm are problematic for systems in which many roots are very close together. We analyze performance on one such system in detail, namely the 'devastating example' that Noferini and Townsend used to demonstrate instability of resultant-based methods.

math.NA↗

arXiv2020

Methodological reconstruction of historical seismic events from anecdotal accounts of destructive tsunamis: a case study for the great 1852 Banda arc mega-thrust earthquake and tsunami

We demonstrate the efficacy of a Bayesian statistical inversion framework for reconstructing the likely characteristics of large pre-instrumentation earthquakes from historical records of tsunami observations. Our framework is designed and implemented for the estimation of the location and magnitude of seismic events from anecdotal accounts of tsunamis including shoreline wave arrival times, heights, and inundation lengths over a variety of spatially separated observation locations. As an initial test case we use our framework to reconstruct the great 1852 earthquake and tsunami of eastern Indonesia. Relying on the assumption that these observations were produced by a subducting thrust event, the posterior distribution indicates that the observables were the result of a massive mega-thrust event with magnitude near 8.8 Mw and a likely rupture zone in the north-eastern Banda arc. The distribution of predicted epicentral locations overlaps with the largest major seismic gap in the region as indicated by instrumentally recorded seismic events. These results provide a geologic and seismic context for hazard risk assessment in coastal communities experiencing growing population and urbanization in Indonesia. In addition, the methodology demonstrated here highlights the potential for applying a Bayesian approach to enhance understanding of the seismic history of other subduction zones around the world.

physics.geo-ph↗