A METHOD FOR RECONSTRUCTING HISTORICAL DESTRUCTIVE EARTHQUAKES USING BAYESIAN INFERENCE

Seismic hazard analysis aims to estimate human risk due to natural disasters such as earthquakes. To improve seismic hazard analysis, our group is focused on earthquake induced tsunamis and the use of statistical models to reconstruct historical earthquakes. Based on the estimated wave heights given in anecdotal historical descriptions, we created observational probability distributions to model the historically recorded observations, and constructed a prior distribution on the relevant earthquake parameters based on known seismicity of a given region. Then we used the software package GeoClaw, and a Metropolis-Hastings sampler to obtain a posterior distribution of earthquake parameters that most closely matches the historically recorded tsunami.

Our method was tested on two main events that occurred in 1820 and 1852 in central and eastern Indonesia respectively. The random walk Metropolis-Hastings sampler we employed appeared to recover the causal earthquake quite well, but the computational costs were prohibitive even though both scenarios we considered were relatively simple. To improve the sampling procedure, we have focused on advanced sampling techniques such as Hamiltonian Monte Carlo where the gradient of the forward model (Geoclaw) is required. This is problematic however as this gradient is not available computationally. To mitigate this problem, we make use of a linearized adjoint solver for the shallow water equations, and exact gradient calculations for the Okada earthquake rupture model, yielding a surrogate gradient that leads to improved sampling.