Markov-chain Monte Carlo Methods for Reconstructing Historical Earthquake-induced Tsunamis

In this work we explore methods for reconstructing historical tsunami events from anecdotal data. We use Markov chain Monte-Carlo (MCMC) methods in combination with various statistical models to construct a probability distribution on tsunami parameters for an event that occurred near south Sulawesi, Indonesia in 1820. After collecting nearly 80,000 samples from this distribution, we find that the Walanae fault best matches the anecdotal data, although we postulate that this particular earthquake and tsunami were caused by a simultaneous rupture of both the Walane fault and Flores thrust.

Exploring the posterior distribution for this scenario is inherently computationally expensive. To lessen this computational expense, we propose implementing a higher order MCMC sampler (Hamiltonian Monte Carlo) that uses the gradient of the tsunami models to determine where next to sample the distribution, theoretically speeding up convergence of the algorithm and yielding a better exploration of the sample space. In our current setting, computing the gradient is prohibitively expensive, so we discuss methods for using surrogate models with similar but easier-to-compute gradients.