Determining risk to human populations due to natural disasters has been a topic of interest in the STEM fields for centuries. Earthquakes and the tsunamis they cause are of particular interest due to their repetition cycles. These cycles can last hundreds of years but we have only had modern measuring instruments for the last century or so which makes analysis difficult. In this document, we explore ways to improve upon an existing method for reconstructing earthquakes from historical accounts of tsunamis. This method was designed and implemented by Jared P Whitehead's research group over the last 5 years. The issue of this method that we address is the relatively slow convergence. One reason for this slow convergence is caused by the random walk proposal step in the Markov Chain Monte Carlo (MCMC) sampling. We explore ways of constructing an approximate gradient of the model in order to apply a more robust MCMC Method called MALA that uses a gradient combined with some randomness to propose new samples. The types of approximate gradients we explore were a heuristic gradient, a data driven gradient and a gradient of a surrogate model. We chose to use the gradient of a simplified tsunami formula for our implementation. Our MALA algorithm under performed the previous random walk method which we believe implies that the simplified tsunami model didn't give sufficient information to guide the proposed samples in the optimal direction. Further experimentation would be needed to confirm this and we are confident that there are other ways we can improve our convergence as specified in the future work section. Our method is built into the existing Python package tsunamibayes. It is available, open-source, on GitHub: https://github.com/jwp37/tsunamibayes.



College and Department

Physical and Mathematical Sciences; Mathematics



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earthquake, tsunami, BYU, applied, math, mcmc, mala, statistics, bayesian