A Markov Chain Monte Carlo approach for complex lava flow simulations driven by satellite-derived data

Abstract

We present a novel optimization strategy for the numerical simulation of lava flows that automatically find the best combination of input parameters to fit observed flows considering their uncertainties. The approach is based on the Metropolis algorithm, a Monte Carlo Markov Chain (MCMC) method that performs a sequence of simulations aiming to refine the sampling of unknown parameters to determine their probability distributions. Using this algorithm, we predict the most likely path of lava flows during ongoing eruptions, taking input parameters such as vent locations and Time Average Discharge Rates from satellite imagery. The approach has been validated against synthetic tests on an inclined plane and the 27 February–01 March 2017 eruption at Mt. Etna. This method is the first attempt to use a MCMC method for lava flow modeling, providing several advantages in constraining best-fit values in high-dimensional spaces with complex likelihood functions.