Hamiltonian Monte Carlo in full waveform inversion

Jinji Li, Kristopher A. Innanen

Classical Markov Chain Monte Carlo (MCMC) methods, while widely used for Bayesian inference, often suffer from computational demands and inefficiencies, particularly when dealing with high-dimensional parameter spaces. However, the Hamiltonian Monte Carlo (HMC) approach represents a notable advancement in the field of Monte Carlo (MC) methods. By simulating Hamiltonian dynamics through numerical integration and incorporating a Metropolis acceptance step, HMC avoids the limitations of random walks typically associated with MCMC. This results in a decent acceptance rate, enabling more efficient parameter space exploration. Additionally, the ability to generate plausible model candidates during the integration process opens up access to the null space, which can be particularly valuable inversion problems such as full-waveform inversion (FWI) where the model space is complex and multidimensional. In this report, we delve into the fundamental workings of HMC, shedding light on its mechanics and advantages. We present results from numerical experiments that showcase the unique features of HMC. Our findings strongly suggest that HMC holds significant promise as a robust tool for improving uncertainty quantification in applications of FWI, where accurately characterizing uncertainties is crucial for obtaining reliable model estimates.