In this abstract, we review the gradient-based Markov Chain Monte Carlo (MCMC) and demonstrate its applicability in inferring the uncertainty in seismic inversion. There are many flavours of gradient-based MCMC; here, we will only focus on the Unadjusted Langevin algorithm (ULA) and Metropolis-Adjusted Langevin algorithm (MALA). We propose an adaptive step-length based on the Lipschitz condition within ULA to automate the tuning of step-length and suppress the Metropolis-Hastings acceptance step in MALA. We consider the linear seismic travel-time tomography problem as a numerical example to demonstrate the applicability of both methods.
EAGE Conference and Exhibition
Computational Imaging

Izzatullah, M, van Leeuwen, T, & Peter, D. (2020). Langevin dynamics Markov Chain Monte Carlo solution for seismic inversion. In 82nd EAGE Annual Conference & Exhibition (pp. 1–5). doi:10.3997/2214-4609.202010496