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Langevin Dynamics Markov Chain Monte Carlo Solution for Seismic Inversion
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 82nd EAGE Annual Conference & Exhibition, Oct 2021, Volume 2021, p.1 - 5
Abstract
Summary
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.
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