Bayesian inference based on algorithms: MH, HMC, MALA and Lip-MALA for prestack seismic inversion

Abstract

Seismic inversion for estimating elastic properties is a key technique for reservoir characterization after drilling. The choice of inversion method strongly influences the accuracy, efficiency, and reliability of results. Bayesian inference based on Markov Chain Monte Carlo (MCMC) algorithms provides a robust framework for incorporating data uncertainty and prior geological knowledge. In this study, we compare the performance of four inversion methods – Metropolis-Hastings (MH), Hamiltonian Monte Carlo (HMC), the Metropolis-Adjusted Langevin Algorithm (MALA), and its variant Lip-MALA – in prestack seismic inversion using both synthetic models and real data from an eastern Venezuelan hydrocarbon reservoir. Results indicate that gradient-based methods (HMC, MALA, Lip-MALA) outperform MH in velocity estimation, while density inversion remains more challenging. MH and MALA achieve shorter execution times, whereas HMC and Lip-MALA improve accuracy at higher computational cost. This analysis evaluates mean values and standard deviation (SD) estimates for P-wave velocity, S-wave velocity, and density, with quality assessed through correlation metrics, objective function behavior, seismic traces, and Root Mean Square Error (RMSE). A two-dimensional inversion with real data further demonstrates algorithms performance under complex geological conditions. The findings highlight trade-offs between accuracy and efficiency, providing practical guidelines for selecting inversion method in seismic reservoir characterization.