Bayesian inference based on algorithms: MH, HMC, Mala and Lip-Mala for Prestack Seismic Inversion

Abstract. Seismic data inversion for estimating elastic properties is a crucial technique for characterizing reservoir properties post-drilling. The choice of inversion method significantly impacts results. Markov chain Monte Carlo (MCMC) algorithms enable Bayesian inference, incorporating seismic data uncertainty and expert information via prior distribution. This study compares the performance of four inversion methods—Metropolis-Hastings (MH), Hamiltonian Monte Carlo (HMC), and two Lagrangian Diffusion variants (MALA and Lip-MALA)—in prestack seismic inversion, using synthetic and real-world data from an eastern Venezuelan hydrocarbon reservoir. All four methods show acceptable performance but differ in specific strengths and weaknesses. Gradient-based methods (HMC, MALA, and Lip-MALA) outperform MH in velocity estimation. Density estimation is more challenging; MH and HMC yield unsatisfactory results, whereas MALA and Lip-MALA show promise. Execution time varies significantly: MH and MALA are substantially faster than HMC and Lip-MALA. Therefore, both accuracy and computational efficiency should be considered when choosing a method. The study evaluates the mean values ​​and standard deviations of the subsequent parameters: P-wave (V_p), S-wave velocity (V_S) and density (ρ). The quality of the MCMC sample is checked using correlations, objective function plots, seismic trace and Root Mean Square Error (RMSE) estimation. Acceptance rate and execution time assessments reveal HMC has the lowest acceptance rate, and MH the shortest execution time. Future research aims to extract additional elastic parameters and reservoir properties, enhancing subsurface understanding. Integrating well log conditioning into the model could improve vertical resolution near wells and align the model with well data at drilling locations.