A multi-scale blocking moving window algorithm for geostatistical seismic inversion. (April 2023) - Hu, Xun; Hou, Jiagen; Yin, Yanshu; Liu, Yuming; Wang, Lixin; Kang, Qiangqiang; Hou, Mingqiu
Abstract: Markov chain Monte Carlo (McMC) methods are suitable for solving the high-dimensional geostatistical seismic inverse problem. However, traditional McMC is impractical to generate desired lithofacies distribution since the repeated geostatistics and seismic forward simulators are very time-consuming. Recently, various strategies (e.g., the sequential geostatistical resampling (SGR) idea, multi-scale strategy, and annealing process) have been individually designed to alleviate the computational burden. However, the coordination between multiple corresponding key parameters (e.g., blocking window sizes, grid level, and temperatures) adds difficulties to combining multiple strategies with McMC. In this context, we propose a Multi-scale Blocking Moving Window algorithm (MsBMW) to effectively combines blocking McMC updating, a multi-scale strategy, and a new simulated annealing (SA) algorithm. In the iterative process, we monitor the mean acceptance rate (AR) to update window sizes, grid level, and temperatures, keeping the AR within the desired range (e.g., between 25% and 50%) for more efficient sampling. To assess the performance of the MsBMW, we tested it on the Standford VI synthetic reservoir. The standard Metropolis-Hastings (MH) sampling is performed to present the posterior probability density function (pdf) as the reference in this study. Compared with the Blocking Moving Window algorithm (BMW) proposed by Alcolea and Renard (2010), the MsBMW allows better quality results in less time. The results show that the multi-scale approach has the effect of accelerating the convergence of inversion. The adaptive cooling schedule circumvents the problem that the cooling rate is difficult to control in SA. Finally, we applied the proposed methodology to two-dimensional (2-D) and three-dimensional (3-D) real study areas and quickly generated multiple realizations that fit geological patterns, well data, and seismic data for uncertainty evaluation. Highlights: The proposed method effectively integrates blocking McMC updating, multi-scale, and adaptive cooling schedule strategies. The generated models are consistent with the expected geology, well data, and seismic data under Bayesian inversion. The proposed models' mean acceptance rate (AR) can be kept in the desired range for more efficient sampling.