Adaptive spatial resampling as a Markov chain Monte Carlo method for uncertainty quantification in seismic reservoir characterization

Seismic reservoir characterization aims to transform obtained seismic signatures into reservoir properties such as lithofacies and pore fluids. We propose a Markov chain Monte Carlo (McMC) workflow consistent with geology, well‐logs, seismic data and rock‐physics information. The workflow uses a multiple‐point geostatistical method for generating realizations from the prior distribution and Adaptive Spatial Resampling (ASR) for sampling from the posterior distribution conditioned to seismic data. Sampling is a general approach for assessing important uncertainties. However, rejection sampling requires a large number of evaluations of forward model, and is not efficient for reservoir modeling. Metropolis sampling is able to perform a reasonably equivalent sampling by forming a Markov chain. The ASR algorithm perturbs realizations of a spatially dependent variable while preserving its spatial structure by conditioning to subset points. The method is used as a transition kernel to produce a Markov chain of geostatistical realizations. These realizations are converted to predicted seismic data by forward modeling, to compute the likelihood. Depending on the acceptation/rejection criterion in the Markov process, it is possible to obtain a chain of realizations aimed either at characterizing the posterior distribution with Metropolis sampling or at calibrating a single realization until an optimum is reached. Thus the algorithm can be tuned to work either as an optimizer or as a sampler. The validity and applicability of the proposed method and sensitivity of different parameters is explored using synthetic seismic data.