Reservoir Modeling Combining Geostatistics with Markov Chain Monte Carlo Inversion

We present a study on the inversion of seismic reflection data generated from a synthetic reservoir model. Our aim is to invert directly for rock facies and porosity of the target reservoir zone. We solve this inverse problem using a Markov chain Monte Carlo (McMC) method to handle the nonlinear, multi-step forward model (rock physics and seismology) and to provide realistic estimates of uncertainties. To generate realistic models which represent samples of the prior distribution, and to overcome the high computational demand, we reduce the search space utilizing an algorithm drawn from geostatistics. The geostatistical algorithm learns the multiple-point statistics from prototype models, then generates proposal models which are tested by a Metropolis sampler. The solution of the inverse problem is finally represented by a collection of reservoir models in terms of facies and porosity, which constitute samples of the posterior distribution.