Geostatistical Inversion Constrained to Multi-Point Statistical Information Derived from Training Images

In the petroleum industry, an accurate characterization of the reservoir in terms of facies distribution is essential for an optimized exploitation of its resources. Methods for geostatistical inversion often are framed within a variogram-based framework. Alternatively several methods for the integration of seismic data in facies models have been proposed, several of which rely on the construction of a facies probability cube by calibrating the seismic data with wells. This facies probability can be input into several well-known geostatistical algorithms to create a facies realization, including multi-point methods. However, the facies realizations do not necessarily match the original seismic amplitude (as is the aim for geostatistical inversion). The objective of this paper is to present a geostatistical methodology, based on a multi-point statistical technique to generate iteratively, facies realizations with the aim of matching the field seismic amplitude data in a physical sense, not merely in a probabilistic sense. The algorithm borrows ideas from the original geostatistical inversion technique but uses the probability perturbation method to iteratively improve an initial facies model to match the amplitude data. The method was applied to part of the Stanford VI dataset, a synthetic dataset mimicking a deltaic sand deposit.