Statistical rock physics: Combining rock physics, information theory, and geostatistics to reduce uncertainty in seismic reservoir characterization

Abstract

“Any physical theory is a kind of guesswork. There are good guesses and bad guesses. The language of probability allows us to speak quantitatively about some situation which may be highly variable, but which does have some consistent average behavior…. Our most precise description of nature must be in terms of probabilities.” —Richard Feynman This paper presents snapshots of current and emerging trends in applied statistical rock physics for reservoir characterization. By integrating fundamental concepts and models of rock physics, statistical pattern recognition, and information theory with seismic inversion and geostatistics, we can quantify and reduce uncertainties in reservoir management. Rock physics allows us to link seismic response and reservoir properties and to extend the available data to generate training data for the classification system. Seismic imaging brings indirect, but nevertheless spatially exhaustive, lateral and vertical information about reservoir properties that are not available from pinpoint well data. Classification and estimation methods based on computational statistical techniques such as nonparametric Bayesian classification, bootstrap, and neural networks help quantitatively measure interpretation uncertainty and the mis-classification risk at each spatial location. Geostatistical stochastic simulations add spatial correlation and small-scale variability which is hard to identify from seismic only because of the limits of resolution. Combining deterministic physical models with statistical techniques leads to new methods for interpretation and estimation of reservoir rock properties from seismic data. These formulations identify the most likely interpretation, the uncertainty of the interpretation, and guide quantitative decision analysis. Subsurface heterogeneity delineation is a key factor in reliable reservoir characterization. These heterogeneities occur at various scales and can include variations in lithology, pore fluids, clay content, porosity, pressure, and temperature. Some methods used in seismic reservoir characterization are purely statistical. Others are deterministic, based on physical models (theoretical, laboratory). Each group of techniques can have some …