Introduction

Well log data provide information about petrophysical and elastic properties of the subsurface but do not necessarily cover all possible scenarios of interest that we could encounter away from well control. To account for plausible variations in the subsurface, we may decide, for example, to stretch a shale interval or increase or reduce the clay content in the sand. One way of implementing such perturbations is to use statistical simulations. Such simulations should be based on realistic spatial distributions of a single property (e.g., porosity) as well as account for deterministic or statistical relations between two or more properties (e.g., between clay content and porosity).

Assume, for example, that we wish to simulate different geological scenarios for a clastic reservoir by changing the porosity values. Also assume that the probability distribution of porosity is known, and then sample from this distribution a porosity value at each point in depth. At two adjacent locations in the borehole, if we sample independently (i.e., we draw a random sample for the first location and then the second random sample for the second location independently of the value we drew at the first location), we may obtain a very high value of porosity at the first location and a very low value at the second location, or vice versa. Such independent random sampling ignores the spatial continuity expected in porosity variations according to depositional and sedimentological laws. Similarly, if we want to simulate clay content, we cannot simulate it independently from the previously obtained values of porosity, since porosity variations can depend on mineralogical variations in sand and clay content. Hence, proposed rock properties should be correlated in space and also with other properties.