Fitting the Boolean parameters in a non-stationary case

Classically, the non stationary lithofacies distribution inside reservoirs is described by the 3D distribution of their proportions. This approach is very attractive because proportions have a physical meaning. Moreover their 3D distribution reflects the qualitative information coming from geology or the quantitative constraints derived from seismic attributes. In models such as the truncated gaussian, the proportions are directly used in the simulation process. In object-based models, such as the Boolean model, the problem is more complex because the proportions are the results of two sets of parameters: the object description (shape and dimensions) and their 3D distribution. The non stationarity in an object-based method can be reproduced either by using a non stationary object description or through a regionalized distribution of the objects. In this paper, we focus on the latter approach. The main contribution of the proposed method is the fact that the fit of the intensity point distribution is obtained globally in one computation step for any non stationary facies distribution. The interest is to constrain, a priori, the lithofacies simulation by a given 3D proportion distribution and not by convergence during the simulation process.