Multiple-point simulations constrained by continuous auxiliary data

An important issue of using the multiple-point (MP) statistical approach for reservoir modeling concerns the integration of auxiliary constraints derived, for instance, from seismic information. There exist two methods in the literature for these non-stationary MP simulations. One is based on an analytical approximation (the "tau-model") of the conditional probabilities that involve auxiliary data. The degree of approximation with this method depends on the parameter tau, whose inference is difficult in practice. The other method is based on the inference of these conditional probabilities directly from training images. This method classifies the auxiliary data into a few classes. This classification is in general arbitrary and therefore inconvenient in practice, especially in the case of continuous auxiliary constraints. In this paper, we propose an alternative method for performing non-stationary MP simulations. This method accounts for the data support in the modeling procedure and allows, in particular, continuous auxiliary data to be integrated into MP simulations. This method avoids the major limitations of the previous methods, namely the use of an approximate analytical model and the reduction of the auxiliary data into a limited number of classes. This method can be easily implemented in the existing MP simulation codes. Numerical tests show good performance of this method both in reproducing the geometrical features of the training image and in honouring the auxiliary data.