MP Simulations Without Computing MP Statistics

In recent years, multiple-point simulation has become an invaluable tool to integrate geological concepts in subsurface models. However, due to the high CPU and RAM demand, its use is restricted to relatively small problems with limited structural complexity. Moreover, it only allows for the simulation of univariate fields. We present an alternative method that produces conditional realizations honoring the high-order statistics of uni- or multivariate training images. It is based on a sampling method introduced by Shannon (1948), strictly equivalent to the original method of Guardiano and Srivastava (1993), but that does not need to compute conditional probabilities and to store them. In the sampling process, we use a distance between data configurations that allows simulating both discrete and continuous variables. As a result, the simulation algorithm is drastically simplified and has more possibilities. Since nothing is stored, neighborhoods can have virtually any size. Moreover, the neighborhoods are not restricted to a template, making multiple-grids unnecessary. Multivariate data configurations can be considered, allowing to generate realizations presenting a given multivariate multiple-point dependence. In addition to having virtually no RAM requirement, the method is straightforward to parallelize. Hence it can produce very large and complex realizations.