Multiple‐point geostatistics for modeling subsurface heterogeneity: A comprehensive review

Abstract

For more than half a century, geostatistics has been developed and has increasingly been used for modeling subsurface heterogeneity. Traditionally, geostatistical simulations are based on a random function model defined according to the specificities of the geological formation under investigation. Unlike traditional geostatistics, multiple‐point (MP) geostatistics avoids the explicit definition of a random function but directly infers the necessary multivariate distributions from training images. This confers on MP geostatistics a potential applicability to any geological environment, provided that there is a training image representative of the geological heterogeneity and that the essential features of this training image can be characterized by statistics defined on a limited point configuration. This paper presents a comprehensive review of MP geostatistics. If the principle of MP geostatistics is straightforward and attractive, its industrial applicability largely depends on the implementation methods. The use of a search tree for storing MP statistics is a great step that made MP geostatistics actually applicable in industry. In the meantime, other methods such as multiple grids and image postprocessing are introduced and allow enhancing the reproduction of patterns observed in training images. Because of the sequential procedure, MP simulations can easily honor local hard data. There are methods available for constraining MP simulations to target global statistics (facies proportions) and also for integrating spatial auxiliary constraints that can tremendously improve the spatial features of MP simulations. Furthermore, both the gradual deformation method and the probability perturbation method are compatible with MP geostatistics and allow integrating hydrodynamic data into MP simulations. More recent developments of MP geostatistics include sequentially simulating patterns instead of points and using different geological scenarios (training images) for dynamic data inversion.