Multiple-point Statistics Simulations Accounting for Block Data

Multiple-point statistics methods allow to generate highly heterogeneous fields reproducing the spatial features within a given training image. Whereas punctual conditioning data can be handled straightforwardly, dealing with information defined at larger scales is challenging. Among multiple-point statistics techniques, the direct sampling method consists in successively simulating each node of the simulation domain by randomly searching in the training image for a compatible pattern with that retrieved in the simulation grid. In this work, we exploit the basic principle of the direct sampling to propose an extension of the method able to deal with block data, i.e. target mean values for given subsets of the simulation grid. The proposed method is able to account for overlapping block data of any geometry and of different sizes. The approach can be used in a range of applications, including for example downscaling. Examples are presented illustrating the simulation of log-permeability fields.