Block Simulation of Multiple Correlated Variables

Abstract

Numerical representations of multivariate natural phenomena, including characteristics of mineral deposits, petroleum reservoirs and geo-environmental attributes, need to consider and reproduce the spatial relationships between correlated attributes of interest. There are, however, only a few methods that can practically jointly simulate large size multivariate fields. This paper presents a method for the conditional simulation of a non-Gaussian vector random field directly on block support. The method is derived from the group sequential simulation paradigm and the direct block simulation algorithm which leads to the efficient joint simulation of large multivariate datasets jointly and directly on the block support. This method is a multistage process. First, a vector random function is orthogonalized with minimum/maximum autocorrelation factors (MAF). Blocks are then simulated by performing LU simulation on their discretized points, which are later back-rotated and averaged to yield the block value. The internal points are then discarded and only the block value is stored in memory to be used for further conditioning through a joint LU, resulting in the reduction of memory requirements. The method is termed direct block simulation with MAF or DBMAFSIM. A proof of the concept using an exhaustive data set demonstrates the intricacies and the performance of the proposed approach.