High-Order Block Support Spatial Simulation Method and Its Application at a Gold Deposit

Abstract

High-order sequential simulation methods have been developed as an alternative to existing frameworks to facilitate the modeling of the spatial complexity of non-Gaussian spatially distributed variables of interest. These high-order simulation approaches address the modeling of the curvilinear features and spatial connectivity of extreme values that are common in mineral deposits, petroleum reservoirs, water aquifers, and other geological phenomena. This paper presents a new high-order simulation method that generates realizations directly at the block support scale conditioned to the available data at point support scale. In the context of sequential high-order simulation, the method estimates, at each block location, the cross-support joint probability density function using Legendre-like splines as the set of basis functions needed. The proposed method adds previously simulated blocks to the set of conditioning data, which initially contains the available data at point support scale. A spatial template is defined by the configuration of the block to be simulated and related conditioning values at both support scales, and is used to infer additional high-order statistics from a training image. Testing of the proposed method with an exhaustive dataset shows that simulated realizations reproduce major structures and high-order relations of data. The practical intricacies of the proposed method are demonstrated in an application at a gold deposit.