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.

High-Order Sequential Simulation via Statistical Learning in Reproducing Kernel Hilbert Space

“…Other essential properties can be found in Stein and Shakarchi (2005). The concepts of reproducing kernel and positive definite function are from Berlinet and Thomas-Agnan (2004) with the modification of the range of kernel function to R.…”

“…The reason for introducing the concept of the positive definite function is that a reproducing kernel is equivalently a positive definite function (Berlinet and Thomas-Agnan 2004). Thus, in practical terms, constructing an RKHS is equivalent to defining a positive definite function.…”

Effects of High-Order Simulations on the Simultaneous Stochastic Optimization of Mining Complexes

“…High-Order Direct Block-Support Simulation Instead of simulating the entire deposit at the point support discretization, the work by de Carvalho et al [48] presents an alternative method that allows the generation of high-order simulations directly at the block scale. Assume is a realization of the RF ( ) at the block support scale, defined in the same domain ∈ , where represents the centroid of the block in This paper presents an application of the high-order direct block-support simulation method [48] used as an input to the simultaneous stochastic optimization of a simplified mine complex, using the framework proposed by Goodfellow and Dimitrakopoulos [6]. As a means of comparison, the same mine complex is optimized using simulations obtained with a second-order method.…”

“…This paper presents an application of the high-order direct block-support simulation method [48] used as an input to the simultaneous stochastic optimization of a simplified mine complex, using the framework proposed by Goodfellow and Dimitrakopoulos [6]. As a means of comparison, the same mine complex is optimized using simulations obtained with a second-order method.…”

Incorporating geological and equipment performance uncertainty while optimising short-term mine production schedules

“…Matamoros and Dimitrakopoulos [21] introduce a model that incorporates both geological and equipment performance uncertainty into an STMPS optimisation. Geostatistical simulations [9,[22][23][24] are coupled with historical equipment performance data to inform a model that aims to meet the monthly grade blending requirements while generating minable shapes that respect a pre-defined direction of mining. This work has four major drawbacks.…”