Quantifying multi-element and volumetric uncertainty, Coleman McCreedy deposit, Ontario, Canada

Goodfellow, Ryan; Consuegra, Francisco Albor; Dimitrakopoulos, Roussos; Lloyd, T A

doi:10.1016/j.cageo.2012.02.018

Cited by 25 publications

(13 citation statements)

References 9 publications

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“…Their main drawbacks are: (1) the high-order statistics are partially and indirectly considered; (2) the methods are not driven by a consistent mathematical framework; and (3) since they are TI-driven, they may not generate results that comply with the statistics of actual available data. The latter shortcoming becomes distinctly clear in mining applications, where dense data sets are used (Osterholt and Dimitrakopoulos 2007 ; Goodfellow et al 2012 ).…”

Section: Introductionmentioning

confidence: 99%

A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments

2018

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Multiple-point simulations have been introduced over the past decade to overcome the limitations of second-order stochastic simulations in dealing with geologic complexity, curvilinear patterns, and non-Gaussianity. However, a limitation is that they sometimes fail to generate results that comply with the statistics of the available data while maintaining the consistency of high-order spatial statistics. As an alternative, high-order stochastic simulations based on spatial cumulants or spatial moments have been proposed; however, they are also computationally demanding, which limits their applicability. The present work derives a new computational model to numerically approximate the conditional probability density function (cpdf) as a multivariate Legendre polynomial series based on the concept of spatial Legendre moments. The advantage of this method is that no explicit computations of moments (or cumulants) are needed in the model. The approximation of the cpdf is simplified to the computation of a unified empirical function. Moreover, the new computational model computes the cpdfs within a local neighborhood without storing the high-order spatial statistics through a predefined template. With this computational model, the algorithm for the estimation of the cpdf is developed in such a way that the conditional cumulative distribution function (ccdf) can be computed conveniently through another recursive algorithm. In addition to the significant reduction of computational cost, the new algorithm maintains higher numerical precision compared to the original version of the high-order simulation. A new method is also proposed to deal with the replicates in the simulation algorithm, reducing the impacts of conflicting statistics between the Geosci (2018) 50:929-960 sample data and the training image (TI). A brief description of implementation is provided and, for comparison and verification, a set of case studies is conducted and compared with the results of the well-established multi-point simulation algorithm, filtersim. This comparison demonstrates that the proposed high-order simulation algorithm can generate spatially complex geological patterns while also reproducing the high-order spatial statistics from the sample data.

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Section: Introductionmentioning

confidence: 99%

A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments

2018

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“…Although the original application domain focused on modeling the internal structures of subsurface deposits ranging from pore-scale (El Ouassini et al, 2008;Okabe and Blunt, 2007;Tahmasebi and Sahimi, 2013;Zhang et al, 2006a) to reservoir-scale (Huysmans and Dassargues, 2012;Ronayne et al, 2008;Yin, 2013), it has thereafter been extended to very different fields such as mining (Goodfellow et al, 2012;Rezaee et al, 2014), soil science (Meerschman et al, 2014), remote sensing (Boucher, 2009;Ge and Bai, 2011;Jha et al, 2013;Stisen et al, 2011;Vannametee et al, 2014), for modeling the occurrence of rainfall (Oriani et al, 2014;Wojcik et al, 2009), and even in medical imaging (Pham, 2012).…”

Section: Introductionmentioning

confidence: 99%

Constraining distance-based multipoint simulations to proportions and trends

Mariethoz¹,

Straubhaar²,

Renard³

et al. 2015

Environmental Modelling & Software

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a b s t r a c tIn the last years, the use of training images to represent spatial variability has emerged as a viable concept. Among the possible algorithms dealing with training images, those using distances between patterns have been successful for applications to subsurface modeling and earth surface observation. However, one limitation of these algorithms is that they do not provide a precise control on the local proportion of each category in the output simulations. We present a distance perturbation strategy that addresses this issue. During the simulation, the distance to a candidate value is penalized if it does not result in proportions that tend to a target given by the user. The method is illustrated on applications to remote sensing and pore-scale modeling. These examples show that the approach offers increased user control on the simulation by allowing to easily impose trends or proportions that differ from the proportions in the training image.

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“…The main limitations of MPS methods are that they do not explicitly account for high-order statistics, nor do they provide consistent mathematical models as they generate TI-driven realizations. Previous studies have shown resulting realizations that comply with the TI used but do not necessarily reproduce the spatial statistics inferred from the data (Osterholt and Dimitrakopoulos 2007;Goodfellow et al 2012). As an alternative, to address the above limitations, a high-order simulation (HOSIM) framework has been proposed as a natural generalization of the second-order-based random field paradigm (Dimitrakopoulos et al 2010;Dimitrakopoulos 2010a, b, 2011;Minniakhmetov and Dimitrakopoulos 2017a, b;Minniakhmetov et al 2018;Yao et al 2018).…”

Section: Introductionmentioning

confidence: 99%

“…In the context of conventional second-order geostatistics, direct block support simulation has been proposed. An approach termed "direct block simulation" was presented by Godoy (2003), which discretizes each block into several internal nodes, but only stores a single block value in memory for the next group simulation. This mechanism drastically reduces the amount of data stored in memory and saves considerable computational effort.…”

Section: Introductionmentioning

confidence: 99%

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

2019

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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.

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Quantifying multi-element and volumetric uncertainty, Coleman McCreedy deposit, Ontario, Canada

Cited by 25 publications

References 9 publications

A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments

A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments

Constraining distance-based multipoint simulations to proportions and trends

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

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