Fast wavelet-based stochastic simulation using training images

Abstract

Spatial uncertainty modelling is a complex and challenging job for orebody modelling in mining, reservoir characterization in petroleum, and contamination modelling in air and water. Stochastic simulation algorithms are popular methods for such modelling. In this paper, discrete wavelet transformation (DWT)-based multiple point simulation algorithm for continuous variable is proposed that handles multi-scale spatial characteristics in datasets and training images. The DWT of a training image provides multi-scale high-frequency wavelet images and one lowfrequency scaling image at the coarsest scale. The simulation of the proposed approach is performed on the frequency (wavelet) domain where the scaling image and wavelet images across the scale are simulated jointly. The inverse DWT reconstructs simulated realizations of an attribute of interest in the space domain. An automatic scale-selection algorithm using dominant mode difference is applied for the selection of the optimal scale of wavelet decomposition. The proposed algorithm reduces the computational time required for simulating large domain as compared to spatial domain multi-point simulation algorithm. The algorithm is tested with an exhaustive dataset using conditional and unconditional simulation in two-and threedimensional fluvial reservoir and mining blasted rock data. The realizations generated by the proposed algorithm perform well and reproduce the statistics of the training image. The study conducted comparing the spatial domain filtersim multiple-point simulation algorithm suggests that the proposed algorithm generates equally good realizations at lower computational cost.

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

“…Strebelle (2002) formalizes the method and developed the first computationally efficient implementation. For over a decade, research has been focused on various issues around mps algorithms, such as computational efficiency and various patch-based extensions (Zhang et al 2006; Arpat and Caers 2007; Wu et al 2008; Boucher 2009; Remy et al 2009; Honarkhah and Caers 2010; Mariethoz et al 2010; Parra and Ortiz 2011; Huang et al 2013; Boucher et al 2014; Strebelle and Cavelius 2014; Chatterjee et al 2016; Li et al 2016). In general, these mps methods are TI-based, and their statistics are estimated from distributions of replicates of data events in the TI.…”

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

“…Initial simulation methods were based on Gaussian assumptions and second-order statistics of corresponding random field models (Journel and Huijbregts 1978;David 1988;Goovaerts 1997). To address the limits of such Gaussian approaches, multiple point statistics (MPS)-based simulation methods were introduced (Guardiano and Srivastava 1993; Strebelle 2002;Zhang et al 2006;Arpat and Caers 2007;Remy et al 2009;Mariethoz et al 2010;Mariethoz and Caers 2014;Mustapha et al 2014;Chatterjee et al 2016;Li et al 2016;Zhang et al 2017) to remove distributional assumptions, as well as to enable the reproduction of complex curvilinear and other geologic features by replacing the random field model with a framework built upon extraction of multiple point patterns from a training image (TI) or geological analogue. 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.…”

Estudo comparativo entre a Simulação Sequencial Gaussiana e a Simulação Baseada em Wavelets aplicado a quantificação de minério de Cu em um depósito sintético

“…Figura 13 -A esquerda um exemplo de decomposição de wavelets da Lenna (Ouahabi, 2012) e a direita as bandas de cada escala da decomposição (Chatterjee, Mustapha e Dimitrakopoulos, 2015).…”