MS-CCSIM: Accelerating pattern-based geostatistical simulation of categorical variables using a multi-scale search in Fourier space

Pattern-based spatial modeling relies on training images as basic modeling component for generating geostatistical realizations. The methodology recognizes that working with the unit of a pattern aids its reproduction, particularly for large systems. In this paper improvements are made, in terms of both the computation time and conditioning, of a pattern-based simulation method that relies on the crosscorrelation-based simulation (CCSIM), introduced by Tahmasebi et al. (2012). The extension lies on the use of a multi-scale (MS) representation of the training image along a pattern projection strategy that is markedly different from the traditional multi-grid methods employed in the current methodologies, and proposes acceleration of the method by carrying out most of the computations in the Fourier space. In the proposed multi-scale representation, we transform the high-resolution training image into a pyramid of consecutively up-gridded views of the same image. The pyramid allows for rapid search of the patterns that can be superimposed over a shared overlap area with previously simulated patterns. A second advantage of the multi-scale view lies in data conditioning by means of a new hard datarelocation algorithm and the use of a co-template for looking for conditioning points ahead of the raster path employed in CCSIM. Using synthetic and real-field multi-million cell examples with sparse, as well as dense datasets, we investigate quantitatively how the improved algorithm performs with respect to CCSIM, as well as the traditional MP simulation algorithms. (c) 2014 Elsevier Ltd. All rights reserved.