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 cross-correlation-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 data-relocation 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.