A practical guide to performing multiple-point statistical simulations with the Direct Sampling algorithm

Abstract

a b s t r a c tThe Direct Sampling (DS) algorithm is a recently developed multiple-point statistical simulation technique. It directly scans the training image (TI) for a given data event instead of storing the training probability values in a catalogue prior to simulation. By using distances between the given data events and the TI patterns, DS allows to simulate categorical, continuous and multivariate problems. Benefiting from the wide spectrum of potential applications of DS, requires understanding of the user-defined input parameters. Therefore, we list the most important parameters and assess their impact on the generated simulations. Real case TIs are used, including an image of ice-wedge polygons, a marble slice and snow crystals, all three as continuous and categorical images. We also use a 3D categorical TI representing a block of concrete to demonstrate the capacity of DS to generate 3D simulations. First, a quantitative sensitivity analysis is conducted on the three parameters balancing simulation quality and CPU time: the acceptance threshold t, the fraction of TI to scan f and the number of neighbors n. Next to a visual inspection of the generated simulations, the performance is analyzed in terms of speed of calculation and quality of pattern reproduction. Whereas decreasing the CPU time by influencing t and n is at the expense of simulation quality, reducing the scanned fraction of the TI allows substantial computational gains without degrading the quality as long as the TI contains enough reproducible patterns. We also illustrate the quality improvement resulting from post-processing and the potential of DS to simulate bivariate problems and to honor conditioning data. We report a comprehensive guide to performing multiple-point statistical simulations with the DS algorithm and provide recommendations on how to set the input parameters appropriately.

Lattice Boltzmann Simulations of Fluid Flow in Continental Carbonate Reservoir Rocks and in Upscaled Rock Models Generated with Multiple-Point Geostatistics

“…They were varied in order to improve the results of the simulations. Liu [53] and Meerschman et al [54] provide an extensive analysis of the influence of the different parameters on the simulations. The most important parameters for upscaling using MPS are described below.…”

Utilizing spatial association analysis to determine the number of multiple grids for multiple-point statistics

“…Many MPS algorithms do not use multiple grids, e.g., the direct sampling method (Meerschman et al, 2013). However, these algorithms require a predefined data template or patch size.…”

Integrating aerial geophysical data in multiple-point statistics simulations to assist groundwater flow models

“…When running MPS simulations, a random variation of MPS parameters where considered aided by instructions detailed in Meerschman et al (2013). A total of 6,000 simulations were generated; 3,160 for TI#1, 1,310 for TI#2 and 1,530 for TI#3.…”

“…The DS algorithm is implemented in the DeeSse software (Mariethoz et al 2010) which requires several input parameters. The three most important are the number of neighbours within the patterns, an acceptance threshold for the discrepancy between patterns, and the maximal fraction of the TI to be scanned which influence the quality of the simulation (see Meerschman et al 2013 for a sensitivity analysis).…”