Multiple-Point Statistics for Training Image Selection

Boisvert, Jeff B.; Pyrcz, Michael J.; Deutsch, Clayton V.

doi:10.1007/s11053-008-9058-9

Cited by 69 publications

(34 citation statements)

References 9 publications

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“…The connectivity function t(h) for a category s is defined as the probability that two points are connected by a continuous path of adjacent cells all belonging to s, conditioned to the fact that the two points belong to s (Boisvert et al, 2007;Emery and Ortiz, 2011;Renard et al, 2011;Renard and Allard, 2012):…”

Section: Simulation Quality Indicatorsmentioning

confidence: 99%

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

Meerschman

Pirot

Mariethoz

et al. 2013

Computers & Geosciences

141

116

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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.

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Section: Simulation Quality Indicatorsmentioning

confidence: 99%

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

Meerschman

Pirot

Mariethoz

et al. 2013

Computers & Geosciences

141

116

View full text Add to dashboard Cite

show abstract

“…Another application could be in synergy with other methodologies (for example, Boisvert et al, 2007) aimed at the selection of TI from comparisons with data statistics.…”

Section: Data Templatementioning

confidence: 99%

3D multiple-point statistics simulation using 2D training images

Comunian¹,

Renard²,

Straubhaar³

2012

Computers & Geosciences

129

101

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a b s t r a c tOne of the main issues in the application of multiple-point statistics (MPS) to the simulation of threedimensional (3D) blocks is the lack of a suitable 3D training image. In this work, we compare three methods of overcoming this issue using information coming from bidimensional (2D) training images. One approach is based on the aggregation of probabilities. The other approaches are novel. One relies on merging the lists obtained using the impala algorithm from diverse 2D training images, creating a list of compatible data events that is then used for the MPS simulation. The other (s2Dcd) is based on sequential simulations of 2D slices constrained by the conditioning data computed at the previous simulation steps. These three methods are tested on the reproduction of two 3D images that are used as references, and on a real case study where two training images of sedimentary structures are considered. The tests show that it is possible to obtain 3D MPS simulations with at least two 2D training images. The simulations obtained, in particular those obtained with the s2Dcd method, are close to the references, according to a number of comparison criteria. The CPU time required to simulate with the method s2Dcd is from two to four orders of magnitude smaller than the one required by a MPS simulation performed using a 3D training image, while the results obtained are comparable. This computational efficiency and the possibility of using MPS for 3D simulation without the need for a 3D training image facilitates the inclusion of MPS in Monte Carlo, uncertainty evaluation, and stochastic inverse problems frameworks.

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“…Simple checks could consist of comparing the experimental univariate distribution (histogram) and variogram of the sample data and training image. The verification of training image consistency remains an area of ongoing research within the MPS field (Boisvert et al, 2007(Boisvert et al, , 2010Pérez et al, 2014). The question remains of what happens when radically different training images (perhaps with different connectivities and anisotropies) are used.…”

Section: Resultsmentioning

confidence: 99%

“…Because training images are borrowed from elsewhere, a potentially important issue, in cases of more dense data, is the consistency between the training image and the actual data. This issue is currently an important area of research in multiplepoint geostatistics as well (Pérez et al, 2014;Boisvert et al, 2007Boisvert et al, , 2010.…”

Section: Discussionmentioning

confidence: 99%