Solving Speed and Memory Issues in Multiple-Point Statistics Simulation Program SNESIM

Strebelle, Sebastien; Cavelius, Claude

doi:10.1007/s11004-013-9489-7

Cited by 57 publications

(33 citation statements)

References 11 publications

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“…However, the original MPS algorithm was impractical, because the method was required to rescan the TI to simulate each new data event and consequently was extremely demanding of central processing unit (CPU) usage. Strebelle [7][8][9] proposed an alternative method, single normal equation simulation (SNESIM), using a search tree structure, an efficient method of accessing high-dimensional data that can overcome the problems associated with the original MPS method. Subsequently, MPS was used in geostatistics modeling and other research.…”

Section: Introductionmentioning

confidence: 99%

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Reconstruction of three-dimensional porous media from a single two-dimensional image using three-step sampling

Gao

Teng

et al. 2015

Phys. Rev. E

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A random three-dimensional (3D) porous medium can be reconstructed from a two-dimensional (2D) image by reconstructing an image from the original 2D image, and then repeatedly using the result to reconstruct the next 2D image. The reconstructed images are then stacked together to generate the entire reconstructed 3D porous medium. To perform this successfully, a very important issue must be addressed, i.e., controlling the continuity and variability among adjacent layers. Continuity and variability, which are consistent with the statistics characteristic of the training image (TI), ensure that the reconstructed result matches the TI. By selecting the number and location of the sampling points in the sampling process, the continuity and variability can be controlled directly, and thus the characteristics of the reconstructed image can be controlled indirectly. In this paper, we propose and develop an original sampling method called three-step sampling. In our sampling method, sampling points are extracted successively from the center of 5×5 and 3×3 sampling templates and the edge area based on a two-point correlation function. The continuity and variability of adjacent layers were considered during the three steps of the sampling process. Our method was tested on a Berea sandstone sample, and the reconstructed result was compared with the original sample, using tests involving porosity distribution, the lineal path function, the autocorrelation function, the pore and throat size distributions, and two-phase flow relative permeabilities. The comparison indicates that many statistical characteristics of the reconstructed result match with the TI and the reference 3D medium perfectly.

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Section: Introductionmentioning

confidence: 99%

“…Based on original multiple grid, Strebelle and Claude [7] proposed a new kind of multiple grid, improving speed and reducing memory usage further, while ensuring the accuracy of the reconstruction, thereby injecting the SNESIM with new vitality.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of three-dimensional porous media from a single two-dimensional image using three-step sampling

Gao

Teng

et al. 2015

Phys. Rev. E

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“…To address the limits of conventional approaches, higher-order spatial statistics-namely multiple-point (MP) models-were introduced in which templates and training images replace conventional two-point variograms or covariances [6,20,38,44,53]. MP methods include a sequential simulation framework and the use of single normal equations [6,30,[44][45][46], filters and resulting filter scores [53,55], patterns [3], object and distance combined [22], direct sampling [37], distance-based [23], wavelet-based [9], or multi-scale simulation in the spatial domain [4,16,47,52]. These methods are based on finding repeatable patterns and their probability of occurrence in a training image representing an analog of the studied geologic environment.…”

Section: Introductionmentioning

confidence: 99%

Fast wavelet-based stochastic simulation using training images

2015

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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.

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“…SNESIM was proposed by Strebelle (2002) and its computational aspects were since revisited and improved (Strebelle and Cavelius, 2014). In the SNESIM algorithm a TI is scanned in order to infer the relative frequency E{A 0 |S(n)=1}.…”

mentioning

confidence: 99%

“…The conditional probabilities and the patterns are saved in a data structure; this facilitates the search when performing the simulation without demanding excessive RAM. Computational aspects of SNESIM have recently been revisited and further improved (Strebelle and Cavelius, 2014). One limitation is related to the scope of the studies that can be done using this method, given that it works only using categorical data.…”

mentioning

confidence: 99%

Stochastic simulation of the Fox kimberlitic diamond pipe, Ekati mine, Northwest Territories, Canada

Robles-Stefoni¹,

Dimitrakopoulos²

2016

J. S. Afr. Inst. Min. Metall.

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Multiple-point simulation (MPS) methods have been developed over the last decade as a means of reproducing complex geological patterns while generating stochastic simulations. Some geological spatial configurations are complex, such as the spatial geometries and patterns of diamondbearing kimberlite pipes and their internal facies controlling diamond quality and distribution.Two MPS methods were tested for modelling the geology of a diamond pipe located at the Ekati mine, NT, Canada. These are the single normal equation simulation algorithm SNESIM, which captures different patterns from a training image (TI), and the filter simulation algorithm FILTERSIM, which classifies the patterns founded on the TI. Both methods were tested in the stochastic simulation of a four-category geology model: crater, diatreme, xenoliths, and host rock. Soft information about the location of host rock was also used. The validation of the simulation results shows a reasonable reproduction of the geometry and data proportions for all geological units considered; the validation of spatial statistics, however, shows that although simulated realizations from both methods reasonably reproduce the fourth-order spatial statistics of the TI, they do not reproduce well the same spatial statistics of the available data (when this differs from the TI). An interesting observation is that SNESIM better imitated the shape of the pipe, while FILTERSIM yielded a better reproduction of the xenolith bodies. multiple-points simulation methods, SNESIM, FILTERSIM, categorical simulation, cumulants, high-order statistics.

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Solving Speed and Memory Issues in Multiple-Point Statistics Simulation Program SNESIM

Cited by 57 publications

References 11 publications

Reconstruction of three-dimensional porous media from a single two-dimensional image using three-step sampling

Reconstruction of three-dimensional porous media from a single two-dimensional image using three-step sampling

Fast wavelet-based stochastic simulation using training images

Stochastic simulation of the Fox kimberlitic diamond pipe, Ekati mine, Northwest Territories, Canada

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