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A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments
Multiple-point simulations have been introduced over the past decade to overcome the limitations of second-order stochastic simulations in dealing with geologic complexity, curvilinear patterns, and non-Gaussianity. However, a limitation is that they sometimes fail to generate results that comply wi...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6404987/ https://www.ncbi.nlm.nih.gov/pubmed/30931019 http://dx.doi.org/10.1007/s11004-018-9744-z |
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author | Yao, Lingqing Dimitrakopoulos, Roussos Gamache, Michel |
author_facet | Yao, Lingqing Dimitrakopoulos, Roussos Gamache, Michel |
author_sort | Yao, Lingqing |
collection | PubMed |
description | Multiple-point simulations have been introduced over the past decade to overcome the limitations of second-order stochastic simulations in dealing with geologic complexity, curvilinear patterns, and non-Gaussianity. However, a limitation is that they sometimes fail to generate results that comply with the statistics of the available data while maintaining the consistency of high-order spatial statistics. As an alternative, high-order stochastic simulations based on spatial cumulants or spatial moments have been proposed; however, they are also computationally demanding, which limits their applicability. The present work derives a new computational model to numerically approximate the conditional probability density function (cpdf) as a multivariate Legendre polynomial series based on the concept of spatial Legendre moments. The advantage of this method is that no explicit computations of moments (or cumulants) are needed in the model. The approximation of the cpdf is simplified to the computation of a unified empirical function. Moreover, the new computational model computes the cpdfs within a local neighborhood without storing the high-order spatial statistics through a predefined template. With this computational model, the algorithm for the estimation of the cpdf is developed in such a way that the conditional cumulative distribution function (ccdf) can be computed conveniently through another recursive algorithm. In addition to the significant reduction of computational cost, the new algorithm maintains higher numerical precision compared to the original version of the high-order simulation. A new method is also proposed to deal with the replicates in the simulation algorithm, reducing the impacts of conflicting statistics between the sample data and the training image (TI). A brief description of implementation is provided and, for comparison and verification, a set of case studies is conducted and compared with the results of the well-established multi-point simulation algorithm, filtersim. This comparison demonstrates that the proposed high-order simulation algorithm can generate spatially complex geological patterns while also reproducing the high-order spatial statistics from the sample data. |
format | Online Article Text |
id | pubmed-6404987 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-64049872019-03-27 A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments Yao, Lingqing Dimitrakopoulos, Roussos Gamache, Michel Math Geosci Article Multiple-point simulations have been introduced over the past decade to overcome the limitations of second-order stochastic simulations in dealing with geologic complexity, curvilinear patterns, and non-Gaussianity. However, a limitation is that they sometimes fail to generate results that comply with the statistics of the available data while maintaining the consistency of high-order spatial statistics. As an alternative, high-order stochastic simulations based on spatial cumulants or spatial moments have been proposed; however, they are also computationally demanding, which limits their applicability. The present work derives a new computational model to numerically approximate the conditional probability density function (cpdf) as a multivariate Legendre polynomial series based on the concept of spatial Legendre moments. The advantage of this method is that no explicit computations of moments (or cumulants) are needed in the model. The approximation of the cpdf is simplified to the computation of a unified empirical function. Moreover, the new computational model computes the cpdfs within a local neighborhood without storing the high-order spatial statistics through a predefined template. With this computational model, the algorithm for the estimation of the cpdf is developed in such a way that the conditional cumulative distribution function (ccdf) can be computed conveniently through another recursive algorithm. In addition to the significant reduction of computational cost, the new algorithm maintains higher numerical precision compared to the original version of the high-order simulation. A new method is also proposed to deal with the replicates in the simulation algorithm, reducing the impacts of conflicting statistics between the sample data and the training image (TI). A brief description of implementation is provided and, for comparison and verification, a set of case studies is conducted and compared with the results of the well-established multi-point simulation algorithm, filtersim. This comparison demonstrates that the proposed high-order simulation algorithm can generate spatially complex geological patterns while also reproducing the high-order spatial statistics from the sample data. Springer Berlin Heidelberg 2018-06-04 2018 /pmc/articles/PMC6404987/ /pubmed/30931019 http://dx.doi.org/10.1007/s11004-018-9744-z Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Article Yao, Lingqing Dimitrakopoulos, Roussos Gamache, Michel A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments |
title | A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments |
title_full | A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments |
title_fullStr | A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments |
title_full_unstemmed | A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments |
title_short | A New Computational Model of High-Order Stochastic Simulation Based on Spatial Legendre Moments |
title_sort | new computational model of high-order stochastic simulation based on spatial legendre moments |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6404987/ https://www.ncbi.nlm.nih.gov/pubmed/30931019 http://dx.doi.org/10.1007/s11004-018-9744-z |
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