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High-Order Spatial Simulation Using Legendre-Like Orthogonal Splines
High-order sequential simulation techniques for complex non-Gaussian spatially distributed variables have been developed over the last few years. The high-order simulation approach does not require any transformation of initial data and makes no assumptions about any probability distribution functio...
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/PMC6411132/ https://www.ncbi.nlm.nih.gov/pubmed/30931017 http://dx.doi.org/10.1007/s11004-018-9741-2 |
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author | Minniakhmetov, Ilnur Dimitrakopoulos, Roussos Godoy, Marcelo |
author_facet | Minniakhmetov, Ilnur Dimitrakopoulos, Roussos Godoy, Marcelo |
author_sort | Minniakhmetov, Ilnur |
collection | PubMed |
description | High-order sequential simulation techniques for complex non-Gaussian spatially distributed variables have been developed over the last few years. The high-order simulation approach does not require any transformation of initial data and makes no assumptions about any probability distribution function, while it introduces complex spatial relations to the simulated realizations via high-order spatial statistics. This paper presents a new extension where a conditional probability density function (cpdf) is approximated using Legendre-like orthogonal splines. The coefficients of spline approximation are estimated using high-order spatial statistics inferred from the available sample data, additionally complemented by a training image. The advantages of using orthogonal splines with respect to the previously used Legendre polynomials include their ability to better approximate a multidimensional probability density function, reproduce the high-order spatial statistics, and provide a generalization of high-order simulations using Legendre polynomials. The performance of the new method is first tested with a completely known image and compared to both the high-order simulation approach using Legendre polynomials and the conventional sequential Gaussian simulation method. Then, an application in a gold deposit demonstrates the advantages of the proposed method in terms of the reproduction of histograms, variograms, and high-order spatial statistics, including connectivity measures. The C++ course code of the high-order simulation implementation presented herein, along with an example demonstrating its utilization, are provided online as supplementary material. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s11004-018-9741-2) contains supplementary material, which is available to authorized users. |
format | Online Article Text |
id | pubmed-6411132 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-64111322019-03-27 High-Order Spatial Simulation Using Legendre-Like Orthogonal Splines Minniakhmetov, Ilnur Dimitrakopoulos, Roussos Godoy, Marcelo Math Geosci Article High-order sequential simulation techniques for complex non-Gaussian spatially distributed variables have been developed over the last few years. The high-order simulation approach does not require any transformation of initial data and makes no assumptions about any probability distribution function, while it introduces complex spatial relations to the simulated realizations via high-order spatial statistics. This paper presents a new extension where a conditional probability density function (cpdf) is approximated using Legendre-like orthogonal splines. The coefficients of spline approximation are estimated using high-order spatial statistics inferred from the available sample data, additionally complemented by a training image. The advantages of using orthogonal splines with respect to the previously used Legendre polynomials include their ability to better approximate a multidimensional probability density function, reproduce the high-order spatial statistics, and provide a generalization of high-order simulations using Legendre polynomials. The performance of the new method is first tested with a completely known image and compared to both the high-order simulation approach using Legendre polynomials and the conventional sequential Gaussian simulation method. Then, an application in a gold deposit demonstrates the advantages of the proposed method in terms of the reproduction of histograms, variograms, and high-order spatial statistics, including connectivity measures. The C++ course code of the high-order simulation implementation presented herein, along with an example demonstrating its utilization, are provided online as supplementary material. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s11004-018-9741-2) contains supplementary material, which is available to authorized users. Springer Berlin Heidelberg 2018-05-17 2018 /pmc/articles/PMC6411132/ /pubmed/30931017 http://dx.doi.org/10.1007/s11004-018-9741-2 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 Minniakhmetov, Ilnur Dimitrakopoulos, Roussos Godoy, Marcelo High-Order Spatial Simulation Using Legendre-Like Orthogonal Splines |
title | High-Order Spatial Simulation Using Legendre-Like Orthogonal Splines |
title_full | High-Order Spatial Simulation Using Legendre-Like Orthogonal Splines |
title_fullStr | High-Order Spatial Simulation Using Legendre-Like Orthogonal Splines |
title_full_unstemmed | High-Order Spatial Simulation Using Legendre-Like Orthogonal Splines |
title_short | High-Order Spatial Simulation Using Legendre-Like Orthogonal Splines |
title_sort | high-order spatial simulation using legendre-like orthogonal splines |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6411132/ https://www.ncbi.nlm.nih.gov/pubmed/30931017 http://dx.doi.org/10.1007/s11004-018-9741-2 |
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