Two-dimensional Conditional Simulations Based on the Wavelet Decomposition of Training Images

Scale dependency is a critical topic when modeling spatial phenomena of complex geological patterns that interact at different spatial scales. A two-dimensional conditional simulation based on wavelet decomposition is proposed for simulating geological patterns at different scales. The method utiliz...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical geosciences 2009-08, Vol.41 (6), p.679-701
Main Authors: Gloaguen, Erwan, Dimitrakopoulos, Roussos
Format: Article
Language:English
Subjects:
Chemistry and Earth Sciences
Computer Science
Decomposition
Earth and Environmental Science
Earth Sciences
Geology
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Physics
Special Issue
Statistics for Engineering
Training
Wavelet transforms
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-a369t-ad194f0baf6db4962d7346a38d90e8570384528d613928f4e53c2300e24cadae3
cites cdi_FETCH-LOGICAL-a369t-ad194f0baf6db4962d7346a38d90e8570384528d613928f4e53c2300e24cadae3
container_end_page 701
container_issue 6
container_start_page 679
container_title Mathematical geosciences
container_volume 41
creator Gloaguen, Erwan
Dimitrakopoulos, Roussos
description Scale dependency is a critical topic when modeling spatial phenomena of complex geological patterns that interact at different spatial scales. A two-dimensional conditional simulation based on wavelet decomposition is proposed for simulating geological patterns at different scales. The method utilizes the wavelet transform of a training image to decompose it into wavelet coefficients at different scales, and then quantifies their spatial dependence. Joint simulation of the wavelet coefficients is used together with available hard and or soft conditioning data. The conditionally co-simulated wavelet coefficients are back-transformed generating a realization of the attribute under study. Realizations generated using the proposed method reproduce the conditioning data, the wavelet coefficients and their spatial dependence. Two examples using geological images as training images elucidate the different aspects of the method, including hard and soft conditioning, the ability to reproduce some non-linear features and scale dependencies of the training images.
doi_str_mv 10.1007/s11004-009-9235-3
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_34709299</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>34709299</sourcerecordid><originalsourceid>FETCH-LOGICAL-a369t-ad194f0baf6db4962d7346a38d90e8570384528d613928f4e53c2300e24cadae3</originalsourceid><addsrcrecordid>eNp1kMtKAzEUhoMoWKsP4G5w4S6a21yy1HorFFxYcRnTyZmaMpPUyVTxbfosfTJTRxQEV-c_8P3n8iN0TMkZJSQ_DzQWgQmRWDKeYr6DBrTIBS5kynd_dEb30UEIC0IyylM6QM_Td4-NbcAF652uk5F3xna9frDNqtbbJiSXOoBJvNusuxfYrJ_0G9TQJVdQ-mbpw5cl8dVmPW21ddbNk3Gj5xAO0V6l6wBH33WIHm-up6M7PLm_HY8uJljzTHZYGypFRWa6ysxMyIyZnItM88JIAkWaE16IlBUmni1ZUQlIeck4IcBEqY0GPkSn_dxl619XEDrV2FBCXWsHfhUUFzmRTMoInvwBF37VxneDYoSzuCXPI0R7qGx9CC1UatnaRrcfihK1DVz1gasYuNoGrnj0sN4TIuvm0P4O_t_0CfwahdI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>203245277</pqid></control><display><type>article</type><title>Two-dimensional Conditional Simulations Based on the Wavelet Decomposition of Training Images</title><source>Springer Link</source><creator>Gloaguen, Erwan ; Dimitrakopoulos, Roussos</creator><creatorcontrib>Gloaguen, Erwan ; Dimitrakopoulos, Roussos</creatorcontrib><description>Scale dependency is a critical topic when modeling spatial phenomena of complex geological patterns that interact at different spatial scales. A two-dimensional conditional simulation based on wavelet decomposition is proposed for simulating geological patterns at different scales. The method utilizes the wavelet transform of a training image to decompose it into wavelet coefficients at different scales, and then quantifies their spatial dependence. Joint simulation of the wavelet coefficients is used together with available hard and or soft conditioning data. The conditionally co-simulated wavelet coefficients are back-transformed generating a realization of the attribute under study. Realizations generated using the proposed method reproduce the conditioning data, the wavelet coefficients and their spatial dependence. Two examples using geological images as training images elucidate the different aspects of the method, including hard and soft conditioning, the ability to reproduce some non-linear features and scale dependencies of the training images.</description><identifier>ISSN: 1874-8961</identifier><identifier>EISSN: 1874-8953</identifier><identifier>DOI: 10.1007/s11004-009-9235-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Chemistry and Earth Sciences ; Computer Science ; Decomposition ; Earth and Environmental Science ; Earth Sciences ; Geology ; Geotechnical Engineering &amp; Applied Earth Sciences ; Hydrogeology ; Physics ; Special Issue ; Statistics for Engineering ; Training ; Wavelet transforms</subject><ispartof>Mathematical geosciences, 2009-08, Vol.41 (6), p.679-701</ispartof><rights>International Association for Mathematical Geosciences 2009</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a369t-ad194f0baf6db4962d7346a38d90e8570384528d613928f4e53c2300e24cadae3</citedby><cites>FETCH-LOGICAL-a369t-ad194f0baf6db4962d7346a38d90e8570384528d613928f4e53c2300e24cadae3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Gloaguen, Erwan</creatorcontrib><creatorcontrib>Dimitrakopoulos, Roussos</creatorcontrib><title>Two-dimensional Conditional Simulations Based on the Wavelet Decomposition of Training Images</title><title>Mathematical geosciences</title><addtitle>Math Geosci</addtitle><description>Scale dependency is a critical topic when modeling spatial phenomena of complex geological patterns that interact at different spatial scales. A two-dimensional conditional simulation based on wavelet decomposition is proposed for simulating geological patterns at different scales. The method utilizes the wavelet transform of a training image to decompose it into wavelet coefficients at different scales, and then quantifies their spatial dependence. Joint simulation of the wavelet coefficients is used together with available hard and or soft conditioning data. The conditionally co-simulated wavelet coefficients are back-transformed generating a realization of the attribute under study. Realizations generated using the proposed method reproduce the conditioning data, the wavelet coefficients and their spatial dependence. Two examples using geological images as training images elucidate the different aspects of the method, including hard and soft conditioning, the ability to reproduce some non-linear features and scale dependencies of the training images.</description><subject>Chemistry and Earth Sciences</subject><subject>Computer Science</subject><subject>Decomposition</subject><subject>Earth and Environmental Science</subject><subject>Earth Sciences</subject><subject>Geology</subject><subject>Geotechnical Engineering &amp; Applied Earth Sciences</subject><subject>Hydrogeology</subject><subject>Physics</subject><subject>Special Issue</subject><subject>Statistics for Engineering</subject><subject>Training</subject><subject>Wavelet transforms</subject><issn>1874-8961</issn><issn>1874-8953</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp1kMtKAzEUhoMoWKsP4G5w4S6a21yy1HorFFxYcRnTyZmaMpPUyVTxbfosfTJTRxQEV-c_8P3n8iN0TMkZJSQ_DzQWgQmRWDKeYr6DBrTIBS5kynd_dEb30UEIC0IyylM6QM_Td4-NbcAF652uk5F3xna9frDNqtbbJiSXOoBJvNusuxfYrJ_0G9TQJVdQ-mbpw5cl8dVmPW21ddbNk3Gj5xAO0V6l6wBH33WIHm-up6M7PLm_HY8uJljzTHZYGypFRWa6ysxMyIyZnItM88JIAkWaE16IlBUmni1ZUQlIeck4IcBEqY0GPkSn_dxl619XEDrV2FBCXWsHfhUUFzmRTMoInvwBF37VxneDYoSzuCXPI0R7qGx9CC1UatnaRrcfihK1DVz1gasYuNoGrnj0sN4TIuvm0P4O_t_0CfwahdI</recordid><startdate>20090801</startdate><enddate>20090801</enddate><creator>Gloaguen, Erwan</creator><creator>Dimitrakopoulos, Roussos</creator><general>Springer-Verlag</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TG</scope><scope>7UA</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>C1K</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>F1W</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>H8D</scope><scope>H96</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KL.</scope><scope>KR7</scope><scope>L.G</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PATMY</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>PYCSY</scope><scope>Q9U</scope></search><sort><creationdate>20090801</creationdate><title>Two-dimensional Conditional Simulations Based on the Wavelet Decomposition of Training Images</title><author>Gloaguen, Erwan ; Dimitrakopoulos, Roussos</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a369t-ad194f0baf6db4962d7346a38d90e8570384528d613928f4e53c2300e24cadae3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Chemistry and Earth Sciences</topic><topic>Computer Science</topic><topic>Decomposition</topic><topic>Earth and Environmental Science</topic><topic>Earth Sciences</topic><topic>Geology</topic><topic>Geotechnical Engineering &amp; Applied Earth Sciences</topic><topic>Hydrogeology</topic><topic>Physics</topic><topic>Special Issue</topic><topic>Statistics for Engineering</topic><topic>Training</topic><topic>Wavelet transforms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gloaguen, Erwan</creatorcontrib><creatorcontrib>Dimitrakopoulos, Roussos</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Meteorological &amp; Geoastrophysical Abstracts</collection><collection>Water Resources Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>Agricultural &amp; Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>Earth, Atmospheric &amp; Aquatic Science Collection</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Aerospace Database</collection><collection>Aquatic Science &amp; Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy &amp; Non-Living Resources</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Meteorological &amp; Geoastrophysical Abstracts - Academic</collection><collection>Civil Engineering Abstracts</collection><collection>Aquatic Science &amp; Fisheries Abstracts (ASFA) Professional</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>Earth, Atmospheric &amp; Aquatic Science Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Mathematical geosciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gloaguen, Erwan</au><au>Dimitrakopoulos, Roussos</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Two-dimensional Conditional Simulations Based on the Wavelet Decomposition of Training Images</atitle><jtitle>Mathematical geosciences</jtitle><stitle>Math Geosci</stitle><date>2009-08-01</date><risdate>2009</risdate><volume>41</volume><issue>6</issue><spage>679</spage><epage>701</epage><pages>679-701</pages><issn>1874-8961</issn><eissn>1874-8953</eissn><abstract>Scale dependency is a critical topic when modeling spatial phenomena of complex geological patterns that interact at different spatial scales. A two-dimensional conditional simulation based on wavelet decomposition is proposed for simulating geological patterns at different scales. The method utilizes the wavelet transform of a training image to decompose it into wavelet coefficients at different scales, and then quantifies their spatial dependence. Joint simulation of the wavelet coefficients is used together with available hard and or soft conditioning data. The conditionally co-simulated wavelet coefficients are back-transformed generating a realization of the attribute under study. Realizations generated using the proposed method reproduce the conditioning data, the wavelet coefficients and their spatial dependence. Two examples using geological images as training images elucidate the different aspects of the method, including hard and soft conditioning, the ability to reproduce some non-linear features and scale dependencies of the training images.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s11004-009-9235-3</doi><tpages>23</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1874-8961
ispartof Mathematical geosciences, 2009-08, Vol.41 (6), p.679-701
issn 1874-8961
1874-8953
language eng
recordid cdi_proquest_miscellaneous_34709299
source Springer Link
subjects Chemistry and Earth Sciences
Computer Science
Decomposition
Earth and Environmental Science
Earth Sciences
Geology
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Physics
Special Issue
Statistics for Engineering
Training
Wavelet transforms
title Two-dimensional Conditional Simulations Based on the Wavelet Decomposition of Training Images
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T15%3A48%3A44IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Two-dimensional%20Conditional%20Simulations%20Based%20on%C2%A0the%C2%A0Wavelet%20Decomposition%20of%C2%A0Training%20Images&rft.jtitle=Mathematical%20geosciences&rft.au=Gloaguen,%20Erwan&rft.date=2009-08-01&rft.volume=41&rft.issue=6&rft.spage=679&rft.epage=701&rft.pages=679-701&rft.issn=1874-8961&rft.eissn=1874-8953&rft_id=info:doi/10.1007/s11004-009-9235-3&rft_dat=%3Cproquest_cross%3E34709299%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a369t-ad194f0baf6db4962d7346a38d90e8570384528d613928f4e53c2300e24cadae3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=203245277&rft_id=info:pmid/&rfr_iscdi=true