用基于距离的先验模型参数化来解决空间反演问题

用基于距离的先验模型参数化来解决空间反演问题

MathGeosci(2008)40:445–469

DOI10.1007/s11004-008-9154-8

ADistance-basedPriorModelParameterization

forConstrainingSolutionsofSpatialInverseProblemsSatomiSuzuki·JefCaers

Received:23January2007/Accepted:3December2007/Publishedonline:12March2008

©InternationalAssociationforMathematicalGeology2008

AbstractSpatialinverseproblemsintheEarthSciencesareoftenill-posed,requir-ingthespeci cationofapriormodeltoconstrainthenatureoftheinversesolutions.Otherwise,invertedmodelrealizationslackgeologicalrealism.Inspatialmodeling,suchpriormodeldeterminesthespatialvariabilityoftheinversesolution,forex-ampleasconstrainedbyavariogram,aBooleanmodel,oratrainingimage-basedmodel.Inmanycases,particularlyinsubsurfacemodeling,onelackstheamountofdatatofullydeterminethenatureofthespatialvariability.Forexample,manydiffer-enttrainingimagescouldbeproposedforagivenstudyarea.Suchalternativetrainingimagesorscenariosrelatetothedifferentpossiblegeologicalconceptseachexhibit-ingadistinctivegeologicalarchitecture.Manyinversemethodsrelyonpriorsthatrepresentasinglesubjectivelychosengeologicalconcept(asinglevariogramwithinamulti-Gaussianmodelorasingletrainingimage).Thispaperproposesanovelandpracticalparameterizationofthepriormodelallowingseveraldiscretechoicesofge-ologicalarchitectureswithintheprior.Thismethoddoesnotattempttoparameterizethepossiblycomplexarchitecturesbyasetofmodelparameters.Instead,alargesetofpriormodelrealizationsisprovidedinadvance,bymeansofMonteCarlosimu-lation,wherethetrainingimageisrandomized.Theparameterizationisachievedbyde ningametricspacewhichaccommodatesthislargesetofmodelrealizations.Thismetricspaceisequippedwitha“similaritydistance”functionoradistancefunctionthatmeasuresthesimilarityofgeometrybetweenanytwomodelrealizationsrelevanttotheproblemathand.Throughexamples,inversesolutionscanbeef cientlyfoundinthismetricspaceusingasimplestochasticsearchmethod.

KeywordsDistancefunction·Stochasticsearch·Inverseproblems·GeostatisticsS.Suzuki·J.Caers()

DepartmentofEnergyResourcesEngineering,StanfordUniversity,367PanamaStreet,Stanford,CA94305,USA

e-mail:jcaers@stanford.edu

S.Suzuki

e-mail:ssuzuki@stanford.edu

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