GEOPHYSICS,VOL.75,NO.4 JULY-AUGUST2010 ;P.S131–S137,12FIGS.,5TABLES.10.1190/1.3457923

Acceleratingmigrationdeconvolutionusinganonmonotonegradientmethod

YanfeiWang1andChangchunYang1

ABSTRACT

Newsolutionmethodswereconsideredformigrationde-convolutioninseismicimagingproblems.Itiswellknownthatdirectmigrationmethods,usingtheadjointoperatorL*,yieldalower-resolutionorblurredimage,andthatthelinear-izedinversionofseismicdataforthere ectivitymodelusu-allyrequiressolvinga regularized least-squaresmigrationproblem.Weobservedthatthe regularized least-squaresmethodiscomputationallyexpensive,whichbecomesase-vereobstacleforpracticalapplications.Iterativegradient-de-scentmethodswerestudiedandanef cientmethodformi-grationdeconvolutionwasdeveloped.Theproblemwasfor-mulatedbyincorporatingregularizingconstraints,andthenanonmonotonegradient-descentmethodwasappliedtoaccel-eratetheconvergence.Totestthepotentialoftheapplicationofthedevelopedmethod,synthetictwo-dimensionalandthree-dimensionalseismic-migration-deconvolutionsimula-tionswereperformed.Numericalperformanceindicatesthatthismethodispromisingforpracticalseismicmigrationimaging.

tothisproblemareill-posed,renderingtheresultssensitivetonoise TikhonovandArsenin,1977 .Least-squaresmigration LSM ,par-ticularlywiththeadditionofregularization,isanotherpromisingap-proachtoimprovingtheresolutionofmigratedimages Schuster,1997a;Nemethetal.,1999;Sacchietal.,2006;Wangetal.,2009 .Thekeytosuccessful,iterativeleast-squaresmigrationistheoptimi-zationstrategy VanDecarandSnieder,1994;TreitelandLines,2001;Bevcetal.,2007 .Becauseleast-squaresmigrationhasacostapproximatelyequaltotwomigrationapplicationsperiteration,itisessentialtocontrolthenumberofiterationsrequiredtoreachasatis-factoryimage Schuster,1997a,b;Nemethetal.,1999;Sjøbergetal.,2003;Wangetal.,2009 .Wehaveadaptedagradient-descentop-timizationtechniquedescribedbyBarzilaiandBorwein 1988 toleast-squaresseismicmigration.Onekeyfeatureofthisapproach,asopposedtothetypicalsteepest-descentorconjugate-gradient CG approaches,isthatitdoesnothavemonotonicconvergence.Thead-vantageofrelaxingtherequirementthateachiterationmusthavealowerresidualthanthepreviousstepisthatthemethodcanconvergetoaloweroverallvalueoftheobjectivefunctioninfeweroverallit-erations.Thisisimportantforleast-squaresmigrationbecauseonewishestokeeptheoverallnumberofiterationsassmallaspossible.

INTRODUCTION

Standardseismicmigrationmethodsgivedistortedimagesofthesubsurface,evenwithanaccuratevelocitymodelbecauseoflimita-tionsinbandwidth,recordingtime,andapertureoftheseismic-re- ectionexperiment.Applicationofinversemethodscanimprovetheresolutionofseismicimagesbycompensatingforthesedistortions TreitelandLines,2001 .Migrationdeconvolutionisonepossibleapproachbecauseitusesknowledgeoftheresolutionkerneloftheseismicexperimenttocompensatefortheeffectsmentioned Schuster,1997a,b;HuandSchuster,1998;HuandValasek,1999;HuandSchuster,2000;Huetal.,2001;Geliusetal.,2002;Sjøbergetal.,2003 .However,itiswellknownthatdeconvolutionapproaches

ITERATIVEREGULARIZATIONSOLVERSFOR

MIGRATIONDECONVOLUTIONANDINVERSIONINSEISMICIMAGINGMigrationdeconvolution

InSchuster 1997a,b andHuandSchuster 1998 ,thetermmi-grationdeconvolutiondescribesinvertingtheblurringoperatorfromthemigrationimageandthuscreatingasharperimageofthere- ectivity.Nemethetal. 1999 showthatbymodelingandmigrationofsyntheticdata,wecanunderstandbettertheimpactofthenoise e.g.,recordingfootprint .Forexample,onemightspecifysource-receivergeometryandare ectivitymodelm,computesyntheticseismicdatadusingsomemodelingoperatorL,andthenmigratethesedatatoobtainthemigratedsectionmmig Claerbout,1985;

ManuscriptreceivedbytheEditor24June2009;revisedmanuscriptreceived25February2010;publishedonline18August2010.1

ChineseAcademyofSciences,InstituteofGeologyandGeophysics,KeyLaboratoryofPetroleumGeophysics,Beijing,China.E-mail:yfwang@mail.iggcas.ac.cn,yfwang_ucf@yahoo.com;ccy@mail.iggcas.ac.cn.©2010SocietyofExplorationGeophysicists.Allrightsreserved.

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