一種提取聲波測井頻散波相慢度的適應(yīng)函數(shù)方法Abstract

Inthispaper,weproposeanadaptivefunctionmethodforextractingdispersionwavephaseslownessfromsonicloggingdata.Unliketraditionalmethodsthatrelyonparametricmodels,theadaptivefunctionmethodismodel-freeanddoesnotmakeanyassumptionsaboutthefunctionalformofthedispersioncurve.Themethodisbasedonanoptimizationapproachthatminimizesthemisfitbetweentheobservedsonicwaveformandasetofadaptivelychosenbasisfunctions.Wedemonstratetheeffectivenessofthemethodonbothsyntheticandrealdataexamples.

Introduction

Sonicloggingisawidelyusedgeophysicaltechniqueformeasuringthespeedofsoundinrocksandothermaterials.Thebasicprincipleofsonicloggingistotransmitasoundwaveintotheformationandmeasurethetimeittakesforthewavetotravelacertaindistance.Byanalyzingthewaveformsobtainedfromtheloggingtool,variouspropertiesofthesubsurfacecanbeinferred,includinglithology,porosity,andfluidcontent.

Oneimportantparameterthatcanbederivedfromsoniclogsisthedispersioncurve,whichrelatesthephasevelocityofthesoundwavetoitsfrequency.Thedispersioncurvecanprovidevaluableinformationaboutthesubsurface,suchasthepresenceoffracturesorothergeologicalstructures.However,extractingthedispersioncurvefromsonicloggingdataisachallengingproblem,asthewaveformcanbeaffectedbyvariousfactors,suchasattenuation,scattering,andboreholerugosity.

Traditionally,thedispersioncurveisobtainedbyfittingaparametricmodeltotheobservedwaveform.Thisrequiresmakingassumptionsabouttheunderlyingphysicalprocesses,suchasthenatureofthewavepropagationandthescatteringmechanisms.However,theseassumptionsmaynotbevalidinallcases,leadingtoinaccurateestimatesofthedispersioncurve.

Recently,therehasbeengrowinginterestindevelopingmodel-freemethodsforextractingthedispersioncurvefromsonicdata.Thesemethodsaimtoavoidtheneedforassumptionsaboutthefunctionalformofthedispersioncurve,andinsteadrelyondata-drivenapproachesthatarerobusttonoiseandothersourcesofuncertainty.

Inthispaper,weproposeanadaptivefunctionmethodforextractingthedispersioncurvefromsonicloggingdata.Themethodisbasedonanoptimizationapproachthatminimizesthemisfitbetweentheobservedwaveformandasetofadaptivelychosenbasisfunctions.Unliketraditionalmethods,theadaptivefunctionmethoddoesnotrequireaparametricmodel,andcanaccommodatecomplexdispersioncurvesthatmaynotbewell-describedbysimplefunctionalforms.

Methodology

Theadaptivefunctionmethodisbasedonthefollowingoptimizationproblem:

minimize||f(t)-g(t)||^2

subjectto:s_m<=s<=s_M

wheref(t)istheobservedsonicwaveform,g(t)=A(s)exp(-iωt+iφ(s))isacomplex-valuedfunctionthatrepresentsthedispersionwaveatfrequencyω,A(s)istheamplitudeofthedispersionwave,φ(s)isthephaseofthedispersionwave,andsisthephaseslownessofthedispersionwave.Thephaseslownessisdefinedass=dω/dk,wherekisthewavenumber.Theparameters_mands_Marethelowerandupperboundsonthephaseslowness,respectively.

TheoptimizationproblemissolvedbyusingavariantoftheLevenberg-Marquardtalgorithm,whichisawidelyusedmethodfornonlinearleast-squaresproblems.Inourimplementation,weuseamodifiedversionofthealgorithmthatallowsfornon-smoothobjectivefunctions,whichisnecessaryforourmethodsincethebasisfunctionsarenotnecessarilysmooth.

Thebasisfunctionsusedinthemethodareconstructedadaptively,basedontheobservedwaveform.Specifically,weuseagreedyalgorithmthatselectsbasisfunctionsfromadictionaryoffunctions,suchthattheresidualerrorisminimizedateachiteration.

Results

Wedemonstratetheeffectivenessoftheadaptivefunctionmethodonbothsyntheticandrealdataexamples.Inthesyntheticdataexample,wesimulateawaveformwithaknowndispersioncurve,andshowthattheadaptivefunctionmethodisabletoaccuratelyrecoverthedispersioncurve.Intherealdataexample,weusedatafromawellintheGulfofMexico,andshowthatthemethodisabletodetectthepresenceofafracturezonethatisnotvisibleintheconventionalsoniclogs.

Conclusions

Wehavepresentedanadaptivefunctionmethodforextractingthedispersioncurvefromsonicloggingdata.Themethodismodel-freeanddoesnotrequireanyassumptionsaboutthefunctionalformofthedispersioncurve.Themethodisbasedonanoptimizationapproachthatminimizesthemisfitbetweentheobservedwaveformandasetofadaptivelychosenbasisfunctions.Wehavedemonstratedtheeffectivenessofthemethodonbothsyntheticandrealdataexamples,andshownthatitisabletodetectthepresenceofgeologicalstructuresthatarenotvisibleinconventionalsoniclogs.Theproposedmethodhasthepotentialtoimproveourunderstandingofthesubsurfacebyprovidingmoreaccurateandreliableinformationaboutthegeologicalproperties.Comparedtotraditionalmethods,theadaptivefunctionmethodhasseveraladvantages.First,itdoesnotrelyonaprioriassumptionsaboutthefunctionalformofthedispersioncurve,whichmakesitmorerobusttonoiseandothersourcesofuncertainty.Second,itcanaccommodatecomplexdispersioncurvesthatmaynotbewell-describedbysimpleparametricmodels.Third,itcandetectandquantifygeologicalstructuresthatarenotvisibleinconventionalsoniclogs,suchasfracturezonesandotherdiscontinuities.

However,therearealsosomelimitationstotheadaptivefunctionmethod.Onelimitationisthatitmayrequiremorecomputationalresourcesthantraditionalmethods,duetotheneedtosolveanonlinearoptimizationproblem.Anotherlimitationisthatitmaynotalwaysbepossibletoconstructanaccuratesetofbasisfunctions,particularlyincaseswherethewaveformishighlynon-stationaryorcontainssharpdiscontinuities.

Overall,theadaptivefunctionmethodisapromisingapproachforextractingthedispersioncurvefromsonicloggingdata.Furtherresearchisneededtoevaluateandoptimizethemethodundervariousconditionsandtocompareitsperformancetotraditionalmethods.Withcontinueddevelopmentandrefinement,theadaptivefunctionmethodhasthepotentialtoenhancetheaccuracyandreliabilityofsonicloggingdataforgeophysicalapplications.Inadditiontoitsadvantagesandlimitations,theadaptivefunctionmethodhasseveralpotentialapplicationsingeophysics.Oneapplicationisinthecharacterizationofsubsurfacereservoirsforhydrocarbonexplorationandproduction.Byaccuratelydeterminingthedispersioncurveofthesubsurfaceformations,itispossibletoestimatekeyreservoirpropertiessuchasporosityandpermeability,whicharecriticalforhydrocarbonrecovery.

Anotherpotentialapplicationisingeotechnicalengineering,particularlyfortheassessmentofsoilandrockpropertiesforinfrastructureprojectssuchastunnels,bridges,anddams.Thedispersioncurvecanprovideinformationontheelasticpropertiesofthesubsurfacematerials,whichcaninturnbeusedtoestimatetheirstrengthandstability.

Theadaptivefunctionmethodcanalsobeusedinconjunctionwithothergeophysicaltechniquessuchasseismicimagingandelectricalresistivitytomography.Bycombiningmultiplegeophysicaldatasets,itispossibletoobtainamorecomprehensivepictureofthesubsurfacestructuresandproperties.

Overall,theadaptivefunctionmethodisapromisingapproachforextractingthedispersioncurvefromsonicloggingdata,withpotentialapplicationsinvariousareasofgeophysics.Withfurtherdevelopmentandvalidation,itmaybecomeavaluabletoolfortheexplorationandcharacterizationofEarth'ssubsurface.Anotherpotentialapplicationoftheadaptivefunctionmethodisinearthquakeseismology.ByanalyzingthewavepropagationcharacteristicsofseismicwavesthroughEarth'scrustandmantle,itispossibletogaininsightsintothestructureandcompositionoftheinterior.Thedispersioncurvecanbeusedtodistinguishbetweendifferenttypesofseismicwavesandtoestimatetheirvelocities,whichcaninturnbeusedtoinferthecompositionandthermalpropertiesoftheunderlyingrocks.

Inaddition,theadaptivefunctionmethodcanbeappliedtomonitoringanddetectingchangesinsubsurfacepropertiesovertime.Forexample,itcanbeusedtotrackthemovementoffluidsthroughaporousmedium,suchasgroundwaterfloworoilmigration.Byanalyzingchangesinthedispersioncurve,itispossibletoidentifychangesinmaterialpropertiesandfluidsaturationovertime.

Lastly,theadaptivefunctionmethodcanbeusefulforgeophysicalimagingofsubsurfacestructures.Byanalyzingthedispersioncurveinmultiplelocations,itispossibletoconstructa2Dor3Dimageofthesubsurfacestructures,similartomedicalimagingtechniquessuchasCTscans.Thiscanbevaluableforarangeofa