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1、GEOPHYSICS,VOL.71,NO.4JULY-AUGUST2006;P.SI33ÐSI46,8FIGS.10.1190/1.2213955Green’sfunctionrepresentationsforseismicinterferometry11KeesWapenaarandJacobFokkematotheGreenÕsfunctionthatwouldbeobservedatoneofthesereceiv-ABSTRACTerpositionsiftherewereanimpulsivesourceatthe
2、other.Thediffu-sivityofthewaveÞeldcanbeduetoarandomdistributionofuncor-ThetermseismicinterferometryreferstotheprincipleofrelatednoisesourcesWeaverandLobkis,2001,2002;Wapenaaretgeneratingnewseismicresponsesbycrosscorrelatingseis-al.,2002,2004b;ShapiroandCampillo,2004;
3、Shapiroetal.,2005;micobservationsatdifferentreceiverlocations.TheÞrstver-Rouxetal.,2005,reverberationsinanenclosurewithanirregularsionofthisprinciplewasderivedbyClaerbout1968,whoboundingsurfaceLobkisandWeaver,2001,multiplescatteringshowedthatthereßectionresponseo
4、fahorizontallylayeredbetweenheterogeneitiesinadisorderedmediumCampilloandmediumcanbesynthesizedfromtheautocorrelationofitsPaul,2003;Derodeetal.,2003a;vanTiggelen,2003;Malcolmetal.,transmissionresponse.Foranarbitrary3Dinhomogeneous2004;Snieder,2004,oranycombinationof
5、thesecauses.losslessmediumitfollowsfromRayleighÕsreciprocitytheo-DiffusivityofthewaveÞeldisnotanecessaryconditionforthere-remandtheprincipleoftime-reversalinvariancethatthetrievaloftheGreenÕsfunctionbymeansofcorrelation.ClaerboutacousticGreenÕsfunctionbetweenanytwopoi
6、ntsintheme-1968showedthattheautocorrelationofthetransmissionresponsediumcanberepresentedbyanintegralofcrosscorrelationsofofanarbitraryhorizontallylayeredlosslessearthyieldsitsreßectionwaveÞeldobservationsatthosetwopoints.Theintegralisresponse.Thisresulthasbeengenera
7、lizedforthree-dimensionalin-alongsourcesonanarbitrarilyshapedsurfaceenclosinghomogeneousmediabytheauthorsWapenaaretal.,2002,2004b.thesepoints.Noassumptionsaremadewithrespecttothedif-Itappearedthatthereßectionresponsebetweenasourceandreceiv-fusivityofthewaveÞeld.TheR
8、ayleigh-Bettireciprocitythe-erattwopositionsattheearthÕsfreesurfacecanbeexpressedasanoremleadstoasimilarrepresentationofthee
