均方根速度反演层速度

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1、TheinversionofintervalvelocitiesForahorizontallylayeredmodel,thermsvelocityfromthesurfacetothebottomoflayernisdefinedby:Vn2=1tni=1nvi2∆ti(1)andtn=i=1n∆ti(2)Thesimplelinearrelationbetweenthesquaredintervalvelocitiesandthesquaredrmsvelocitiesinexpressions

2、1and2proposesapracticalchoiceofdataandmodelparameters.Letthedatavectordcontainthesquaredrmsvelocitiespickedfromthevelocityanalysis:d=[V12,V22,………………Vn2]T,(3)andletmbetheunknownsquaredintervalvelocitiesm=[v12,v22,………………vn2]T,(4)wherenisthenumberofpickedr

3、msvelocities.Therelationbetweenthesquaredpickedrmsvelocitiesindandtheunknownsquaredintervalvelocitiesinmcanbewrittenasd=Gm(5)whereGisanintegralorsummationoperatorwithdimensionn×n,inthispaper,weconsiderthecasethat∆t1=∆t2=…∆tn.SothematrixGwillbefollow:G=1

4、0000012120000.....………….1n1n1n1n...1nObjectFunction：在此处键入公式。∅v=eTe+λ2L2=(dobs-Gmest)T(dobs-Gmest)+λ2mTm(6)=i=1nVi-1ij=1iviTVi-1ij=1ivi+i=1nvTλ2vlet∂∅(v)∂v=0wecangetthefollowingform:GTG+λ2Im=GTGdThenwesolvethelinearequationbytheCholeskydecompositionmethod

5、.Thisistheresultofonetrace:Figure1Theintervalvelocitiesobtainedfromthedixformula(redlines),thebluelinesistheresultoftheinversion.