二维介质中的空间变量分离速度成像技术
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摘要
二维介质速度成像的新方法是基于地震波的旅行时间,由射线路径沿线的速度分布特征所决定的,将二维介质中的速度分布用两个分别以二维空间坐标为自变量的勒让德多项式的线性组合来描述。根据走时积分方程,即可建立地震波走时与其射线路径沿线的速度分布之间的对应关系,进而重建出地震波射线覆盖区域的速度结构。该成像技术是一个迭代过程,且适用于折射波及反射波。
This paper puts forward a new velocity imaging method using variable partition technique. The method is based on that the travel time of seismic wave is constrained by the velocity distribution along the ray path and that the distribution in the 2D media is described by a linear combination of two Legendre polynomials, of which the independent variables are horizontal coordinate x and vertical coordinate z with different rank, respectively. The 2D velocity structure can be reconstructed iteratively by solving a set of linear equations that is deduced from the relationship between the travel times of seismic wave and the path velocity distribution of ray propagating. The method can be applied for the both velocity imaging of seismic reflection and refraction waves.
This paper puts forward a new velocity imaging method using variable partition technique. The method is based on that the travel time of seismic wave is constrained by the velocity distribution along the ray path and that the distribution in the 2D media is described by a linear combination of two Legendre polynomials, of which the independent variables are horizontal coordinate x and vertical coordinate z with different rank, respectively. The 2D velocity structure can be reconstructed iteratively by solving a set of linear equations that is deduced from the relationship between the travel times of seismic wave and the path velocity distribution of ray propagating. The method can be applied for the both velocity imaging of seismic reflection and refraction waves.
引文
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[12] RiahiMA,LundCE,PedersonLB.Three-dimensionalimageoftheMohoundulationsbeneaththeGulfofBothniausingwide-angleseismicdata[J].JGeophysInt,1997,102,653.
[13] ZeltCA,BartonPJ.Three-dimensionalseismicrefractiontomography:acomparisonoftwomethodsappliedtodatafromtheFaeroeBasin[J].JGeophysRes,1998,103,7187.
[14] ZeltBC,EllisRM,ClowesRM,etal.Inversionofthree-dimentionalwide-angleseismicdatafromthesouthwesternCanadiaCordillera[J].JGeophysRes,1996,286,209.
[15] ZeltCA,HojkaAM,FluehER,etal.3Dsimultaneousseismicrefractionandreflectiontomographyofwide-angledatafromthecentralChileanmargin[J].JGeophysResLett,1999,26,2577.
[16] ZeltCA.3-Dvelocitystructurefromsimultaneoustraveltimeinversionofin-lineseismicdataalongintersectingprofiles[J].JGeophysInt,1994,118,795.
[17] ZeltCA,SmithRB.Seismictraveltimeinversionfor2-Dcrustalvelocitystructure[J].JGeophysInt,1994,108,16.
[18] McCaugheyM,SinghSC.Simultaneousvelocityandinterfacetomographyofnormo-incidenceandwide-apertureseismictravel-timedata[J].JGeophysInt,1997,131,87.
[19] RawlinsonN,HousemanGA,CollinsCD.Inversionofseismicrefractionandwide-anglereflectiontraveltimesforthree-dimen-sionallayeredcrustalstructure[J].JGeophysInt,2001,145,381.
[2] FirbasP.Approximatemethodforcalculationofseismicvelocitiesinlaterallyheterogeneousmedia[M].ProcVIIConfCzechoslovakGeophisicists,Gottwaldov,Czechoslovoakia(inCzech),1980.
[3] LutterWJ,NowackRL.InversionforcrustalstructureusingreflectionsfromPASSCALOuachitaexperiment[J].JGeophysRes,199095,4633.
[4] LutterWJ,NowackRL,BraileL.SeismicimagingofuppercrustalstructureusingtraveltimesfromthePASSCALOuachitaexperi-ment[J].JGeophysRes,1990,95,4621.
[5] WhiteDJ.Two-dimensionalseismicrefractiontomography[J].GeophysJ,1989,97,223.
[6] HoleJA.Nonlinearhigh-resolutionthree-dimensionaltraveltimetomography[J].JGeophysRes,1992,97,6553.
[7] HoleJA,ClowesRM,EllisRM.Interfaceinversionusingbroadbandseismicrefractiondataandthree-dimensionaltraveltimecal-culations[J].JGeophysRes,1992,97,3417.
[8] ChiuSKL,KanasewithER,PhadekeS.Three-dimensionaldeterminationofstructureandvelocitybyseismictomography[J].Geophysics,1986,51,1559.
[9] CarrollS,BeresfordG.Combiningreflectiontomographywithlayerreplacementforvelocityanalysisofnear-surfacereefs[J].Geo-physics,1996,51,561.
[10] WilliamsonPR.Tomographicinversioninreflectionseismology[J].JGeophysInt,1990,100,255.
[11] FarraV,MadriagaR.Non-linearreflectiontomography[J].GeophysJ,1988,95,135.
[12] RiahiMA,LundCE,PedersonLB.Three-dimensionalimageoftheMohoundulationsbeneaththeGulfofBothniausingwide-angleseismicdata[J].JGeophysInt,1997,102,653.
[13] ZeltCA,BartonPJ.Three-dimensionalseismicrefractiontomography:acomparisonoftwomethodsappliedtodatafromtheFaeroeBasin[J].JGeophysRes,1998,103,7187.
[14] ZeltBC,EllisRM,ClowesRM,etal.Inversionofthree-dimentionalwide-angleseismicdatafromthesouthwesternCanadiaCordillera[J].JGeophysRes,1996,286,209.
[15] ZeltCA,HojkaAM,FluehER,etal.3Dsimultaneousseismicrefractionandreflectiontomographyofwide-angledatafromthecentralChileanmargin[J].JGeophysResLett,1999,26,2577.
[16] ZeltCA.3-Dvelocitystructurefromsimultaneoustraveltimeinversionofin-lineseismicdataalongintersectingprofiles[J].JGeophysInt,1994,118,795.
[17] ZeltCA,SmithRB.Seismictraveltimeinversionfor2-Dcrustalvelocitystructure[J].JGeophysInt,1994,108,16.
[18] McCaugheyM,SinghSC.Simultaneousvelocityandinterfacetomographyofnormo-incidenceandwide-apertureseismictravel-timedata[J].JGeophysInt,1997,131,87.
[19] RawlinsonN,HousemanGA,CollinsCD.Inversionofseismicrefractionandwide-anglereflectiontraveltimesforthree-dimen-sionallayeredcrustalstructure[J].JGeophysInt,2001,145,381.
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