地震波散射研究的若干重要进展
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摘要
本文从地球介质的复杂性与非均匀性的普遍性以及地震波在其中的传播过程的复杂性出发,对地震波散射理论及方法研究的历史进行了简要的回顾,并对该领域从20世纪90年代以来的某些进展作了简要的介绍与评述.本文分两大部分进行阐述.(1)历史回顾:简介并回顾了地震波散射理论几十年的发展历程、存在的问题及对解决这些问题的潜在的基本途径.(2)20世纪90年代以来的若干进展:简要介绍了弱散射理论体系的形成及强散射问题研究的部分成果,提出了散射理论未来发展的可能方向之一,即在无近似的拟微局部分析理论的基础上,建立并发展可处理高度复杂的地球固体介质中地震波传播问题的地震波散射及全波理论.
Starting from discussing the complexity of the earth media and universality of heterogeneity,as well as the complication of seismic waves propagating in the media,this paper provides a brief historical retrospect on theory of seismic wave scattering and its methodological research,and briefly introduces and comments on some progress in this field since 1990s.This paper is divided into two parts:(1).Historical review.This part introduces research upon seismic wave scattering theory in the last decades,problems still existing and potentially fundamental ways for problems solving;(2).Important progress in this field since 1990s.This part briefly introduces forming of the theoretical system of weak scattering and some results of research upon problems on strong scattering.It expresses one of a probable development directions of the scattering theory in the future,namely on the basis of quasi-microlocal analysis theory without approximating,establishing and developing seismic wave scattering and full-wave theory,which can deal with the problem of seismic wave propagating in solid earth of high complexity.
Starting from discussing the complexity of the earth media and universality of heterogeneity,as well as the complication of seismic waves propagating in the media,this paper provides a brief historical retrospect on theory of seismic wave scattering and its methodological research,and briefly introduces and comments on some progress in this field since 1990s.This paper is divided into two parts:(1).Historical review.This part introduces research upon seismic wave scattering theory in the last decades,problems still existing and potentially fundamental ways for problems solving;(2).Important progress in this field since 1990s.This part briefly introduces forming of the theoretical system of weak scattering and some results of research upon problems on strong scattering.It expresses one of a probable development directions of the scattering theory in the future,namely on the basis of quasi-microlocal analysis theory without approximating,establishing and developing seismic wave scattering and full-wave theory,which can deal with the problem of seismic wave propagating in solid earth of high complexity.
引文
[1]Aki K.Analysis of the seismic coda of local earthquakes asscattered waves[J].J Geophys Res.1969,74:615~631.
[2]Aki K.Scattering of P Waves under the Montana LASA[J].JGeophys Res,1973,78:1334~1346.
[3]Aki K.Scattering and attenuation of shear waves in the litho-sphere[J].J Geophys Res,1980,85:6495~6504.
[4]Berteussen K A,Christoffersson A E S.Husebye E S,DahleA.Wave scattering theory in analysis of P wave anomalies atNORSAR and LASA[J].Geophys J R Astron Soc,1975,42:403~417.
[5]Brown M G.The transient wave field in vicinity of the cuspoidcaustics[J].J Acoust Soc Am,1986,79:1367~1384.
[6]Capon J.Characterization of crust and upper mantle structureunder LASA as a random medium[J].Bull Seis Soc Am,1974,64:235~266.
[7]Chapman C H.Anew method of computing synthetic seismo-grams[[J].Geophys J R Astron Sco,1978,54:481~518.
[8]Chapmam C H,Drummond R.Long-period corrections tobody-waves theory[J].Geophys J R Astron Sco,1982,64:321~518.
[9]Chen X.Seismogram synthesis for multi-layered media with ir-regular interfaces by global generalized relection/transmissionmatrices method[D].Ph D.dissertation,University ofSouthern California,Los Angeles,1991.
[10]Chernov L A.Wave propagation in a random medium[M].McGraw-Hill,New York,1960.
[11]Cleary J R,Haddon R A W.Seismic wave scattering near thecore-mantle boundary:a new interpretation of prcursors toPKIKP[J].Nature,1972,240:549~551.
[12]De Hoop M V,Wu R S,Rousseau J L.General formulationof screen methods for the scattering of acoustic waves.WaveMotion[J].2000,31(1):43~70.
[13]Flatt S M,Wu R S.Small scale structure in the lithospherededuced from arrival time amplitude fluctuations[J].J Geo-phys Res.1988,93:6601~6614.
[14]Gao L S,Lee L C,Biswas N N,Aki K.Comparison of theeffects between single and multiple-scattering on coda wavefor local earthquakes[J].Bull Seism Soc Am,1983,73:377~389.
[15]Gao L S,Biswas N N,Lee L C,Aki K.Effects of multiplescattering on coda waves in three-dimensional medium[J].Pure Appl Geophys,1983,121:3~15.
[16]Korvin G.General theorem on mean wave attenuation[J].Geophys Trans,1983,29(2),191~202.
[17]Garcia-Abdeslem J.2D modeling and inversion of gravitydada using density contrast varying with depth and source-basement geometry described by the Fourier series[J].Geo-physics,2003,68(6):1909~1916.
[18]Haddon R A W.Scattering of seismic body waves by smallrandom inhomogeneities in the Earth[J].NORSAR Sci.Rep,3~77/78,Norw.Seismic Array,Oslo,1978.
[19]Herman G C.Transmission of acoustic waves throughstrongly heterogeneous two-dimensional velocity models[J].Wave Motion,1994,20:111~130.
[20]H rmander L.The analysis of partial differential equations,I,II,III,IV,Springer-Verlag,1985.
[21]H rmander L.Non-linear hyperbolic defferential equations,Lecture Notes,Lunds Univ,1986~1987.
[22]Huang L J,Fehler M C,Wu R S.Extended local Born Fou-rier migration method[J].Geophysics,1999,64(5):1524~1534.
[23]Huang L J,Fehler M C,Wu R S.Extended local Rytov Fou-rier migration method[J].Geophysics,1999,64(5):1535~1545.
[24]Huang L J,Fehler M C.Accuracy analysis of the split-stepFourier propagator:Implicationd for seismic modeling andmigration[J].Bull Seismol Sco Am,1998,88:18~29.
[25]Huang L J,Wu R S.Prestack depth migration with acousticpseudo-screen propagators,Mathematical Methods in Geo-physical Imaging IV[J].SPIE 1996,2822:40~51.
[26]Hudson J A.The scattering of elastic waves by granularmedia[J].Qu J Mech Appl Math,1968,21:487~502.
[27]Hudson J A.The parabolic approximation for wave propaga-tion as guided modes[J].J Phys D:Appl Phys.1980,13:145~152.
[28]Hudson J A,Heritage J R.The Use of the Born approxima-tion in seismic scattering problems[J].Geophys J R astr Soc,1981,66:221~240.
[29]Jin S,Mosher C C,Wu R S.3-D prestack wave equationcommon-offset pseudo-screen depth migration,Expanded ab-stracts,SFG 70thAnnual Meeting,2000,842~845.
[30]Jin S,Wu R S,Peng C.Prestack depth migration using a hy-brid pseudo-screen propagator[A].Expanded abstracts,SFG68thAnnual Meeting[C].1999,1819~1822.
[31]Jin S,Wu R S,Peng C.Seismic depth migration with screenpropagatoes[J].Comput Geosci,1999,3:321~335.
[32]Kendall J M,Tomson C J.Maslov ray summation,psedo-caustics,Lagrangian equvilence and transient seismic wave-forms[J].Geophys.J Int,1993,113:186~214.
[33]Kennett B L N.On the density distribution within the Earth[J].Geophys J Int,1998,132:374~382.
[34]Knopoff L,Hudson J A.Scattering of elastic waves by smallinhomogeneities[J].J Acoust Sco Am,1964,36:338~343.
[35]Li Xiaofan.Elastic scattering of P and S wave from a continu-ous and heterogeneous layer[J].R R Univ of Cambridge,1993,7:1~61.
[36]Li Xiaofan,Hudson J A.Elastic scattered waves from a con-tinuous and heterogeneous layer[J].Geophys J Int,1995,121:82~102.
[37]Li Xiaofan,Hudson J A.Multiple scattering of elastic wavesfrom a continuous and heterogeneous region[J].Geophys JInt,1996,126:845~862.
[38]Li Xiaofan,Hudson J A.Time-domain computation of elasticscattering from a heterogeneous layer[J].Geophys J Int,1997,128,197~203.
[39]Li Xiaofan.Scattering of seismic waves in arbitrarily hetero-geneous and acoustic media:A general Solution and simula-tions[J].Geophs Res Letts,2001,28(15):3003~3006.
[40]Maslov V P.Theory of perturbations and asymptotic meth-ods(in Russian)[M].lzd.MGU,Moscow.USSR,1965.
[41]Maslov V P,Fedoriuk M V.Semi-classical approximations inquantum mechanics[M].Holland:Reided Dordrecht,1981.
[42]Maslov V P,Nazaikinskii V G.Asymptotics of operator andpseudo-differential equations[M].New York:ConsultantsBureau,1988.
[43]Sato H.Energy propagation including scattering effect;sin-gle isotropic scattering approximation[J].J Phys Earth,1977,25:27~41.
[44]Sato H.Amplitude attenuation of impulsive waves in randommedia based on travel time corrected mean wave formalism[J].J Acoust Soc Am,1982a,71:559~564.
[45]Sato H.Attenuation of S waves in the lithosphere due toscattering by its random velocity structure[J].J GeophysRes,1982b,87:7779~7785.
[46]Sato H.Unified approach to Amplitude attenuation and codaexcitation in the randomly inhomogeneous lithosphere[J].Pure Appl Geophys,1990,132:93~122.
[47]Steinberg B Z,Mccoy J J.Maching acoustic fields in a phacespace[J].J Acoust Soc Am,1993,93:188~204.
[48]Steinberg B Z.Evolution of local spectra in smoothly varyingnon-homogeneous environment-local canonization and marc-hing algorithms[J].J Acoust Soc Am,1993,93:2566~2580.
[49]Steinberg B Z,Birman R.Phace space marching algorithm inthe presence of aplanar wave velocity discontinuity A Qualita-tive study[J].J Acoust Soc Am,1998,98:484~494.
[50]Taylor M.Pseudodifferential operators and nonlinear PDE[M].Berlin:Birkhauser,1991.
[51]Taylor M.Micro-local analysis in spectral and scattering the-ory and index theory[A].Proc of ICM 90 Kyoto,JMS[C],1991,1225~1234.
[52]Tomson C J,Chapman C H.An introduction to Maslov's as-ymptotic method[J].Geophs J R Astr Soc,1985,83:143~168.
[53]Val rica C F,et al.Gravity inversion of a discontinuous reliefstabilized by weighted smoothness constraints on depth[J].Geophysics,1999,64(5):1429~1437.
[54]Wen L,Helmberger D V.Ultra-low velocity zone near thecore-mantle boundary from broadband PKP precursors[J].Science,1998,279:1701~1703.
[55]Wu R S.The attenuation of seismic waves due to scatteringin a randommedium(abstract)[J].Eos Trans AGV,1980,61(46):1049.
[55]Wu R S.Attenuation of short period seismic waves due toscattering,Geophys[J].Res.Lett,1982,9:9~12.
[56]Wu R S.Seismic Wave scattering and small scale inhomoge-neities in thelithosphere[D].Ph D thesis,Dep Earth,At-oms,Planet Sci,Mass Inst Technol,Cambridge,Mass,1984.
[57]Wu R S.Multiple scattering and energy transfer of seismicwaves-separation of scattering effect from intrinsic attenua-tion-I.Theoretical modelling[J].Geophys J R Astron Sco,1985,82:57~80.
[58]Wu R S.The perturbation method in elastic scattering[J].Pure appl Geophys,1989,131(4):605~637.
[59]Wu R S.Wide-angle elastic wave one-way propagation in het-erogeneous media and an elastic wave complex-screen method[J].J Geophys Res,1994,4:751~716.
[60]Wu R S,Aki K.Scattering Characteristics of Elastic Wavesby an Elastic Heterogeneity[J].Geophysics,1985,50:582~595.
[61]Wu R S,Aki K.Elastic wave scattering by a random mediumand the small-scale inhomogeneities in the lithosphere[J].JGeophys Res,1985,90:10261~10273.
[62]Wu R S,Aki K.Multiple scattering and energy transfer ofseismic waves-separation of scattering effect from intrinsic at-tenuation-II.Application of the theory to Hindu Kush Region[J].Pure Appl Geophys,1988,128(1):49~80.
[63]Wu R S.Synthetic seismograms in heterogeneous media byone-return approximation[J].PAGEOPH,1996,148(1/2):155~173.
[64]Xie X B,Wu R S.Improve the wide angle accuracy of screenmethod under large contrast,Expanded abstracts[A].SFG68thAnnual Meeting[C],1998:1811~1814.
[65]Xie X B,Wu R S.Improve the wide angle accuracy of thescreen propagator for elastic wave propagation[A].SFG 69thAnnual Meeting[C],1999:1863~1866.
[66]Xie X B,Wu R S.Modeling elastic wave forward propagationand reflection using the complex-screen method[J].J AcoustSoc Am,in press,2000.
[67]杨晓春,李小凡,张美根.地震波反演方法研究的某些进展及其数学基础[J].地球物理学进展,2001,16(4):96~109.
[68]张美根,王妙月,李小凡,杨晓春.时间域全波场各向异性弹性参数反演[J].地球物理学报,2003,46(1):94~100.
[69]张美根,王妙月,李小凡,杨晓春,王磊.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384~389.
[70]黄联捷,杨文采.声波方程逆散射反演的近似方法[J].地球物理学报,1991,34(5):626~634.
[71]杨文采.地震波场反演的BG逆散射方法[J].地球物理学报,1995,38(5):358~361.
[72]李小凡.国家自然科学基金委员会资助项目计划书(重点项目):地球深部高分辨探测中的地震波散射及全波理论与方法研究[M].北京:科学出版社,2004.
[2]Aki K.Scattering of P Waves under the Montana LASA[J].JGeophys Res,1973,78:1334~1346.
[3]Aki K.Scattering and attenuation of shear waves in the litho-sphere[J].J Geophys Res,1980,85:6495~6504.
[4]Berteussen K A,Christoffersson A E S.Husebye E S,DahleA.Wave scattering theory in analysis of P wave anomalies atNORSAR and LASA[J].Geophys J R Astron Soc,1975,42:403~417.
[5]Brown M G.The transient wave field in vicinity of the cuspoidcaustics[J].J Acoust Soc Am,1986,79:1367~1384.
[6]Capon J.Characterization of crust and upper mantle structureunder LASA as a random medium[J].Bull Seis Soc Am,1974,64:235~266.
[7]Chapman C H.Anew method of computing synthetic seismo-grams[[J].Geophys J R Astron Sco,1978,54:481~518.
[8]Chapmam C H,Drummond R.Long-period corrections tobody-waves theory[J].Geophys J R Astron Sco,1982,64:321~518.
[9]Chen X.Seismogram synthesis for multi-layered media with ir-regular interfaces by global generalized relection/transmissionmatrices method[D].Ph D.dissertation,University ofSouthern California,Los Angeles,1991.
[10]Chernov L A.Wave propagation in a random medium[M].McGraw-Hill,New York,1960.
[11]Cleary J R,Haddon R A W.Seismic wave scattering near thecore-mantle boundary:a new interpretation of prcursors toPKIKP[J].Nature,1972,240:549~551.
[12]De Hoop M V,Wu R S,Rousseau J L.General formulationof screen methods for the scattering of acoustic waves.WaveMotion[J].2000,31(1):43~70.
[13]Flatt S M,Wu R S.Small scale structure in the lithospherededuced from arrival time amplitude fluctuations[J].J Geo-phys Res.1988,93:6601~6614.
[14]Gao L S,Lee L C,Biswas N N,Aki K.Comparison of theeffects between single and multiple-scattering on coda wavefor local earthquakes[J].Bull Seism Soc Am,1983,73:377~389.
[15]Gao L S,Biswas N N,Lee L C,Aki K.Effects of multiplescattering on coda waves in three-dimensional medium[J].Pure Appl Geophys,1983,121:3~15.
[16]Korvin G.General theorem on mean wave attenuation[J].Geophys Trans,1983,29(2),191~202.
[17]Garcia-Abdeslem J.2D modeling and inversion of gravitydada using density contrast varying with depth and source-basement geometry described by the Fourier series[J].Geo-physics,2003,68(6):1909~1916.
[18]Haddon R A W.Scattering of seismic body waves by smallrandom inhomogeneities in the Earth[J].NORSAR Sci.Rep,3~77/78,Norw.Seismic Array,Oslo,1978.
[19]Herman G C.Transmission of acoustic waves throughstrongly heterogeneous two-dimensional velocity models[J].Wave Motion,1994,20:111~130.
[20]H rmander L.The analysis of partial differential equations,I,II,III,IV,Springer-Verlag,1985.
[21]H rmander L.Non-linear hyperbolic defferential equations,Lecture Notes,Lunds Univ,1986~1987.
[22]Huang L J,Fehler M C,Wu R S.Extended local Born Fou-rier migration method[J].Geophysics,1999,64(5):1524~1534.
[23]Huang L J,Fehler M C,Wu R S.Extended local Rytov Fou-rier migration method[J].Geophysics,1999,64(5):1535~1545.
[24]Huang L J,Fehler M C.Accuracy analysis of the split-stepFourier propagator:Implicationd for seismic modeling andmigration[J].Bull Seismol Sco Am,1998,88:18~29.
[25]Huang L J,Wu R S.Prestack depth migration with acousticpseudo-screen propagators,Mathematical Methods in Geo-physical Imaging IV[J].SPIE 1996,2822:40~51.
[26]Hudson J A.The scattering of elastic waves by granularmedia[J].Qu J Mech Appl Math,1968,21:487~502.
[27]Hudson J A.The parabolic approximation for wave propaga-tion as guided modes[J].J Phys D:Appl Phys.1980,13:145~152.
[28]Hudson J A,Heritage J R.The Use of the Born approxima-tion in seismic scattering problems[J].Geophys J R astr Soc,1981,66:221~240.
[29]Jin S,Mosher C C,Wu R S.3-D prestack wave equationcommon-offset pseudo-screen depth migration,Expanded ab-stracts,SFG 70thAnnual Meeting,2000,842~845.
[30]Jin S,Wu R S,Peng C.Prestack depth migration using a hy-brid pseudo-screen propagator[A].Expanded abstracts,SFG68thAnnual Meeting[C].1999,1819~1822.
[31]Jin S,Wu R S,Peng C.Seismic depth migration with screenpropagatoes[J].Comput Geosci,1999,3:321~335.
[32]Kendall J M,Tomson C J.Maslov ray summation,psedo-caustics,Lagrangian equvilence and transient seismic wave-forms[J].Geophys.J Int,1993,113:186~214.
[33]Kennett B L N.On the density distribution within the Earth[J].Geophys J Int,1998,132:374~382.
[34]Knopoff L,Hudson J A.Scattering of elastic waves by smallinhomogeneities[J].J Acoust Sco Am,1964,36:338~343.
[35]Li Xiaofan.Elastic scattering of P and S wave from a continu-ous and heterogeneous layer[J].R R Univ of Cambridge,1993,7:1~61.
[36]Li Xiaofan,Hudson J A.Elastic scattered waves from a con-tinuous and heterogeneous layer[J].Geophys J Int,1995,121:82~102.
[37]Li Xiaofan,Hudson J A.Multiple scattering of elastic wavesfrom a continuous and heterogeneous region[J].Geophys JInt,1996,126:845~862.
[38]Li Xiaofan,Hudson J A.Time-domain computation of elasticscattering from a heterogeneous layer[J].Geophys J Int,1997,128,197~203.
[39]Li Xiaofan.Scattering of seismic waves in arbitrarily hetero-geneous and acoustic media:A general Solution and simula-tions[J].Geophs Res Letts,2001,28(15):3003~3006.
[40]Maslov V P.Theory of perturbations and asymptotic meth-ods(in Russian)[M].lzd.MGU,Moscow.USSR,1965.
[41]Maslov V P,Fedoriuk M V.Semi-classical approximations inquantum mechanics[M].Holland:Reided Dordrecht,1981.
[42]Maslov V P,Nazaikinskii V G.Asymptotics of operator andpseudo-differential equations[M].New York:ConsultantsBureau,1988.
[43]Sato H.Energy propagation including scattering effect;sin-gle isotropic scattering approximation[J].J Phys Earth,1977,25:27~41.
[44]Sato H.Amplitude attenuation of impulsive waves in randommedia based on travel time corrected mean wave formalism[J].J Acoust Soc Am,1982a,71:559~564.
[45]Sato H.Attenuation of S waves in the lithosphere due toscattering by its random velocity structure[J].J GeophysRes,1982b,87:7779~7785.
[46]Sato H.Unified approach to Amplitude attenuation and codaexcitation in the randomly inhomogeneous lithosphere[J].Pure Appl Geophys,1990,132:93~122.
[47]Steinberg B Z,Mccoy J J.Maching acoustic fields in a phacespace[J].J Acoust Soc Am,1993,93:188~204.
[48]Steinberg B Z.Evolution of local spectra in smoothly varyingnon-homogeneous environment-local canonization and marc-hing algorithms[J].J Acoust Soc Am,1993,93:2566~2580.
[49]Steinberg B Z,Birman R.Phace space marching algorithm inthe presence of aplanar wave velocity discontinuity A Qualita-tive study[J].J Acoust Soc Am,1998,98:484~494.
[50]Taylor M.Pseudodifferential operators and nonlinear PDE[M].Berlin:Birkhauser,1991.
[51]Taylor M.Micro-local analysis in spectral and scattering the-ory and index theory[A].Proc of ICM 90 Kyoto,JMS[C],1991,1225~1234.
[52]Tomson C J,Chapman C H.An introduction to Maslov's as-ymptotic method[J].Geophs J R Astr Soc,1985,83:143~168.
[53]Val rica C F,et al.Gravity inversion of a discontinuous reliefstabilized by weighted smoothness constraints on depth[J].Geophysics,1999,64(5):1429~1437.
[54]Wen L,Helmberger D V.Ultra-low velocity zone near thecore-mantle boundary from broadband PKP precursors[J].Science,1998,279:1701~1703.
[55]Wu R S.The attenuation of seismic waves due to scatteringin a randommedium(abstract)[J].Eos Trans AGV,1980,61(46):1049.
[55]Wu R S.Attenuation of short period seismic waves due toscattering,Geophys[J].Res.Lett,1982,9:9~12.
[56]Wu R S.Seismic Wave scattering and small scale inhomoge-neities in thelithosphere[D].Ph D thesis,Dep Earth,At-oms,Planet Sci,Mass Inst Technol,Cambridge,Mass,1984.
[57]Wu R S.Multiple scattering and energy transfer of seismicwaves-separation of scattering effect from intrinsic attenua-tion-I.Theoretical modelling[J].Geophys J R Astron Sco,1985,82:57~80.
[58]Wu R S.The perturbation method in elastic scattering[J].Pure appl Geophys,1989,131(4):605~637.
[59]Wu R S.Wide-angle elastic wave one-way propagation in het-erogeneous media and an elastic wave complex-screen method[J].J Geophys Res,1994,4:751~716.
[60]Wu R S,Aki K.Scattering Characteristics of Elastic Wavesby an Elastic Heterogeneity[J].Geophysics,1985,50:582~595.
[61]Wu R S,Aki K.Elastic wave scattering by a random mediumand the small-scale inhomogeneities in the lithosphere[J].JGeophys Res,1985,90:10261~10273.
[62]Wu R S,Aki K.Multiple scattering and energy transfer ofseismic waves-separation of scattering effect from intrinsic at-tenuation-II.Application of the theory to Hindu Kush Region[J].Pure Appl Geophys,1988,128(1):49~80.
[63]Wu R S.Synthetic seismograms in heterogeneous media byone-return approximation[J].PAGEOPH,1996,148(1/2):155~173.
[64]Xie X B,Wu R S.Improve the wide angle accuracy of screenmethod under large contrast,Expanded abstracts[A].SFG68thAnnual Meeting[C],1998:1811~1814.
[65]Xie X B,Wu R S.Improve the wide angle accuracy of thescreen propagator for elastic wave propagation[A].SFG 69thAnnual Meeting[C],1999:1863~1866.
[66]Xie X B,Wu R S.Modeling elastic wave forward propagationand reflection using the complex-screen method[J].J AcoustSoc Am,in press,2000.
[67]杨晓春,李小凡,张美根.地震波反演方法研究的某些进展及其数学基础[J].地球物理学进展,2001,16(4):96~109.
[68]张美根,王妙月,李小凡,杨晓春.时间域全波场各向异性弹性参数反演[J].地球物理学报,2003,46(1):94~100.
[69]张美根,王妙月,李小凡,杨晓春,王磊.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384~389.
[70]黄联捷,杨文采.声波方程逆散射反演的近似方法[J].地球物理学报,1991,34(5):626~634.
[71]杨文采.地震波场反演的BG逆散射方法[J].地球物理学报,1995,38(5):358~361.
[72]李小凡.国家自然科学基金委员会资助项目计划书(重点项目):地球深部高分辨探测中的地震波散射及全波理论与方法研究[M].北京:科学出版社,2004.
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