横向不均匀介质中Kirchhoff-Helmholtz积分合成地震图
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摘要
本文将Kirchhoff-Helmholtz积分方法应用于横向非均匀介质的合成地震图计算.与反射率方法及二维有限差分方法进行了比较.表明KH积分方法能很好的模拟反射波震相,且精度较高.KH积分方法能够计算复杂界面的反射波,且其计算效率明显大于有限差分.
We synthesize the reflection seismograms in a laterally inhomogeneous elastic medium with the asymptotic method named Kirchhoff-Helmholtz(KH) integral.The accuracy of this approximation is justified by comparing the numberical results with that of the refletivity method and finite-difference method.The KH method can work quickly on curved or irregular interface,and its computing speed is superior to the finite-difference method.
We synthesize the reflection seismograms in a laterally inhomogeneous elastic medium with the asymptotic method named Kirchhoff-Helmholtz(KH) integral.The accuracy of this approximation is justified by comparing the numberical results with that of the refletivity method and finite-difference method.The KH method can work quickly on curved or irregular interface,and its computing speed is superior to the finite-difference method.
引文
[1]朱良保.Maslov渐近理论地震图[博士论文].北京:中国地震局地球物理研究所,1993.Zhu L B.Maslov’s asymptotic theoretical seismogram[Ph.D.thesis](in Chinese).Beijing:Institute of Geophysics,ChinaEarthquake Administration,1993.
[2]Alterman Z S,Karal F C.Propagation of elastic waves in lay-ered media by finite difference methods[J].Bull.Seismol.Soc.Am,1968,58:367~398.
[3]Smith W D.The application of finite element analysis to body-wave propagation problems[J].Geophys.J.R.Astr.Soc,1975,42:747~768.
[4]Wu R S.The Perturbation Method in Elastic Wave Scattering[J].Pure.Appl.Geophy,1989,131:605~637.
[5]Frazer L N,Sen M K.Kirchhoff-Helmholtz reflection seismo-grams in a laterally inhomogeneous multi-layered elastic medi-um-Ⅰ.Theory[J].Geophys.J.R.astr.Soc,1985,80:121~147.
[6]Cerveny V.Synthetic body wave seismograms for laterally va-rying layered structures by Gaussian beam method[J].Geo-phy.J.R.astr.Soc,1983,73:389~426.
[7]Chapman C H,Drumnood R.Body wave seimograms in inho-mogeneous media using Maslov asymptotic theory[J].Bull.Seismol.Soc.Am,1982.
[8]Baag C E,Langston C A.A WKBJ spectral method for compu-tation of SV synthetic seismograms in a cylindrically symmetricmedium[J].Geophy.J.R.astr.Soc,1985,80(2):387~417.
[9]Sen M K,Frazer L N.Synthetic seismograms using multifoldpath integrals-Ⅱ[J].Theory Geophys.J.R.astr.Soc,1987,88:647~671.
[10]Scott P,Helmberger D Applications of the Kirchhoff-Helm-holtz integral to problems in seismology[J].Geophys.J.R.astr..Soc,1983,72:237~254.
[11]谢小碧,姚振兴.二维不均匀介质中点源P-SV波响应的有限差分近似算法[J].地球物理学报,1988,31(5):540~555.Xie X B,Yao Z X.P-SV wave responses for a point sourcein two-dimensional heterogeneous media:finite-differencemethod[J].Chinese J.Geophys.(in Chinese),1988,31(5):540~555.
[12]Fuchs K,Muller G.Computation of synthetic seismogramswith the reflectivity method and comparison with observation[J].Geophy.J.R.astr.Soc,1971,23(2):417~433.
[13]Frazer L N.Synthetic seismograms using multifold path inte-grals-Ⅰ[J].Theory Geophys.J.R.astr.Soc,1987,88:621~646.
[14]Alexander D,Helle P.Elastic Kirchhoff-Helmholtz syntheticseismograms[J].Pure appl.Geophys.1998,151:17~45.
[15]Aki K,Richards P.G.Quantitative Seismology.Theory andMethods[M].1&2,San Francisco:W H Freeman,1980,1~932.
[2]Alterman Z S,Karal F C.Propagation of elastic waves in lay-ered media by finite difference methods[J].Bull.Seismol.Soc.Am,1968,58:367~398.
[3]Smith W D.The application of finite element analysis to body-wave propagation problems[J].Geophys.J.R.Astr.Soc,1975,42:747~768.
[4]Wu R S.The Perturbation Method in Elastic Wave Scattering[J].Pure.Appl.Geophy,1989,131:605~637.
[5]Frazer L N,Sen M K.Kirchhoff-Helmholtz reflection seismo-grams in a laterally inhomogeneous multi-layered elastic medi-um-Ⅰ.Theory[J].Geophys.J.R.astr.Soc,1985,80:121~147.
[6]Cerveny V.Synthetic body wave seismograms for laterally va-rying layered structures by Gaussian beam method[J].Geo-phy.J.R.astr.Soc,1983,73:389~426.
[7]Chapman C H,Drumnood R.Body wave seimograms in inho-mogeneous media using Maslov asymptotic theory[J].Bull.Seismol.Soc.Am,1982.
[8]Baag C E,Langston C A.A WKBJ spectral method for compu-tation of SV synthetic seismograms in a cylindrically symmetricmedium[J].Geophy.J.R.astr.Soc,1985,80(2):387~417.
[9]Sen M K,Frazer L N.Synthetic seismograms using multifoldpath integrals-Ⅱ[J].Theory Geophys.J.R.astr.Soc,1987,88:647~671.
[10]Scott P,Helmberger D Applications of the Kirchhoff-Helm-holtz integral to problems in seismology[J].Geophys.J.R.astr..Soc,1983,72:237~254.
[11]谢小碧,姚振兴.二维不均匀介质中点源P-SV波响应的有限差分近似算法[J].地球物理学报,1988,31(5):540~555.Xie X B,Yao Z X.P-SV wave responses for a point sourcein two-dimensional heterogeneous media:finite-differencemethod[J].Chinese J.Geophys.(in Chinese),1988,31(5):540~555.
[12]Fuchs K,Muller G.Computation of synthetic seismogramswith the reflectivity method and comparison with observation[J].Geophy.J.R.astr.Soc,1971,23(2):417~433.
[13]Frazer L N.Synthetic seismograms using multifold path inte-grals-Ⅰ[J].Theory Geophys.J.R.astr.Soc,1987,88:621~646.
[14]Alexander D,Helle P.Elastic Kirchhoff-Helmholtz syntheticseismograms[J].Pure appl.Geophys.1998,151:17~45.
[15]Aki K,Richards P.G.Quantitative Seismology.Theory andMethods[M].1&2,San Francisco:W H Freeman,1980,1~932.
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