Kirchhoff-Helmholtz积分方法计算远震转换波
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摘要
将Kirchhoff-Helmholtz积分方法推广到远震转换波的合成地震图的计算,其优点是,能够计算复杂界面的地震波。通过与反射率法及动力学射线追踪的对比,表明KH积分方法能很好地模拟远震转换波震相,且精度较高。KH积分方法能够计算任意复杂界面的地震波,是一种研究地壳上地幔结构的有效方法。
We synthesize the teleseismic conversion wave seismograms in a laterally inhomogeneous elastic medium with an asymptotic method named Kirchhoff-Helmholtz integral,which does not break down when there is a caustic on the reflector.The accuracy of this approximation is justified by comparing the numerical results with the method of reflectivity and dynamic ray tracing.KH method can work quickly on curved or irregular interface,so it will be an efficacious method for researching the structure of the crust and upper mantle.
We synthesize the teleseismic conversion wave seismograms in a laterally inhomogeneous elastic medium with an asymptotic method named Kirchhoff-Helmholtz integral,which does not break down when there is a caustic on the reflector.The accuracy of this approximation is justified by comparing the numerical results with the method of reflectivity and dynamic ray tracing.KH method can work quickly on curved or irregular interface,so it will be an efficacious method for researching the structure of the crust and upper mantle.
引文
田小波,吴庆举,曾融生.2004.弹性波场数值模拟的隐式差分多重网格算法[J].地球物理学报,47(1):81～87
杨顶辉.2002.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,45(4):575～583
Aki K,Richards P G.1980.Quantitative Seismology Theory and Methods[M].1&2,San Francisco:W H Freeman,1～932
Alterman Z S,Karal F C.1968.Propagation of elastic waves inlayered media by finite difference methods[J].Bull SeismolSoc Am,58,367～398
Berryhill J R.1979.Wave-equation datuming[J].Geophysics,44,1329～1344
Carter J A,Frazer L N.1983.A methodfor modeling reflection data from media withlateral velocity changes[J].J geophysRes,88,6469～647
Cerveny V,Molotkov I A.1977.Ray methodin seismology[M].Karlova University:Praha
Cerveny V.1983.Synthetic body wave seismograms for laterally varying layered structures by Gaussian beam method[J].Geophy J Rastr Soc,73,389～426
Chapman C H.1978.Anew method for computing synthetic seismograms[J].Geophy J Rastr Soc,54,481～518
Chapman C H,Drumnood R.1982.Body wave sei mograms in inhomogeneous media using Maslov asymptotic theory[J].Bull Seismol Soc Am,72(6):277～317
Cormier V F,Richards P G.1977.Full wave theory applied to a discontinuous velocityincrease:theinner core boundary[J].J Geophys,43,3～22
Deregowski S M,Brown S M.1983.A theory of acoustic diffractors applied to2D models[J].Geophys Prospect,31,293～333
Frazer L N,Sen M K.1985.Kirchhoff-Hel mholtz reflection seismograms in a laterallyinhomogeneous multi-layered elasticmedium—ⅠTheory[J].Geophys J Rastr Soc,80,121～147
Fuchs K,Muller G.1971.Computation of synthetic seismograms withthe reflectivity method and comparison with observa-tion[J].Geophy J Rastr Soc,23(2):417～433
Hel mberger D V.1968.Crust-mantle transitionin the Bering sea[J].Bull SeismSoc Amer,58,179～214
Hel mberger D V.1974.Generalized ray theory for shear dislocations[J].Bull SeismSoc Amer,64,45～54
Hilterman F J.1970.Three di mensional seismic modeling[J].Geophysics,35,1020～1037
Scott P,Hel mberger D.1983.Applications of the Kirchhoff-Hel mholtz integral to problemsin seismology[J].Geophys J RAstr Soc,72,237～254
Sen M K,Frazer L N.1987.Synthetic seismograms using multifold pathintegrals—Ⅱ.Theory[J].Geophys J R Astr Soc,88,647～671
Smith WD.1975.The application of finite element analysis to body-wave propagation problems[J].Geophys J R Astr Soc,42,747～768
Wu R S.1989.The perturbation methodin elastic wave scattering[J].Pure Appl Geophy,131,605～637
杨顶辉.2002.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,45(4):575～583
Aki K,Richards P G.1980.Quantitative Seismology Theory and Methods[M].1&2,San Francisco:W H Freeman,1～932
Alterman Z S,Karal F C.1968.Propagation of elastic waves inlayered media by finite difference methods[J].Bull SeismolSoc Am,58,367～398
Berryhill J R.1979.Wave-equation datuming[J].Geophysics,44,1329～1344
Carter J A,Frazer L N.1983.A methodfor modeling reflection data from media withlateral velocity changes[J].J geophysRes,88,6469～647
Cerveny V,Molotkov I A.1977.Ray methodin seismology[M].Karlova University:Praha
Cerveny V.1983.Synthetic body wave seismograms for laterally varying layered structures by Gaussian beam method[J].Geophy J Rastr Soc,73,389～426
Chapman C H.1978.Anew method for computing synthetic seismograms[J].Geophy J Rastr Soc,54,481～518
Chapman C H,Drumnood R.1982.Body wave sei mograms in inhomogeneous media using Maslov asymptotic theory[J].Bull Seismol Soc Am,72(6):277～317
Cormier V F,Richards P G.1977.Full wave theory applied to a discontinuous velocityincrease:theinner core boundary[J].J Geophys,43,3～22
Deregowski S M,Brown S M.1983.A theory of acoustic diffractors applied to2D models[J].Geophys Prospect,31,293～333
Frazer L N,Sen M K.1985.Kirchhoff-Hel mholtz reflection seismograms in a laterallyinhomogeneous multi-layered elasticmedium—ⅠTheory[J].Geophys J Rastr Soc,80,121～147
Fuchs K,Muller G.1971.Computation of synthetic seismograms withthe reflectivity method and comparison with observa-tion[J].Geophy J Rastr Soc,23(2):417～433
Hel mberger D V.1968.Crust-mantle transitionin the Bering sea[J].Bull SeismSoc Amer,58,179～214
Hel mberger D V.1974.Generalized ray theory for shear dislocations[J].Bull SeismSoc Amer,64,45～54
Hilterman F J.1970.Three di mensional seismic modeling[J].Geophysics,35,1020～1037
Scott P,Hel mberger D.1983.Applications of the Kirchhoff-Hel mholtz integral to problemsin seismology[J].Geophys J RAstr Soc,72,237～254
Sen M K,Frazer L N.1987.Synthetic seismograms using multifold pathintegrals—Ⅱ.Theory[J].Geophys J R Astr Soc,88,647～671
Smith WD.1975.The application of finite element analysis to body-wave propagation problems[J].Geophys J R Astr Soc,42,747～768
Wu R S.1989.The perturbation methodin elastic wave scattering[J].Pure Appl Geophy,131,605～637
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