P-SV波展平变换的精确求解——以地震面波为例
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摘要
以地震面波问题为例,提出P-SV波展平变换的精确求解方法,并以此为基础讨论了近似求解方法的适用性及适用范围.结果表明,展平变换指数m对最终结果没有显著影响,因此可选取任意值;在短波近似条件下,展平变换的近似解法是适当且合理的;展平变换的近似解法比精确解法的效率高一倍.对于频率较低的问题,应采用精确的求解方法.
Taking surface wave as an example,this paper proposed an exact solution of earth-flattening transformation for P-SV waves and discussed the applicability of the approximate methods.The results show that the transform parameter m has little influence on the final results,and on the condition of short wave approximation,approximate earth-flattening transformation is suitable.In addition,the efficiency of approximate transformation is twice of that of exact transformation.For low frequency problems we should use exact earth-flattening transformation.
Taking surface wave as an example,this paper proposed an exact solution of earth-flattening transformation for P-SV waves and discussed the applicability of the approximate methods.The results show that the transform parameter m has little influence on the final results,and on the condition of short wave approximation,approximate earth-flattening transformation is suitable.In addition,the efficiency of approximate transformation is twice of that of exact transformation.For low frequency problems we should use exact earth-flattening transformation.
引文
何耀峰,陈蔚天,陈晓非.2006.利用广义反射-透射系数方法求解含低速层水平层状介质模型中面波频散曲线问题[J].地球物理学报,49(4):1074--1081.
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Bhattacharya S N.1996.Short notes:Earth-flattening transformation for P-SV waves[J].Bull Seism Soc Amer,86:1979--1982.
Bhattacharya S N.2005.Synthetic seismograms in a spherical Earth using exact flattening transformation[J].GeophysRes Lett,32(21):L21303.
Bhattacharya S N,Arora S.1997.Aflattening transformation for P-SV waves in a transverselyisotropic earth[J].BullSeismSoc Amer,87:1297--1304.
Biswas N.1972.Earth-flattening procedure for the propagation of Rayleigh wave[J].Pure Appl Geophys,96:61--74.
Biswas N,Knopoff L.1970.Exact earth-flattening calculation for Love waves[J].Bull Seism Soc Amer,60:1123--1137.
Chen X F.1993.Asystematic and efficient method of computing normal modes for multi-layered half space[J].GeophysJInt,115:391--409.
Chen X F.1999.Seismograms synthesis in multi-layered half-space(Ⅰ):Theoretical formulations[J].Earthquake Re-search in China,13(2):149--174.
Dahlen F A,Tromp J.1998.Theoretical Global Seismology[M].Princeton:Princeton University Press:268--272.
Kennett B L N.1983.Seismic Wave Propagation in Stratified Media[M].New York:Cambridge University Press:25--44.
叶其孝,沈永欢.2006.实用数学手册[M].北京:科学出版社:16--18.
Aki K,Richards P G.1980.Quantitative Seismology:Theory and Methods[M].San Francisco:W H Freeman:267--286.
Bhattacharya S N.1996.Short notes:Earth-flattening transformation for P-SV waves[J].Bull Seism Soc Amer,86:1979--1982.
Bhattacharya S N.2005.Synthetic seismograms in a spherical Earth using exact flattening transformation[J].GeophysRes Lett,32(21):L21303.
Bhattacharya S N,Arora S.1997.Aflattening transformation for P-SV waves in a transverselyisotropic earth[J].BullSeismSoc Amer,87:1297--1304.
Biswas N.1972.Earth-flattening procedure for the propagation of Rayleigh wave[J].Pure Appl Geophys,96:61--74.
Biswas N,Knopoff L.1970.Exact earth-flattening calculation for Love waves[J].Bull Seism Soc Amer,60:1123--1137.
Chen X F.1993.Asystematic and efficient method of computing normal modes for multi-layered half space[J].GeophysJInt,115:391--409.
Chen X F.1999.Seismograms synthesis in multi-layered half-space(Ⅰ):Theoretical formulations[J].Earthquake Re-search in China,13(2):149--174.
Dahlen F A,Tromp J.1998.Theoretical Global Seismology[M].Princeton:Princeton University Press:268--272.
Kennett B L N.1983.Seismic Wave Propagation in Stratified Media[M].New York:Cambridge University Press:25--44.
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