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利用Zoeppritz方程建立了反射系数对地震波波矢向量偏导方程,导出了Zoeppritz方程矩阵元对波矢向量偏导数解析表示.通过求解波矢向量偏导方程获得了反射系数对地震波波矢向量的偏导数,给出了利用反射系数对波矢向量偏导数计算地震波Goos-Hnchen效应横向偏移的计算方法,实现了反射P波和VS转换波横向偏移的准确计算,绘制了地震波Goos-Hnchen效应横向偏移曲线,分析了曲线的变化特点和规律.算例表明:对掠入射波或入射角在临界角(包括第一、第二临界角)附近的入射波,反射P波的横向偏移较大,地震波将沿界面滑行较长的距离后才返回入射介质,在其他角的入射P波的横向偏移与波长为同一个数量级,不同的反射界面横向偏移存在大的差别,泥岩-砂岩反射界面P波存在负横向偏移;VS转换波与P波类似在第一、第二临界角附近,也存在大的Goos-Hnchen横向偏移,不同反射界面的S波横向偏移同样存在大的差异,且在入射角逐渐趋向于90时S波的横向偏移逐渐减小.Goos-Hnchen横向偏移对广角反射波产生了不可忽略的影响,因此在实际地震资料处理中需要进行横向偏移效应校正,本文的研究为广角反射波深度偏移归位及时差校正的Goos-Hnchen横向偏移效应校正研究提供了理论依据.
The partial derivative equation of wave vector with reflection coefficient and seismic wave was established by using Zoeppritz equation and the partial derivative of wave vector of Zoeppritz equation was deduced. The partial derivative of wave vector was derived by solving partial derivative equation of wave vector. The calculation method of calculating the lateral offset of the Goos-Hönchen effect of the seismic wave by using the partial derivative of the wave vector is given by the reflection coefficient, and the accurate calculation of the lateral offset of the reflection P wave and the VS converted wave is achieved. The Goos- H nchen effect of lateral shift curve, analysis of the curve characteristics and changes of the curve.Examples show that: for grazing incidence or angle of incidence in the critical angle (including the first and second critical angle) near the incident wave reflection P wave , The seismic wave will glide back a long distance along the interface before it returns to the incident medium. The lateral shift of incident P wave at the other corner is the same order of magnitude as that of the wavelength, and there is a large lateral offset at different reflection interfaces The P wave of mudstone-sandstone reflection interface has a negative lateral offset. Similar to the P wave, the VS converted wave has a large Goos-Hönchen lateral offset near the first and second critical angles, There is also a big difference in the S-wave lateral offset at the interface, and the lateral shift of the S-wave gradually decreases when the incident angle approaches 90. The lateral offset of the Goos-Hönchen produces a non-negligible effect on the wide-angle reflected wave Therefore, lateral offset effect correction is needed in actual seismic data processing. The research in this paper provides a theoretical basis for the study of Goos-Hönchen lateral offset effect correction of wide-angle reflection depth migration and time difference correction.