高斯束射线法在二维非均匀介质复杂构造中的应用
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摘要
高斯束射线法是地震勘探中一种非常有效的数值模拟方法，是一般射线方法的概括和推广．它克服了一般射线方法在奇异性区域（如焦散区，临界区和阴影区等）振幅趋于无穷以及对介质近似和模型小细节变化敏感的缺点，高斯束射线法在奇异性区域比一般射线方法得到的结果要好得多．高斯束射线法是沿集中于中心射线邻近的正则性区域求解波动方程的高频近似解，该解主分量的振幅分布沿垂直于中心射线方向是高斯分布，所以称为高斯束射线法．高斯束射线法能对二维甚至三维的横向非均匀介质复杂构造计算合成地震记录，而且从计算的观点看，它避开了耗时的两点射线追踪，所需内存少，计算速度快．
This paper is on the basic works of Cerreny's, from the viewpoint of physics, the principsl Components distribution of their amplitude solutions is Gaussian-shaped along the direction perpendicular to the ray, So this method is called Gaussian beams method. Gaussian beams solutions derive from the high-frequency approximate method of elastodynamic equations (including linear absorption) in smooth 2-D laterally inhomogeneous media concentrated close to rays of P or S waves and their converted waves. Numerical modelling of high-frequency seismic body wave field generated by the Gaussian beams method, then the total wave field at a receiver is obtained as an integral superposition of all Gaussian beams arrivingin a neighborhood of the receiver. Surface seismic and VSP seismograms can be computed with any curved interface. Unlike the common ray methods, the Gaussian beams method is valid even in caustic region, critical region, transitions from illuminant to shadow region, etc., moreover, the computation precision of this method is ok (compare with the finite-difference method). So we can say that this method will be practical value.
This paper is on the basic works of Cerreny's, from the viewpoint of physics, the principsl Components distribution of their amplitude solutions is Gaussian-shaped along the direction perpendicular to the ray, So this method is called Gaussian beams method. Gaussian beams solutions derive from the high-frequency approximate method of elastodynamic equations (including linear absorption) in smooth 2-D laterally inhomogeneous media concentrated close to rays of P or S waves and their converted waves. Numerical modelling of high-frequency seismic body wave field generated by the Gaussian beams method, then the total wave field at a receiver is obtained as an integral superposition of all Gaussian beams arrivingin a neighborhood of the receiver. Surface seismic and VSP seismograms can be computed with any curved interface. Unlike the common ray methods, the Gaussian beams method is valid even in caustic region, critical region, transitions from illuminant to shadow region, etc., moreover, the computation precision of this method is ok (compare with the finite-difference method). So we can say that this method will be practical value.
引文
［1］Cerveny．Molotkov，I．A．，Psencik，I．著，地震学中的射线方法．刘福田等译，北京：地质出版社，1986．［2］Beydoun，W．，Keho，T．，Theperaxialraymethod，Geophysics，52，1639－1653，1987．［3］Muller，EfficientcalcufationofGaussianbeamseismogramsfor2－Dinhomogeneusmedia，Geoghys．J．R．astr．Soc．12，303－324，1984．［4］Cerveny，Gaussianbeamsyntheticseismograms．J．Geophys．58，44－72，1985．［5］Cerveny．Raysyntheticseismogramsforcomplex2－Dand3－Dstructures，J．Geophys，58，2－26，1985b．［6］董孝义编著，光波电子学，天津：南开大学出版社，1987．［7］李庆杨、王能超、易大义编，数值分析．武汉：华中工学院出版杜，1982．［8］曾建章．朱光明．高斯束方法合成地震记录．石油地球物理勘探，27，593—604，1992．［9］Geoge，SeismicwavesynthesisbyGaussianbeamsummation：Acomparisionwithfinitedifference，Geophysics，52，1065－1073，1987．
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