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在非均匀各向同性速度层构成的三维介质中,我们用三维中心射线的4×4T传播矩阵确定了通过模型的中心射线附近的一组旁轴射线的二阶(抛物线或双曲线)两点旅行时近似。该传播矩阵由重要地震参量构成。这些射线是通过扰动光滑弯曲的前后界面上中心射线的始点和终点确定的。每一射线终点的扰动由一个二分量矢量确定。文中采用T传播算子确定了双曲线和抛物线旁轴两点旅行时近似值(用一组有效的三维地震模型),并特别强调了按双曲线近似表述旁轴一次反射射线的旅行时。该方法已用于求解几个正反演地震问题,我们的结果简化了用三分量矢量描述曲界面射线终点的扰动方法,为了强调双曲线表达式的重要性,文中指出,双曲线旁轴射线旅行时(为四个独立变量的函数)对均匀速度介质上的平滑倾斜面产生的一次反射射线而言是精确的。
In a three-dimensional medium consisting of a heterogeneous isotropic velocity layer, we use a 4 × 4T propagation matrix of three-dimensional central rays to determine the second-order (parabolic or hyperbola) two-point of a set of paraxial rays that pass near the central ray of the model Approximate when traveling The propagation matrix consists of important seismic parameters. These rays are determined by perturbing the start and end points of the center ray at the smooth curved front and back interfaces. The perturbation at the end of each ray is determined by a two-component vector. In this paper, the T-propagation operator is used to determine the travel-time approximations (using a set of valid 3D seismic models) of hyperbolic and parabolic paraxial two-point travel, with special emphasis on the trip time of reflecting the ray by paraxial approximation. This method has been used to solve several forward and inverse seismic problems. Our results simplify the three-component vector to describe the perturbation of the end of the ray. In order to emphasize the importance of the hyperbolic expression, we point out that hyperbolic paraxial ray Traveling (a function of four independent variables) is accurate for the primary reflection of a smooth incline on a uniform velocity medium.