二步法射线追踪

TWO-STEP RAY TRACING METHOD

本文提出的二步法射线追踪,能够在复杂地质模型下有效、准确地确定射线在炮点的出射角,使得射线恰好到达检波点.射线到达地面的位置是射线在炮点的出射角的函数,称为出射函数.二步法射线追踪通过搜索出射函数的极值点来确定其单调变化的区间;然后通过比较检波点位置与出射函数极值的大小,确定与检波点相对应的出射角究竟落在出射函数的哪一个单调变化的区间里;最后,利用出射函数在局部区域里单调变化的性质,迅速、准确地确定与检波点相对应的出射角.出射函数的极值点,对于共炮集中每一个检波点和检波点中每一个不同方向的入射射线都是适用的,因此,二步法射线追踪只需要进行一次一维全局搜索(极值点搜索).另外,本文采用B-样条的线性组合来表示速度函数,通过提高B-样条的阶数,可以改善速度函数的光滑程度,从而既满足射线追踪对于速度函数光滑性的要求,又加强射线在炮点的出射角对于射线的控制作用.

This paper proposes a two-step ray tracing method which is an accurate and efficient procedure for determination of the raypaths in complex geological model.As well known, in surface, the location of arrival is a function, called shooting function, of the shoot angle in shot location. Since the shooting function is not monotone in complex model, the conventional ray tracing method is usually time consuming, inaccurate and unstable. The principle of two-step ray tracing is as following. Firstly, determine the monotonicity ranges of the shooting function by searching the extreme values, then find the proper monotonicity range to the shoot angle associated with the receiver by comparing the receiver position and the extreme values; secondly, determine the shoot angle and the ray path by means of the monotonicity of the shooting function. The second step is very efficient and the convergence is guaranteed. Because the extreme values are valid for all receivers and shoot angles in a common-shot gather, therefore, the searching of extreme values is needed only once for a common-shot gather.Besides, the velocity function is represented by the linear combination of B-splines in the paper. By increasing the order of B-splines, the smoothing of the velocity function can be improved for ray tracing and controlling the ray path by the shoot angle .