一种快速、高精度的共转换点轨迹计算方法

A method for fast and accurately computing the common conversion point locus.

转换波数据的叠加要求真正的共转换点选排。当地下介质为水平层状时,其共转换点(CCP)坐标可通过在单个均匀层情况下导出的解析表达式来近似地确定。然而,对实际应用来说,这个表达式显得很冗长、计算量大,式中参数对共转换点坐标的影响关系也不明显。而且,当地下反射界面为非水平时,建立这样的解析表达式将十分困难。本文在单个均匀层情况下,导出了一种转换点轨迹的迭代算法,该算法运算速度快、精度高、收敛快。如果用前一个深度点的迭代结果作为后一个深度点的迭代初值.一般只需迭代一次便可使相对误差远远小于0.1%,其运算量可比原解析表达式算法提高近7倍。该算法的表达式简单,且从中可以清楚地看到速度比及炮检距与深度之比对 CCP 坐标的影响关系。最主要的是,这种迭代算法很容易推广到地下反射界面为非水平的情形。

The stack of converted wave requires real common conversion point(CCP) gathering.When medium is horizontally layered,CCP coordinates can be determined by using the analytic expression that is derived in the ease of single uniform layer. However,in practical application,the analytic expression is too tediously long and causes much computation,and its parameters show indistinct influence on CCP coor- dinates.What is more,it is very difficult to derive such analytic expression in the case of slant interfaces. An iterative algorithm for CCP locus is derived in the case of single uniform layer.The algorithm leads to fast calculation,accurate result and rapid convergence. If the iteration result of a depth point is used as the initial value of the next point,a single iteration usually makes the relative error much smaller than 0.1%.This algo- rithm is seven times faster than the original one.This algorithm is expressed by a concise formula,from which people can see how velocity ratio and offset/depth ratio influence CCP coordinates.Essentially,this iterative algorithm can be easy applied to the case where reflectors slope down.