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近些年来研制了建立在地震波传播原理基础上的波动方程偏移法。它是一种基于偏微分方程数值解的地震资料偏移方法。其基本原理是将在地面测线接收到的地震资料用计算机向下延拓到任一深度的假想接收测线所接收到的地震资料,于是完成了地震资料的偏移归位。本文就上述波动方程偏移原理作了简单叙述,推导了水平迭加剖面向下延拓的二维偏微分方程。结合法国CGG公司的波动偏移程序,讨论了波动方程差分解法的一种计算机算法。该算法是将差分系数通过Z变换分解成为一个褶积因子和二个反褶积因子,采用褶积和递推运算,求解波动方程的数值解。该解法比用矩阵法更为简单。
In recent years, the wave equation migration method based on the principle of seismic wave propagation has been developed. It is a method of seismic data migration based on the numerical solution of partial differential equations. The basic principle is that the seismic data received on the ground survey line are down-scaled by the computer to the seismic data received by the hypothetical survey line at any depth, so that the offset of the seismic data is completed. In this paper, we briefly describe the above principle of wave equation migration and derive the two-dimensional partial differential equation with the continuation of the horizontal superposition profile downward. A computer algorithm for the differential equation method of wave equation is discussed in combination with the CGG program of France. The algorithm decomposes the differential coefficients by Z transform into a convolution factor and two deconvolution factors, and uses the convolution and recursion algorithms to solve the numerical solution of the wave equation. The solution is simpler than the matrix method.