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在众多的二维波动方程求解算法中,一般都需要对方程进行一定的简化,最后得到一个适合于不同倾角偏移的方程。本文所介绍的方法,不对二维波动方程进行任何简化处理,试图得到较为精确的波动方程的数值解。由于求解过程是非简化的,原则上适用于任何倾角的偏移和具有横向速度变化的情况。 本文使用付氏变换的方法求得一个亥姆霍兹方程,并用差分法求该方程的近似解。文中给出了两个差分格式,并讨论了它们的稳定性和差分解法。此外还给出了该算法的成像法则。
In many algorithms for solving two-dimensional wave equation, we need to simplify the equation to a certain extent, finally we get an equation suitable for different tilt angles. The method presented in this paper does not make any simplification of the two-dimensional wave equation, trying to get the numerical solution of the more accurate wave equation. Since the solution process is non-simplified, it applies in principle to any inclination offsets and changes with lateral velocities. In this paper, a Helmholtz equation is obtained by the Fourier transform method, and the approximate solution of the equation is obtained by the difference method. Two difference schemes are given in the paper, and their stability and difference solution are discussed. In addition, the algorithm of imaging is given.