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本文提出了近似波动方程的分裂算法。用小数步长延拓及弱近似方法对问题进行了讨论。给出了有限差分分裂算法的延拓公式,并证明了分裂的方程与原方程等价;推导出频率—波数域分裂的外推公式,速度横向变化部分是做为独立一步处理的;利用解算子概念讨论外推算子的可交换性,得到了不交替方向使用方程的方法;对于同层速度相同的各条测线,设计的外推算子可重复使用,这样可节省许多运算时间。
In this paper, the splitting algorithm of approximate wave equation is proposed. The problem is discussed with the method of fractional step extension and weak approximation. The continuation formula of the finite difference splitting algorithm is given and it is proved that the splitting equation is equivalent to the original one. The extrapolation formula of the frequency-wavenumber domain splitting is deduced, and the horizontal speed change is treated as an independent step. The concept of operators discusses the interchangeability of extrapolation operators, and the method of using equations without alternation direction is obtained. For each line with the same layer speed, the design of extrapolation operators can be reused, which can save a lot of computing time.