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边界值偏移法是G.A.McMechan(1983)提出的。此法属于波动方程有限差分法一类,但有别于其它有限差分法,它不受倾角大小的限制,即使是90°的断面也能正确地偏移。它可以同时在不同深度上成像。文中详细地分析了边界值偏移法有限差分方程的稳定性、误差、边界条件及速度选择等问题。有限差分方程解的稳定性与格点形式有关,要求欧氏距离最近的外推点对计算点的影响最大,则认为所求的解是稳定的。精心选择差分网格可以减少截断误差。截断误差和波场对空间坐标的四阶及更高阶的偶次导数有关,而与奇次导数无关。
The boundary value shift method is proposed by G.A. McMechan (1983). This method belongs to the finite difference method of wave equation, but unlike other finite difference methods, it is not limited by the size of the dip angle. Even the 90 ° cross section can be correctly shifted. It can be imaged at different depths at the same time. In this paper, the stability, error, boundary conditions and speed selection of the finite difference equation of boundary value migration are analyzed in detail. The stability of the solution of the finite difference equation is related to the form of lattice points. The extrapolated point with the nearest Euclidean distance is required to have the greatest influence on the calculation point, so the solution is considered to be stable. Careful selection of differential grid can reduce the truncation error. The truncation error is related to the fourth and higher orders of the even-order derivatives of the spatial coordinates, but not the odd derivatives.