格子法在起伏地表叠前逆时深度偏移中的应用

Prestack reverse-time migration by the grid method

基于全程波波动方程的逆时偏移(Reverse Time Migration)可以对回转波、多次反射波成像,不受横向速度变化影响,没有倾角限制,随着计算机软硬件技术的进步,再次成为偏移方法研究热点.本文将格子法用于叠前逆时深度偏移成像.格子法作为波场延拓方法,处理起伏地表边界条件容易,可用于含起伏地表边界条件的逆时波场延拓;可利用变尺度非规则对计算域进行离散,因此可根据速度模型调整网格尺度来降低存储量,放大时间步长,降低计算量.采用光滑的曲人工边界,也可避免常规的PML吸收边界存在的角点区域需特别处理的麻烦.本方法通过事先计算和存储边界单元的局部几何参数,与直边界PML方法相比不增加任何计算量.格子法还具有容易实现并行计算的特点,非常适用于叠前逆时偏移.本文给出了二维问题算例.

The two-way wave equation based reverse-time migration （RTM） attracts much research interest recently, because it has potential to image overturning wave and multiple reflections, canproperly hande strong lateral velocity variations and does not impose dip limitations on the images. In this work the grid method is applied to prestack RTM with surface topography. By discretizing the domain with the irregular grid, this method allows larger time steps and requires less memory storage during reverse-time migration, which enables higher efficiency. Moreover, it is easy to implement the grid method in parallel computation. By using a smoothed artificial boundary, the irregular-grid PML method can also avoid the special treatments to the corners, which lead to complex computer implementations in the conventional PML method. Owing to that the local geometrical coefficients are computed and stored in a table in advance, no extra computational costs arise when we use the irregular-grid PML method rather than the conventional PML method. A 2D acoustic case is presented here.