波动方程的高阶广义屏叠前深度偏移

High order generalized screen propagator for wave equation prestack depth migration

不同于常规广义屏传播算子的推导中使用散射理论,本文利用单平方根算子的渐近展开,推导出了单程波方程广义屏传播算子的高阶表达式.高阶广义屏传播算子不仅可提高常规广义屏传播算子的计算精度,而且还能改善广义屏传播算子对速度强横向变化介质的适应性.把高阶广义屏传播算子应用于波动方程叠前深度偏移,可得到比常规广义屏传播算子更好的效果.高阶广义屏传播算子的阶数越高,计算精度越高,但计算量也越多.以SEG-EAGE二维盐丘模型数据的波动方程叠前深度偏移为例,二阶广义屏传播算子相对于常规(一阶)广义屏传播算子增加了30%的计算量.高阶广义屏传播算子是常规广义屏传播算子理论的发展和完善.

Different from the scattering theory used in the derivation of conventional generalized screen propagator, in this paper, a high order formula of generalized screen propagator for one-way wave equation is proposed by using the asymptotic expansion of single-square-root operator. The high order generalized screen propagator not only improves the calculation precision of conventional generalized screen propagator, and facilitates the suitability of generalized screen propagator to the media with strong lateral velocity variation. Applying the high order generalized screen propagator to wave equation prestack depth migration can get a better migration result than that of conventional generalized screen propagator. The higher the order number of generalized screen propagator, the higher the calculation precision, and the more the calculation amount. Using the wave equation prestack depth migration on SEG-EAGE 2-D salt dome model as an example, the two-order generalized screen propagator increases 30% calculation work relative to the conventional （one-order） generalized screen propagator. The presentation of high order generalized screen propagator is a theoretic development and improvement to the conventional generalized screen propagator.