相位移加有限差分法波动方程正演模拟

Phase-shift plus finite-difference wave equation forward modeling

本文提出用相位移加有限差分法来实现速度纵横向变化、复杂陡倾地质模型的正流模拟，为复杂波场的地震、地质解释提供了精确、实用的方法。一般情况下，相位移延拓方法对徒倾斜地层成像精度高、稳定性好、计算快，但实现速度的横向变化困难；而频率、空间域的有限差分法算法简单、稳定性好、能适应速度的纵横向任意变化，但偏移陡断地层存在很多问题。用快速的45°有限差分对相位移延拓作补充，能使整个延拓过程既适应速度的纵横向变化，同时也能够得到陡倾地层的精确归位，通常称为混合法。我们把混合法的思想用于正演之中，得到了较好的效果。该方法在延拓中不作任何时深转换，始终在深度域进行，比在时间域作正演有更高的精确度。复杂地质模型正演试验结果表明，相位移加有限差分波动方程正演完全达到了我们的预期目的。

In the paper, the phase-shift plus finite-difference method is proposed to implement theforward modeling of complex steep-dipping geological structure with arbitrary varying vel0cities,which can be used for the seismic and geologica1 interpretation of complex wavefield. Generally,the phase-shift method is accurate, stable and fast for the imaging of steep-dipping strata but isdifficult to process the lateral velocity variation j The finite-difference method in frequency-spacedomain is simple, stable and adaptab1e to arbitrary velocity variation, but there are still manyproblems in dealing with steep-dipping strata. Using the fast 45' finite-difference wave equation asa complement to the phase-shift continuation, we can make the whole continuation process adaptto the longitudinal and lateral vel0city variation and a1so get the accurate homing of steep-dippingstrata. The method is commonly called the hybrid-migration method. We make use of the idea ofthe hybrid-migration method in forward mode1ing and thus obtain good results. In wavefieIdcontinuation, the method is used in depth domain from beginning to end and is more accuratethan that in time domain.The forward modeling results of complex geo1ogica1 structure demonstrate that our goal hasbeen attained successfully by use of the phase-shift plus finite-difference wave equation forwardmodeling.