三维混合延拓一步法波动方程正演模拟
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摘要
提出三维相位移加有限差分混合延拓法，以此为基础，实现速度纵横向变化、构造任意复杂的三维介质一步法正演模拟，为三维复杂波场的地震、地质解释提供了精确、实用的方法。对于二维介质，相位移延拓方法对陡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，但偏移陡倾地层存在很多问题。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。把混合法的思想推广到三维一步法正演模拟之中，发展出一种新的三维正演模拟方法。该方法在延拓过程中，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。
The authors present the 3D phase shift plus finite difference hybrid extrapolating method in this paper. Based on this, the forward modeling of a complex structure with velocity varying arbitrarily can be done accurately and efficiently. In 2D media, the phase shift is a fast ,stable and accurate method in computation for dealing with steep dips, but it is difficult to process lateral velocity variation. In contrast, the finite difference formula is a very good way in the proceeding of arbitrary velocity variation , and in X domain, it is simple and stable in computation, but there are still many problems in dealing with steep dip events. If a fast 45° finite difference wave equation is used as a complement to phase shift extrapolation, a way suited to the variation of velocity in all directions will be got. In this way, a steep dip geological structure can be processed accurately. Now, the idea in 3D media’s data proceeding is used and expanded into 3D phase shift plus finite difference hybrid formula. Based on this, the so called 3D hybrid one step wave equation forward modeling formula is deduced.
The authors present the 3D phase shift plus finite difference hybrid extrapolating method in this paper. Based on this, the forward modeling of a complex structure with velocity varying arbitrarily can be done accurately and efficiently. In 2D media, the phase shift is a fast ,stable and accurate method in computation for dealing with steep dips, but it is difficult to process lateral velocity variation. In contrast, the finite difference formula is a very good way in the proceeding of arbitrary velocity variation , and in X domain, it is simple and stable in computation, but there are still many problems in dealing with steep dip events. If a fast 45° finite difference wave equation is used as a complement to phase shift extrapolation, a way suited to the variation of velocity in all directions will be got. In this way, a steep dip geological structure can be processed accurately. Now, the idea in 3D media’s data proceeding is used and expanded into 3D phase shift plus finite difference hybrid formula. Based on this, the so called 3D hybrid one step wave equation forward modeling formula is deduced.
引文
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