起伏地表下基于无网格有限差分的弹性波逆时偏移成像方法研究

Nowadays, with the exploration target being more complicated, the elastic wave imaging method aimed at complex topography and complex geological structures becomes more needed. The elastic reverse-time migration (ERTM) is a powerful tool for complex structures imaging, and its key technologies are numerical solution for the two-way wave equation, the absorbing boundary condition (ABC), the separation of P- and S-waves, the imaging condition and the low frequency noise suppression. The finite-difference (FD) method, as one of the numerical solutions, has the advantages of high computational efficiency, small memory and easy implementation. While the conventional FD method could not fit the irregular interface well, the mesh-free method has no grid constraint, and its discrete nodes could fit the rugged topography interface. The project aims to develop an optimal mesh-free FD method based on least square with high computational efficiency, high simulation accuracy and good adaptability to rugged topography. In addition, the developed FD modeling method is introduced into ERTM to solve wave equation. For the high-accuracy and high-efficiency imaging for rugged topography, ERTM’s key technologies, including the hybird ABC, spatial domain vector separation, normalized imaging conditions and Laplacian noise suppression, are developed to match the mesh-free FD. To demonstrate the effectiveness of our method, the imaging tests are implemented on models. The project is of great theoretical and practical value in elastic wave numerical simulation and migration imaging under rugged topography.

目前勘探对象日趋复杂，复杂地表与复杂构造背景下的弹性波成像方法日趋重要。弹性波逆时偏移是解决复杂构造成像问题的有力工具，其关键技术在于双程波动方程数值求解、吸收边界条件、纵波与横波分离、成像条件与低频噪音压制。数值求解方法之一的有限差分法计算效率高、内存占用小、方便实现，但常规的有限差分法不能较好地逼近不规则界面。无网格法摆脱了网格约束，离散节点能更好地拟合起伏地表界面。本项目拟发展一种计算效率高、模拟精度高、可以较好适应起伏地表的最小二乘优化无网格有限差分法，再将发展的有限差分模拟方法引入逆时偏移中求解波动方程。相应地研究基于无网格有限差分的混合吸收边界条件、空间域矢量分离、归一化成像条件、拉普拉斯滤波噪音压制，实现复杂地表下高精度、高效率逆时偏移成像，并通过模型试算验证其有效性。该研究对起伏地表条件下弹性波数值模拟和偏移成像具有非常重要的理论意义和实际应用价值。

随着地震勘探对象日趋复杂，能够适应起伏地表、复杂构造区域的勘探方法越来越受到重视。无网格法摆脱了网格约束，离散节点能更好地拟合起伏地表；有限差分因其计算效率高、内存占用小、模拟精度高等优点广泛用于地震勘探中。本项目围绕无网格节点分布，从三个方面展开研究：基于无网格的有限差分方法、基于无网格的吸收边界条件、基于无网格的逆时偏移成像。首先，本项目对比了基于GA、IMQ和PHS三种基函数的无网格有限差分法的频散曲线、误差和波场快照，从而选择更适合起伏地表条件的有限差分法。其次，本项目将混合吸收边界条件引入基于无网格节点的时间域数值模拟中；将完全匹配层吸收边界条件引入基于无网格节点的频率域数值模拟中。此外，将前面研究的有限差分方法与吸收边界条件引入逆时偏移的波场延拓中，实现起伏地表、复杂模型条件下的基于无网格有限差分逆时偏移成像。最后，本项目将研究的基于无网格有限差分数值模拟方法应用到实际资料中，实现了某起伏地表地区的数值模拟。