Lebedev网格黏弹性介质起伏地表正演模拟

Numerical simulation of Lebedev grid for viscoelastic media with irregular free-surface

在前人研究的基础上,采用一种新的交错网格(Lebedev网格)进行曲坐标系下的黏弹性介质正演模拟,避免了标准交错网格在处理曲坐标系方程时进行波场插值而引入的数值误差,从而提高了模拟精度。在正演模拟的过程中,首先基于广义标准线性固体,推导了曲坐标系下黏弹性介质的波动方程,随后利用在各向异性介质中使用的Lebedev网格有限差分方法对波动方程进行了离散化,在地表附近采用牵引力镜像法来实施自由表面条件,其他三个边界引进多轴卷积完全匹配层技术提高吸收效果,最后通过模型试算分析了黏滞性的引入以及地形起伏对波场的双重影响,并验证了引入的边界条件具有较好的吸收效果。模型试算结果表明,由于黏弹性介质中吸收衰减的影响导致地震波能量降低且主频向低频端移动,同时由于速度频散导致走时差异及波形变化。

Based on previous research, this paper adopts a Lebedev grid (LG) for viscoelastic media as a new kind of staggered grid scheme for finite-difference modeling. Compared to Virieux's standard staggered grid (SSG), this scheme can avoid numerical dispersion from the interpolate wavefield when dealing with equations in the curvilinear coordinates. First of all, we deduce viscoelastic media wave equations based on the generalized standard linear solid (GSLS) under the curved coordinate system. And in the process of implementation, Lebedev grid in anisotropy media is used to discretize the equations. The traction image method is used to implement free-surface conditions. And for other boundaries multi-axial convolution perfectly matched layer (MC-PML) technique is chosen to absorb waves. Based on numerical tests on synthetic data, influence of both viscosity and topography on wavefield is showed, and the MC-PML in this study is stable and can effectively absorb artificial boundary reflections. Test results show that the absorption in viscoelastic media reduces seismic energy and decreases the dominant frequency, and at the same time the velocity dispersion produces traveltime difference and waveform change. © 2016, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.