三维VTI介质qP波方程频率空间域有限差分高阶加权算子

波动方程有限差分法是波场模拟的一个重要方法,为解决常规有限差分法存在着数值频散的问题,本文从具有垂直对称轴的三维横向各向同性(VTI)介质频率-空间域qP波动方程出发,在常规差分算子的基础上构造了适合三维VTI介质的频率空间域有限差分优化算子,然后利用最优化理论中的Gauss-Newton法求解了优化算子的系数,使差分方程的相速度与波动方程的相速度尽量吻合,从而在理论上使网格数值频散达到极小,精度对比分析及数值测试表明,有限差分优化算子具有较高的波场数值模拟精度,有效地压制了数值频散现象,为三维VTI介质频率一空间域qP波正演模拟研究提供了理论基础.

Finite difference high-order weighted-averaging operator for frequency-space domain qP wave in 3-D VTI media

The finite difference is an important method of wave-field numerical simulation .In order to solve the problem of numerical dispersion of the conventional finite difference method, we start with frequency-space domain qP wave equation in 3-D transversely isotropy with a vertical axis of symmetry (VTI) media, and present the optimal finite difference operators based on conventional finite difference operators. Then we get the optimal coefficient by the Gauss-Newton method in optimization theory to make the finite-difference equation phase velocity equal to that of wave equation, so the numerical dispersion and numerical anisotropy will be minimum in theory. The results of velocity dispersion analysis and numerical simulation show that the finite-difference method using optimal operators can improve the numerical simulation accuracy, and decrease the numerical dispersion efficiently which can supply the foundation for qP wave simulation in frequency-space domain in 3-D VTI media.