TTI介质qP波方程频率—空间域加权平均有限差分算子

Weighted mean finite-difference operator of qP wave equation in frequency-space domain for TTI medium

波动方程有限差分方法能够较精确地模拟任意非均匀介质中的地震波场,但它本身存在着数值频散问题。在具有倾斜对称轴的横向各向同性介质(TTI介质)地震波正演模拟中,为了解决常规有限差分算子的数值频散问题,本文构造了频率—空间域qP波方程加权平均有限差分算子,求取了归一化相速度,并根据最优化理论中的高斯—牛顿法确定了加权平均差分算子的最优加权系数。利用常规差分算子和加权平均差分算子对归一化相速度进行了频散分析,并对均匀TTI介质(包括各向同性介质和椭圆各向异性介质)中的qP波地震波场进行了有限差分数值模拟。结果表明:加权平均有限差分算子具有较高的数值精度,能有效地压制常规有限差分算子的数值频散,为TTI介质频率—空间域qP波正演模拟奠定了基础。

Wave-equation finite-difference algorithm can more preciously simulate seismic wavefield for any non-uniform medium,but have the issue of numeric dispersion. In a seismic wave forward simulation in titled transversely isotropic medium (TTI medium) with titled symmetric axis, in order to solve the issue of numeric dispersion of ordinary finite-difference operator, the paper constructed the weighted mean finite-difference operator of qP-wave equation in frequency-space domain,computed normalized phase velocity and determined the optimal weighted coefficient of weighted mean difference operator according to Gauss-Newton approach of optimization theory. Using ordinary difference operator and weighted mean difference operator to analyze the dispersion of normalized phase velocity and carry out numeric finite-difference simulation of qP-wave seismic wavefield in u-niform TTI medium (including isotropic medium and ellipsoid anisotropic medium). The simulated results showed that the weighted mean finite-difference operator is characterized by higher numeric precision and capable to effectively suppress the numeric dispersion by ordinary finite-difference operator,laying the foundation of qP-wave forward simulation of TTI medium in frequency-space domain.