TTI介质一阶qP波稳定方程波场数值模拟及逆时偏移

相比于各向异性介质弹性波波动方程,利用声学近似的各向异性介质qP波方程进行波场数值模拟及逆时偏移更具优势。常规的声学近似方法往往会造成非均匀TTI介质中倾角剧变区域出现数值不稳定。为此,基于精确的TTI介质qP-qSV波耦合频散关系,首先引入一个各向异性控制参数σ,推导了新的TTI介质二阶qP波稳定方程,并通过引入波场的伪速度分量,将其转换为等价的一阶应力-速度形式波动方程。然后,利用优化的最小二乘交错网格高阶有限差分(LS-SGFD)方法数值求解TTI介质一阶qP波稳定方程,构建波场延拓算子,实现了精确的各向异性介质波场模拟及逆时偏移成像。模型试算结果表明,TTI介质一阶qP波方程能够稳定地模拟qP波的波场传播特征,利用优化的LS-SGFD方法能够有效地提高波场模拟的精度,进一步可以改善偏移成像质量。

Wave-field numerical simulation and reverse-time migration based on the stable TTI first-order qP-wave equations

Compared with anisotropic elastic wave equation, it is more advantageous to use approximate anisotropic qP-wave equation for wave-field numerical simulation and reverse-time migration (RTM). However, the conventional acoustic approximation method usually causes numerical instability in heterogeneous TTI media with rapid dip variation. Therefore we propose in this paper a new approach of wave-field numerical simulation and RTM based on stable first-order qP-wave equations. First based on the exact qP-qSV wave dispersion relation, the new TTI second-order qP-wave equations are derived by introducing an anisotropic control parameter σ, and meanwhile they are transformed into the equivalent first-order stress-velocity form wave equations through introducing the pseudo-velocity components of the wave-fields. Then, we apply the optimal high-order least-squares stagger-grid finite-difference (LS-SGFD) method to solve the stable TTI first-order wave equations and construct the wave-field extrapolators. In this way the accurate wave-field simulation and RTM of anisotropic media are achieved. Model test results show that TTI first-order qP-wave equation can steadily simulate the wave-field propagation features of qP-wave. Utilizing the optimal LS-SGFD method can effectively enhance the modeling accuracy, and further improve the imaging quality.