基于最佳平方逼近的TTI介质解耦qP波与qSV波逆时偏移

Reverse time migration of decoupled qP-and qSV-waves in TTI media with the optimal quadratic approximation

在实际地震资料处理中,若忽略各向异性影响、TTI介质对称轴倾角变化,会造成目标体成像位置偏差,甚至由焦散问题造成振幅不均衡。传统TI介质耦合拟声波方程正演模拟与逆时偏移存在伪横波干扰,且在各向异性参数ε<δ时数值模拟不稳定。为此,借鉴前人经验,首先使用最佳平方逼近(OQA)近似VTI介质精确相速度公式,分别得到较高精度的近似qP波、qSV波相速度公式。然后从近似相速度公式出发,推导了二维TTI介质解耦qP波、qSV波波动方程。为实现高效、稳定的数值模拟,使用有限差分-伪谱混合法求解波动方程。最终,建立了高精度、高效率、稳定的TTI介质正演模拟与逆时偏移成像算法。数值模拟实验表明,所提方法可实现复杂TTI介质偏移成像。

In the seismic data processing,if the influence of anisotropy and the symmetry inclination of TTI medium changes are ignored,the imaging position of targets will be deviated,and even the amplitude imbalance may be caused by the caustic problem.The pseudo-shear-wave interference exists in the forward modeling and RTM when using the conventional TI coupled pseudo-acoustic wave equations,and the numerical simulation is unstable when the anisotropy parameterε<δ.To solve the problem,a new approach is proposed.By referring to the experience of predecessors,the idea of the optimal quadratic approximation(OQA)is used to approximate the accurate phase velocity formula in VTI medium,and approximate phase velocity formulas of qP-wave and qSV-wave with relatively high accuracy are obtained respectively.Then,based on the approximate phase velocity formula,the decoupled qP-wave and qSV-wave equations in TTI medium are derived.In order to realize efficient and stable numerical simulation,a hybrid finite-difference/pseudo-spectral method is used to solve the wave equations.Finally,a high-precision,high-efficiency,and stable TTI media forward modeling and RTM is established.Numerical simulation results show that the proposed method can achieve migration imaging in complex TTI media.