复杂TTI介质稳定的纯qP波波场模拟方法

作为各向异性逆时偏移技术的基础，复杂各向异性介质情况下精确而稳定的波场模拟至关重要。本文给出一种针对复杂倾斜横向各向同性（tilted transversely isotropic，TTI）介质的稳定的纯qP波波场模拟方法。该方法基于Xu提出的伪微分算子分解思路，通过分析新算子的频散特性，引入旋转坐标系下的自共轭算子以保证稳定性，导出新的TTI介质一阶纯qP波控制方程；在Lebedev交错网格框架下推导了新方程的高阶有限差分形式，给出2次计算波场梯度的数值算法实施策略，以进一步保证波场模拟精度。均匀各向异性介质及复杂TTI介质模型的数值试算结果表明：新控制方程不受伪横波影响；相对于有限横波qP波波场模拟等算法，新算法可得到更稳定的各向异性纯qP波波场，即能更适应各向异性对称轴参数的空间变化，可应用于高精度纯qP波逆时偏移，改善对各向异性介质的成像质量。

Pure quasi-P wave stable simulation in complex TTI media

Facing to more complicated targets, seismic exploration drops on an increasing demand for accurate subsurface imaging.We analyse the dispersion features of the decomposed scalar operator and elliptic differential operator produced by elliptic pseudo differential decomposition method proposed by Xu et al (2015).Then the corresponding first-order differential equation of pure quasi-P wave for tilted transverse isotropic (TTI) media is derived by introducing self-adjoint operators under rotated coordinates to preserve stability.Under the Lebedev staggered grid framework, we deduce the high-order finite difference scheme of the equation and give out the strategy of 2 times calculation of wavefield gradient to preserve the simulating accuracy.We test our algorithm in homogeneous and complex TTI media.The results show that the quasi-P wavefiled is not affected by pseudo-S-waves.Compared with other quasi-P wave simulating methods, our solution produces more stable wavefield in complex anisotropic media which shows that it has a high tolerance to the spatial variation of anisotropic parameters, especially the abrupt changes of the TTI symmetric axis.Our solution can be used for accurate pure quasi-P wave reverse time migration (RTM) to improve the imaging accuracy of subsurface with complex anisotropy.