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相比于VTI介质q P波数值模拟方法,考虑倾角因素的TTI介质q P波数值模拟方法能够更加准确地描述各向异性介质中波场的传播特征。常规的声学近似方法往往会造成TTI介质中倾角急剧变化的区域出现数值不稳定,笔者首先引入一个各向异性控制参数,推导了稳定形式的TTI介质二阶q P波方程,保证q P波场的稳定传播;其次,通过引入波场的伪速度分量,推导了其等价的一阶应力—速度形式及相应的PML边界条件,并应用优化的旋转交错网格有限差分(RSGFD)方法实现了精确的数值模拟。数值结果表明:TTI介质一阶q P波方程能够稳定、有效地模拟q P波的运动学特征,利用优化的RSGFD方法可以得到精确的合成地震记录,同时可以相对地提高计算效率。
Compared with the qP wave numerical simulation method of VTI media, the qP wave numerical simulation method of TTI media considering the tilt factor can more accurately describe the wave propagation characteristics in anisotropic media. Conventional acoustic approximation method often results in instability in the region where dip angle in TTI medium changes sharply. The author first introduces an anisotropic control parameter and deduces the second-order q P-wave equation in stable form of TTI medium to ensure q P wave field Secondly, by introducing the pseudo-velocity component of the wavefield, the equivalent first-order stress-velocity form and the corresponding PML boundary conditions are deduced, and the optimal rotational staggered grid finite difference (RSGFD) method is implemented Accurate numerical simulation. The numerical results show that the first-order q P-wave equation in TTI media can simulate the kinematic characteristics of q P wave in a stable and effective manner. The optimized synthetic seismogram can be obtained by the optimized RSGFD method and the computational efficiency can be improved relatively.