基于LS-RSGFD方法优化的横向各向同性(TI)介质一阶qP波高精度数值模拟

为克服各向异性介质弹性波数值模拟中存在着计算量大和波场分离困难等局限,研究了声学近似的VTI介质和TTI介质一阶qP波数值模拟方法.首先对VTI介质弹性波方程进行声学近似,推导了VTI介质一阶qP波方程;然后基于精确的TTI介质频散关系,引入一个包含各向异性控制参数σ的新辅助波场,推导了稳定的TTI介质二阶耦合qP波波动方程,并通过引入波场的伪速度分量,推导了等价的一阶应力-速度形式.结合旋转交错网格有限差分(RSGFD)和基于最小二乘优化的有限差分(LS-FD)两种各具优势的方法,研究了最小二乘旋转交错网格有限差分(LS-RSGFD)方法,并用其数值求解VTI和TTI介质一阶qP波方程,然后通过构造其LS-RSGFD格式,实现了高精度的各向异性介质qP波波场数值模拟.数值模拟结果表明:TI介质一阶qP波方程能够准确地模拟各向异性介质中qP波的运动学特征,引入控制参数σ能够有效地减弱不稳定性问题,保证非均匀TTI介质中qP波场的稳定传播;利用优化的LS-RSGFD方法可以得到高精度的合成地震记录,同时还可以相对地提高计算效率.

High-precision numerical simulation of first-order qP-waves in the transversely isotropic (TI) medium optimized by the LS-RSGFD method

In order to overcome the limitations of anisotropic elastic wave modeling, such as large computational costs, and the difficulty of wave-field separation, we have studied the numerical simulation methods of first-order qP-waves in the acoustic approximated VTI and TTI media. Starting from the acoustic approximated VTI elastic wave equation, we derived the VTI first-order qP-wave equation. Then based on the accurate TTI dispersion relation, the stable TTI second-order coupled qP-wave equation was derived by introducing a new auxiliary function including an anisotropic control parameter σ, and the equivalent first-order stress-velocity form was deduced. Combining the RSGFD with the LS-FD two advantageous method, we studied the LS-RSGFD method to solve VTI and TTI first-order qP-wave equation numerically, and then implemented high-precision numerical simulation through constructing the LS-RSGFD form of first-order qP-wave equation. Numerical results demonstrate that TI first-order qP-wave equation can describe the kinematics features of qP-waves in anisotropic media; introducing a control parameter can mitigate the instability problem and thus stabilize qP-wave propagation in heterogeneous TTI media; and applying the optimal LS-RSGFD method can acquire high-precision synthetic seismic recordings. Meanwhile it can enhance computational efficiency relatively.