黏弹TTI介质中旋转交错网格高阶有限差分数值模拟

Rotated staggered grid high-order finite-difference numerical modeling for wave propagation in viscoelastic TTI media

以Carcione黏弹各向异性理论为基础,给出了适用于黏弹性具有任意倾斜对称轴横向各向同性介质(黏弹TTI介质)的二维三分量一阶速度-应力方程,采用旋转交错网格任意偶数阶精度有限差分格式求解该方程,并推导出了二维黏弹TTI介质完全匹配层(PML)吸收边界条件公式和相应的旋转交错网格任意偶数阶精度有限差分格式,实现了该类介质的地震波场数值模拟.数值模拟结果表明:该方法模拟精度高,边界吸收效果好,可以得到高精度的波场快照和合成记录;并且波场快照和合成记录能较好地反映地下介质的各向异性特征和黏弹性特征.

On the basis of Carcione′s theories of viscoelasticity and anisotropy,two-dimensional,three-component,first-order velocity-stress wave equations of viscoelastic tilted transversely isotropic（viscoelastic TTI） media are presented and a rotated staggered grid any-order finite-difference scheme is used to numerically solve the equations.Equations of the perfectly matched layer（PML） are derived for the wave equations in viscoelastic TTI media and the rotated staggered grid any-order finite-difference scheme is also used to solve these equations.Results of numerical modeling indicate that the modeling precision is high and the absorbing boundary condition is good in the viscoelastic TTI media,and high-precision snapshots of wave field and synthetic seismograms can be obtained,and they can reflect the characteristic of viscoelasticity and anisotropy.