三维各向异性介质中弹性波方程交错网格高阶有限差分法数值模拟

Three-dimensional numerical simulation of elastic wave propagation in 3-D anisotropic media with staggered-grid high-order difference method

三维数值模拟是研究各向异性介质中复杂弹性波波场特征和传播规律的重要手段。根据Taylor展开式,推导出了交错网格一阶空间导数的任意偶数阶精度有限差分近似式和相应的差分系数计算式,给出了三维各向异性介质中弹性波一阶双曲型应力速度方程交错网格任意偶数阶精度差分格式和稳定性条件,并推导出了三维各向异性介质PML法吸收层边界条件公式和相应的交错网格差分格式。对方位各向异性介质模型和正交各向异性介质模型中弹性波的传播进行的三维数值模拟结果表明,弹性波在三维各向异性介质中传播时存在拟P波、拟SV波和拟SH波,并出现横波分裂、横波分裂盲区、波面三分叉等特殊现象,另外,弹性波场在空间是变化的,其拟P波、拟SV波和拟SH波的耦合关系比较复杂。

The characteristics of wave fields and propagation of elastic wave in anisotropic media can be studied using 3-D numerical simulation. An even-order accurate difference scheme of one-order spatial derivative and relevant calculating formula of any even-order difference coefficients on a staggered grid were derived from the expansion of Taylor series. The even-order accurate difference scheme of one-order hyperbolic elastic wave equation and its stability condition in 3-D anisotropic media were presented. A perfectly matched absorbing layer boundary conditions and its staggered-grid high-order difference scheme were given. The results of 3-D numerical modeling of the transversely isotropic media with horizontal symmetry axis and the orthorhombic symmetry media showed that quasi-P wave,quasi-SV wave and quasi-SH wave occurred during elastic wave propagation in 3-D anisotropic media. Meanwhile, the special phenomena such as the S wave splitting, the blind zone of S wave splitting and quasi-SV wave-front triplication were clearly observed. In addition, the elastic wave-fronts are spatially changed, and the coupled relations among the quasi-P wave,quasi-SV wave and quasi-SH wave in 3-D anisotropic media are very complex.