TTI介质弹性波频率-空间域有限差分数值模拟

Frequency-Space Domain Finite Difference Numerical Simulation of Elastic Wave in TTI Media

由周期性薄互层引起的VTI介质是研究比较广泛的一类各向异性介质。当VTI介质对称轴偏离垂向,本构坐标系与观测坐标系不重合时,会形成观测坐标系下的TTI介质。引入25点优化差分算子,推导出二维TTI介质频率域弹性波动方程;为压制边界反射,采用完全匹配层法吸收边界条件,并计算出优化差分系数;最后采用集中力源,模拟了弹性波在TTI介质中的传播过程。从波场快照和地面共炮记录可以看出,笔者采用的数值模拟算法能有效压制数值频散。TTI介质中的波场传播比较复杂,纵波传播相对稳定,横波波前的三分叉现象比较明显,并存在振幅奇异性。当VTI介质的对称轴偏转后,还会增加地面地震记录的复杂性。

The VTI media is caused by fine periodic thin layers, and it is one of most sedimentary rocks researched by geophysicists. In dipping thin layers, the symmetry axis of VTI media should be tilted by dip angle in observing reference system, and in this case, VTI media is named transversely isotropic media with tilted symmetry axis （TTI media）. In the paper, in order to overcome the numerical dispersion, we have adopted a 25--points finite difference numerical simulation scheme and derived fre- quency-space domain elastic wave equations of TTI media. We make use of elastic wave equation in perfect matched layer to attenuate reflection of elastic wave at artificial boundary, and get optimized coefficients on the basis of optimization theory. Finally, we successfully implement numerical simulation of seismic elastic wave field in TTI media with concentrating force source. The results of seismic wave simulation illustrate that elastic wave fields of anisotropic media are very complex, transverse waves often have phenomena of singularity, and the difficulties of surface seismic record processing increase owing to TTI media.