六分量弹性波场数值模拟与分析

地震波传播过程中,质点的振动不仅包括三个独立的平移部分,还包括三个独立的旋转部分.本文基于一阶速度-应力弹性波方程,采用分裂完全匹配层(SPML)的吸收边界条件,推导了时间导数二阶精度和空间导数高阶精度的交错网格有限差分格式的弹性波速度与应力各分量计算公式,模拟了各向同性介质中均匀模型和层状模型下的六分量波场,并对二维各向同性层状模型下的三个分量地震记录做高分辨率线性拉东变换得到各自的频散能谱.数值模拟分析结果表明:(1)旋转分量的能量要比平动分量弱的多;(2)在平动分量上,面波能量强,频率低,反射P波能量较强,反射S波能量稍弱;在旋转分量上,反射P波能量很弱,S波能量强;(3)与平动分量相比,旋转分量的频散能谱效果更好,能看到基阶和完整的高阶面波,即旋转分量能反映更多的地下介质信息.

Numerical simulation of the six-component elastic-wave field

In the seismic wave propagation, the particle motion includes not only three independent translations, but also three independent rotations. In this paper, we simulate seismic wave propagation in the elastic medium, including body and surface waves, and analyze the wave characteristics of all the six components. Based on the theory of first-order velocity-stress elastic wave equation, we use the absorbing boundary condition of the Splitting Complete Matching Layer (SPML) in the simulation. The calculation formulas of the velocity and stress in the staggered grid finite difference scheme are derived to simulate the six-component wave field in the isotropic medium. And then the three-component dispersive-energy spectra in a two-dimensional isotropic two-layer model are obtained by a high-resolution linear Radon transform. The simulation results show that the energy of rotational components is much weaker than that of translational components. In the translational components, surface waves have stronger energy and lower frequency, while the P-wave energy is stronger and the S-wave energy is weaker. On the contrary, in the rotational components, the P-wave energy is weaker and the S-wave energy is stronger. The dispersion energy spectra of rotational components contain more information on fundamental and higher modes, namely rotational components carry more underground information.