各向异性黏弹性介质波场数值模拟

Wavefield numeric simulation in anisotropic viscoelastic media

地层不仅表现为各向异性,还表现为内在的黏弹性特征.为准确描述地震波在地球介质中的传播特征,选取的模型应该能够模拟岩石的各向异性特征和衰减特征.基于玻尔兹曼叠加原理,考虑本构方程,建立二维黏弹性VTI介质的波动方程及其差分格式,利用交错网格有限差分法分别对弹性和黏弹性VTI介质进行数值模拟,并且分析不同品质因子组合对波场能量衰减和频率吸收作用的影响.数值模拟结果表明:膨胀滞弹性形变的品质因子主要影响qP波衰减,并且品质因子越小,qP波衰减越大;剪切滞弹性形变的品质因子主要影响qSV波的能量衰减,并且品质因子越小,qSV波衰减越大;各向异性黏弹性中qP波、qSV波主频向低频方向移动,高频吸收明显,有效频带变窄.

In view of the fact that layers not only show anisotropic behavior,but also show intrinsic viscoelastics,thus an accurate description of wave propagation in earth medium requires a model that accounts for the anisotropic and viscoelastic behavior of rocks. This paper established a wave equation and the difference scheme of 2D viscoelastic VTI media based on the Boltzmann superposition principle,starting from the constitutive equations. The simulation wave field propagation in elastic and viscoelastic VTI medium used grid high order finite difference,and compared and analyzed the effects of energy attenuation and frequency absorption related to different Q factor pair. The results of numerical simulation show:the Q factor related to dilation inelastic deformation affects energy attenuation of qP wave,and the smaller the Q factor is,the greater the qP-wave attenuation. The Q factor related to shear inelastic deformation affects energy attenuation of qSV wave,and the smaller the Q factor,the greater the qSV-wave attenuation. While the frequency of qP wave and qSV wave in the anisotropic viscoelastic tend to be of low frequency,absorption of high frequency is obvious and the effective frequency band narrows. The research work is useful for further understanding of seismic wave propagation in anisotropic viscoelastic media.