简化的三维TTI介质黏滞纯声波方程及其数值模拟

地球介质普遍具有非弹性和各向异性特征,因此在研究地震波在地下空间传播时应该同时考虑各向异性和黏滞性。在各向异性介质波场模拟、偏移成像和波形反演中,目前主要采用的是伪声波方程,该类方程是在直接将横波速度设置为0的基础上发展的,当介质参数不满足假设条件时容易产生伪横波数值干扰及模拟不稳定。考虑到伪声波方程存在的问题,文中应用泊松算子和有限差分相结合的策略求解高精度的三维TTI介质纯声波方程。同时,考虑到衰减介质对地震波振幅和相位的影响,在各向同性黏滞声波方程的基础上,推导了一种简化的三维TTI介质黏滞纯声波方程,该方程能够模拟纯声波的相位畸变和振幅衰减。应用三维层状模型、TTI楔状体模型和改进的Marmousi模型验证了方法的有效性和适用性。

A simplified pure visco-acoustic wave equation for 3D TTI media and its numerical simulation

As earth media are generally characterized by inelasticity and anisotropy, both anisotropy and viscosity should be considered in research on seismic wave propagation in underground spaces. At present, pseudo-acoustic wave equations are the ones mainly applied in wavefield simulation, migration imaging, and waveform inversion regarding anisotropic media. As these equations are deve-loped on the basis of a shear-wave (S-wave) velocity directly set to zero, numerical pseudo-S wave artifacts and simulation instability are prone to occur when medium parameters do not satisfy the assumed conditions. Given the problem faced with pseudo-acoustic wave equations, this paper solves the high-precision pure acoustic wave equation for 3D tilted transversely isotropic (TTI) media by combining the Poisson operator with finite diffe-rence. Moreover, considering the influence of attenuating media on the amplitude and phase of seismic waves, this paper derives a simplified pure visco-acoustic wave equation for 3D TTI media on the basis of the isotropic visco-acoustic wave equation. This equation can be used to simulate the phase distortion and amplitude attenuation of pure acoustic waves. The effectiveness and applicability of the proposed method are verified with a 3D la-yered model, a TTI wedge model, and a modified Marmousi model.