Seismic anisotropy, wave attenuation, and dispersion are critical phenomena of wave propagation in real media. Full-wavefield modeling of wave behavior in such media plays an important role in investigating dynamic features of the earth’s interior and in full-waveform inversion of anisotropic parameters and velocity dispersion. We have developed a numerical scheme to model the full-waveform response from a point source in a vertically varying viscoelastic medium of arbitrary anisotropy. The method is implemented in the frequency domain, so the complexity of anelasticity and anisotropy can be described by a complex elastic stiffness matrix and frequency-dependent moduli can also be readily incorporated. In our scheme, we solve the elastodynamic equations for general anisotropy through finite-element method in the frequency-wavenumber domain and we use the stiffness reduction method to suppress reflections from artificial boundaries along the depth direction. A nonuniform 2D Fourier transform strategy is developed to reconstruct the spatial-domain counterparts from the wavenumber-domain solutions. The time-domain responses are then obtained by taking inverse fast Fourier transform with respect to frequency. We validate the method by comparing the numerical results with the exact solutions for a homogeneous transversely isotropic model and a two-layered model. In the application example, we further proved the feasibility and generality of the scheme using an attenuative, dispersive model with velocity and attenuation anisotropy. Our scheme enjoys significant advantages in incorporating various viscoelastic/dispersive behaviors and general anisotropy, and thus provides a useful tool for numerical simulation of dynamic responses in practical application.

中文翻译：

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具有一般各向异性的垂直变化粘弹性介质中的地震波建模

地震各向异性、波衰减和色散是真实介质中波传播的关键现象。此类介质中波浪行为的全波场建模在研究地球内部的动态特征以及各向异性参数和速度色散的全波形反演中起着重要作用。我们开发了一种数值方案来模拟来自任意各向异性的垂直变化粘弹性介质中的点源的全波形响应。该方法是在频域中实现的，因此非弹性和各向异性的复杂性可以通过复杂的弹性刚度矩阵来描述，并且频率相关的模量也可以很容易地合并。在我们的方案中，我们通过频波数域中的有限元方法求解一般各向异性的弹性动力学方程，并使用刚度降低方法抑制沿深度方向来自人工边界的反射。开发了一种非均匀二维傅立叶变换策略，以从波数域解中重建空间域对应物。然后通过对频率进行逆快速傅立叶变换来获得时域响应。我们通过将数值结果与均匀横向各向同性模型和两层模型的精确解进行比较来验证该方法。在应用实例中，我们使用具有速度和衰减各向异性的衰减色散模型进一步证明了该方案的可行性和通用性。