Under the conditions of acoustic approximation and isotropic attenuation, we derive the pseudo- and pure-viscoacoustic wave equations from the complex constitutive equation and the decoupled P-wave dispersion relation, respectively. Based on the equations, we investigate the viscoacoustic wave propagation in vertical transversely isotropic media. The favourable advantage of these formulas is that the phase dispersion and the amplitude dissipation terms are inherently separated. As a result, we can conveniently perform the decoupled viscoacoustic wavefield simulations by choosing different coefficients. In the computational process, a generalised pseudo-spectral method and a low-rank decomposition scheme are adopted to calculate the wavenumber-domain and mixed-domain propagators, respectively. Because low-rank decomposition plays an important role in the simulated procedure, we evaluate the approximation accuracy for different operators using a linear velocity model. To demonstrate the effectiveness and the accuracy of our method, several numerical examples are carried out based on the new pseudo- and pure-viscoacoustic wave equations. Both equations can effectively describe the viscoacoustic wave propagation characteristics in vertical transversely isotropic media. Unlike the pseudo-viscoacoustic wave equation, the pure-viscoacoustic wave equation can produce stable viscoacoustic wavefields without any SV-wave artefacts.

中文翻译：

---

VTI介质中各向异性黏声波的频率依赖性复数速度建模

在声学近似和各向同性衰减的条件下，我们分别从复本构方程和解耦的P波频散关系推导了伪粘声波方程和纯粘声波方程。基于这些方程，我们研究了垂直横观各向同性介质中的粘声波传播。这些公式的有利优点是，相位色散和幅度耗散项固有地分开。结果，我们可以通过选择不同的系数来方便地执行去耦粘声波场模拟。在计算过程中，分别采用广义伪谱方法和低秩分解方案来计算波数域和混合域的传播子。由于低秩分解在模拟过程中起着重要作用，因此我们使用线速度模型来评估不同算子的近似精度。为了证明我们方法的有效性和准确性，在新的伪声波方程和纯粘声波方程的基础上进行了几个数值算例。这两个方程都可以有效地描述垂直横观各向同性介质中的粘声波传播特性。与伪粘声波方程不同，纯粘声波方程可以产生稳定的粘声波场，而没有任何SV波伪影。基于新的伪声波方程和纯粘声波方程，进行了几个数值示例。这两个方程都可以有效地描述垂直横观各向同性介质中的粘声波传播特性。与伪粘声波方程不同，纯粘声波方程可以产生稳定的粘声波场，而没有任何SV波伪影。基于新的伪声波方程和纯粘声波方程，进行了几个数值示例。这两个方程都可以有效地描述垂直横观各向同性介质中的粘声波传播特性。与伪粘声波方程不同，纯粘声波方程可以产生稳定的粘声波场，而没有任何SV波伪影。