The quality factor (Q) links seismic wave energy dissipation to physical properties of the Earth’s interior, such as temperature, stress and composition. Frequency independence of Q, also called constant Q for brevity, is a common assumption in practice for seismic Q inversions. Although exactly and nearly constant Q dissipative models are proposed in the literature, it is inconvenient to obtain constant Q wave equations in differential form, which explicitly involve a specified Q parameter. In our recent research paper, we proposed a novel weighting function method to build the first- and second-order nearly constant Q dissipative models. Of importance is the fact that the wave equations in differential form for these two models explicitly involve a specified Q parameter. This behaviour is beneficial for time-domain seismic waveform inversion for Q, which requires the first derivative of wavefields with respect to Q parameters. In this paper, we extend the first- and second-order nearly constant Q models to the general viscoelastic anisotropic case. We also present a few formulations of the nearly constant Q viscoelastic anisotropic wave equations in differential form.

品质因数 ( Q ) 将地震波能量耗散与地球内部的物理特性（例如温度、应力和成分）联系起来。Q 的频率独立性，也称为常数Q为简洁起见，是地震Q反演实践中的常见假设。尽管文献中提出了精确且几乎恒定的Q耗散模型，但以微分形式获得恒定Q波动方程并不方便，其中明确涉及指定的Q参数。在我们最近的研究论文中，我们提出了一种新的加权函数方法来构建一阶和二阶几乎恒定的Q耗散模型。重要的是，这两个模型的微分形式的波动方程明确涉及指定的Q参数。这种行为有利于Q 的时域地震波形反演，这需要波场关于Q参数的一阶导数。在本文中，我们将一阶和二阶几乎恒定的Q模型扩展到一般粘弹性各向异性情况。我们还以微分形式提出了一些几乎恒定的Q粘弹性各向异性波动方程的公式。