Time-domain seismic forward and inverse modeling for a dissipative medium is a vital research topic for investigating the attenuation structure of the earth. Constant $Q$, also called the frequency independence of the quality factor, is a common assumption for seismic $Q$ inversion. We have developed first- and second-order nearly constant $Q$ dissipative models of the generalized standard linear solid type, using a novel $Q$-independent weighting function approach. The two new models, which originate from the Kolsky model (a nearly constant $Q$ model) and the Kjartansson model (an exactly constant $Q$ model), result in the corresponding wave equations in differential form. Even for extremely strong attenuation (e.g., $Q=5$), the quality factor and phase velocity for the two new models are close to those for the Kolsky and Kjartansson models, in a frequency range of interest. The wave equations for the two new models explicitly involve a specified $Q$ parameter and have compact and simple forms. We provide a novel perspective on how to build a nearly constant $Q$ dissipative model, which is beneficial for time-domain large-scale wavefield forward and inverse modeling. This perspective could also help obtain other dissipative models with similar advantages. We also discuss the extension beyond viscoacousticity and other related issues, for example, extending the two new models to viscoelastic anisotropy.

中文翻译：

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广义标准线性实体类型的近常数 Q 模型及相应的波动方程

耗散介质的时域地震正反演建模是研究地球衰减结构的重要研究课题。不变$问$，也称为品质因数的频率独立性，是地震的常见假设 $问$反转。我们已经开发出一阶和二阶几乎恒定的$问$ 广义标准线性实体类型的耗散模型，使用一种新颖的 $问$-独立加权函数方法。源自 Kolsky 模型的两个新模型（几乎恒定的$问$ 模型）和 Kjartansson 模型（完全恒定的 $问$模型），产生相应的微分形式的波动方程。即使对于极强的衰减（例如， $问=5$)，在感兴趣的频率范围内，两个新模型的品质因数和相速度接近 Kolsky 和 ​​Kjartansson 模型的品质因数和相速度。两个新模型的波动方程明确涉及一个指定的$问$参数并具有紧凑和简单的形式。我们提供了一个关于如何建立一个几乎恒定的新视角$问$耗散模型，有利于时域大尺度波场正反演建模。这种观点也有助于获得具有类似优势的其他耗散模型。我们还讨论了粘声性以外的扩展和其他相关问题，例如，将两个新模型扩展到粘弹性各向异性。