Nearly constant Q models of the generalized standard linear solid type and the corresponding wave equations

Abstract

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 [Formula: see text], also called the frequency independence of the quality factor, is a common assumption for seismic [Formula: see text] inversion. We have developed first- and second-order nearly constant [Formula: see text] dissipative models of the generalized standard linear solid type, using a novel [Formula: see text]-independent weighting function approach. The two new models, which originate from the Kolsky model (a nearly constant [Formula: see text] model) and the Kjartansson model (an exactly constant [Formula: see text] model), result in the corresponding wave equations in differential form. Even for extremely strong attenuation (e.g., [Formula: see text]), 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 [Formula: see text] parameter and have compact and simple forms. We provide a novel perspective on how to build a nearly constant [Formula: see text] 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.