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

TL;DR

This paper introduces new nearly constant Q dissipative models for seismic wave equations, improving time-domain modeling accuracy in strongly attenuating media and offering a novel approach for large-scale wavefield simulations.

Contribution

The paper presents the first- and second-order nearly constant Q models based on a novel Q-independent weighting function, derived from Kolsky and Kjartansson models, with explicit Q parameter inclusion.

Findings

Models closely match Kolsky and Kjartansson models at Q=5

Wave equations have simple, explicit Q dependence

Effective for strong attenuation scenarios

Abstract

Time-domain seismic forward and inverse modeling for a dissipative medium is a vital research topic to investigate the attenuation structure of the Earth. Constant Q, also called frequency independence of the quality factor, is a common assumption for seismic Q inversion. We propose the 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 involve explicitly 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.