Nearly constant Q dissipative models and wave equations for general viscoelastic anisotropy

Abstract

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.