  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.
