  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 behavior 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 formulation of the nearly constant Q viscoelastic
anisotropic wave equations in differential form.
