  The P-wave slowness and group-velocity surfaces in elliptically anisotropic
media are ellipsoids. Elliptical anisotropy is convenient to use as the
reference medium in perturbation methods designed to solve P-wave
wave-propagation problems for transverse isotropy (TI). Here, we make the
elliptically anisotropic TI model attenuative and discuss the corresponding
P-wave dispersion relation and the wave equation. Our analysis leads to two
conditions in terms of the Thomsen-type parameters, which guarantee that the
P-wave slowness surface and the dispersion relation satisfy elliptical
equations. We also obtain the viscoacoustic wave equation for such elliptically
anisotropic media and solve it for point-source radiation using the
correspondence principle. Numerical examples validate the proposed elliptical
conditions and illustrate the behavior of the P-wavefield in attenuative
elliptical TI models.
