Though physically impossible, the acoustic wave equation for *P*-waves
in transversely isotropic media with
a vertical symmetry axis (VTI media) that I have derived
yields good kinematic approximations to the
familiar elastic wave equation for VTI media. The fourth-order nature of this acoustic equation
results in two sets of complex conjugate solutions. One set of solutions are just perturbations
of the familiar acoustic wavefield solutions
in isotropic media for incoming and outgoing waves.
The second set describes a wave type that propagates
at speeds slower than the *P*-wave
for the positive anisotropy parameter, , and grows exponentially, becoming unstable, for negative
values of . Most values corresponding to anisotropies in the subsurface are likely to have positive values.
Placing the source or receivers in an isotropic
layer, a common occurrence in marine surveys
where the water layer is isotropic, will eliminate most of the
energy of this additional wave type. Numerical examples, provided in this paper,
prove the usefulness of this acoustic equation in simulating
wave propagation in VTI media.

A ray theoretical (high-frequency) approximation is used to derive the eikonal and transport equations that describe the traveltime and amplitude behavior, respectively. These equations are also simpler than those we have grown accustomed to in anisotropic media.

10/9/1997