The equation for general anisotropic elastic wave propagation is
Transverse isotropy is the next more complex symmetry class after isotropy. It allows the description of material properties like those of shale or layered isotropic mixtures (Muir 1990).
In approaching the anisotropic forward propagation problem I followed Etgen: I used the explicit finite-difference stress-strain formulation to solve the anisotropic wave equation. Since the time step size is limited by a stability criterion, this method is somewhat more expensive than methods using one way equations. On the other hand, within the stability limit accurate amplitudes are obtained in the computed wavefield, without any dip limitation. An additional advantage is material parameters that are freely variable in space.
Recent processing techniques tend to emphasize preservation of amplitude information during all processing steps. When not only imaging subsurface structure, but also determination material properties is important, algorithms based on two-way equations are the best way to ensure correct amplitudes and allow for full complexity of the wavefield. Algorithms based on the one-way equation will necessarily give incorrect reflection amplitude information.