In the following examples, I will show fans of *P* wave
ray paths in different models
for a cross-well configuration (Appendix B shows the elastic
constants used for each model). The fans are traced at constant intervals
in
the phase angle which only correspond to constant intervals in the ray angle
when the medium is isotropic. This is shown in Figure a, where
rays have been traced in the simplest model: homogeneous isotropic.
When the model is transversely isotropic with vertical axis of symmetry,
the density of rays changes with angle, as Figure b shows.
Figure c shows the rays paths in a homogeneous
transversely isotropic
model with axis of symmetry tilted with respect to the vertical ().
If two point ray tracing for the same receiver positions
is performed in the corresponding
homogeneous models,
we won't see any difference among the three ray path diagrams because
the ray angles depend only on the relative positions of source and receivers.
The differences among the three cases will be in the traveltimes.

Figure 6

Models like the ones shown in Figure may arise after different combinations of deposition, erosion and rotation of the layers involved. The areas of the model that are finely layered can be modeled as homogeneous anisotropic layers with axis of symmetry perpendicular to the layering. The only difference between the two models in Figure is in the axis of symmetry the third layer. Figure show the rays traced through these models for a source at 3500 ft.

Figure 7

11/18/1997