Conclusions

The foregoing examples show that reflection amplitudes depend on the material filling of the cracks, crack shape, and crack density. P-wave reflection magnitudes are most affected near critical angles, yet there is also significant azimuthal variation at precritical angles in some of the models. P-wave reflection magnitudes display different degrees of azimuthal behavior as the aspect ratio, volume density and filling material of the cracks are varied.

Generally, as we have seen, fracture direction aligns with elongation of contour lines. However, we may run into trouble for model B of cracks when trying to fit an ellipse on the P-wave pattern, as recently proposed by Lefeuvre 1994. The pattern for this model has the interesting property that azimuthal behaviors for precritical angles are only observed for out-of-axis propagation angles. All in all, the patterns obtained for the models suggest that a double elliptic approximation should be used to model P-wave reflection amplitudes. In future research, I hope to tackle the problem of obtaining an approximate theory to model TI reflection coefficients that is valid for any degree of anisotropy and of discontinuities in the elastic properties across boundaries, and valid for any angle of propagation. Such theory should reproduce the results obtained here, and explain the different behaviors.