Exact seismic velocities for TI media and extended Thomsen formulas for stronger anisotropies

HTI Symmetry

Figures 7-12 present results for vertical fractures having their normals (axes of symmetry) aligned in some direction (say $x_3 = x$). The fracture models considered are the same and use the same data as for the preceding (VTI) case.

Thomsen's approximation and the new one are virtually identical here in $v_{sh}(\theta)$ for both $\nu _0 = 0.00$ and $\nu _0 = 0.4375$. For $v_{sv}(\theta)$, Thomsen's approximation is higher than the exact result, while the new approximation is lower.

Results for $v_p(\theta)$ in both Thomsen's and the new approximation are comparable to the exact results for $\theta$'s up to about $45^o$-$50^o$, but are not identical to each other or to the exact result. For $\nu _0 = 0.4375$, agreement among the three curves is good for $v_p(\theta)$, but not so good for $v_{sv}(\theta)$ or $v_{sh}(\theta)$.

Exact seismic velocities for TI media and extended Thomsen formulas for stronger anisotropies