For TI media, the elastic
constants that control the *P*- and *SV*-wave propagation can be estimated
from *P*-wave measurements near the axes, as equation (24) shows.
Figure shows an example. The left column shows the given *P*-wave
impulse response (continuous line) and the approximating
ellipses (dashed lines) around the horizontal and around the vertical for two
different apertures. The central column shows the given and approximate
impulse responses for *P*- and *SV*-waves, the approximate
impulse responses calculated from
the estimated elastic constants. The right column shows the
absolute value of the error made in the estimation of the
elastic constants. Unlike the previous approximations,
the *P*-wave double elliptic approximation is valid only at very
small angles ( degrees). At greater angles it
yields highly inaccurate results, particularly in the estimation
of *W _{44}* (L), which controls the shear wave propagation along
the axes. Note that
for an aperture of
10 degrees, the shear wave impulse response has been considerably
underestimated.

Figure 5

This approximation may be hard to use in practical situations because it works only for very small angles near the axes.

11/17/1997