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 W44 (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.
This approximation may be hard to use in practical situations because it works only for very small angles near the axes.