Approximate conditions for the off-axis triplication in transversely isotropic media

The presented approximate formulas yield a critical value of anisotropy parameter a for which an incipient off-axis SV-wave triplication occurs in transversely isotropic media. The formulas are simple but approximate the exact solution with a high accuracy. The best results are obtained using the third-order approximation, which yields accuracy at least 30 times higher than the formulas presented by Thomsen and Dellinger (2003). The formula works safely for parameters kappa = a(33)/a(44) > 2 and 0.2 > epsilon = (a(11)-a(33))/2a(33) > -0.2, and yields critical values of sigma from 0.1 to 0.7. Outside this interval, it is recommended to use an exact solution.