Approximate Conditions for the Off-Axis Triplication in Transversely Isotropic Media

The presented approximate formulas yield a critical value of anisotropy parameter , 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  = a ₃₃/a ₄₄ > 2 and 0.2 >  = (a ₁₁ – a ₃₃)/2a ₃₃ > –0.2, and yields critical values of from 0.1 to 0.7. Outside this interval, it is recommended to use an exact solution.