Pure mode P- and S-wave phase velocity equations in elastic orthorhombic media

In an elastic model with orthorhombic (ORT) symmetry, there are nine independent stiffness coefficients that control the propagation of all intrinsically coupled wave modes. For practical applications in P-wave modeling and inversion, it is important to derive the approximate solutions that support propagation of P-waves only and depend on fewer independent parameters. Due to the increasing interest in S-wave propagation in anisotropic media, we also derive an approximate equation that supports propagation of S-waves only. However, the reduction in the number of independent parameters for the S-wave equation is not possible. We derive pure P-and S-wave equations in an elastic ORT model and find that the accuracy is sufficient for practical applications.