On construction of uniform asymptotics for Love waves near the surface of an anisotropic elastic body

The uniform high-frequency asymptotics for surface waves (Love modes) near the surface of an anisotropic elastic body is constructed. The individual mode is represented as the sum of a caustic expansion (analogous to Kravtsov's ansatz) and two correction terms in the form of space-time ray series with complex eikonals. Using as a vector basis, eigenfunctions of the symmetric matrix, occurring in the asymptotic solutions, we proceed to obtain the sufficient conditions for the determinant of the nonhomogeneous system (arised from the boundary conditions) proves to be non-zero.