Semiclassical analysis can be employed to describe surface waves in an elastic half space which is quasi-stratified near its boundary. The propagation of such waves is governed by effective Hamiltonians on the boundary with a space-adiabatic behavior. Effective Hamiltonians of surface waves correspond to eigenvalues of ordinary differential operators, which, to leading order, define their phase velocities. In case of isotropic medium, the surface wave decouples up to principal parts, into Love and Rayleigh waves.

We present the conditional recovery of the Lamé parameters from spectral data, in two inverse problems approaches:- semiclassical techniques using the semiclassical spectra as the data;- exact methods for Sturm-Liouville operators, using the discrete and continuous spectra, or the Weyl function, as the data based on the solution of the Gel’fand-Levitan-Marchenko equation.

We conclude with discussion using resonances (leaking modes) as data.