  In this paper we prove an inverse resonance theorem for the half-solid with
vanishing stresses on the surface via Weyl-Titchmarsh function. Using a
semi-classical approach it is possible to simplify this three-dimensional
problem of the elastic wave equation for the half-solid as a Schr\"odinger
equation with Robin boundary conditions on the half-line. The goal of the paper
is to establish a method to recover the potential from the Weyl-Titchmarsh
function for non self-adjoint problems and to establish a one-to-one and onto
map between suitable function spaces. Moreover, we produce an algorithm in
order to retrieve the shear modulus from the eigenvalues and resonances, via
the spectral data.
