Inverse spectral Love problem via Weyl-Titchmarsh function

Abstract

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.