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In this paper we solve an inverse resonance problem for the half-solid withvanishing stresses on the surface: Lamb's problem. Using a semi-classicalapproach we are able to simplify this three-dimensional problem of the elasticwave equation for the half-solid as a Schr\"odinger equation with Robinboundary conditions on the half-line. We obtain asymptotic values on the numberand the location of the resonances with respect to the wave number. Moreover,we prove that the mapping from real compactly supported potentials to the Jostfunctions in a suitable class of entire functions is one-to-one and onto and weproduce an algorithm in order to retrieve the shear modulus from theeigenvalues and resonances.

Inverse resonance problem for Love seismic surface waves