Direct and inverse resonance problems for seismic surface waves

Abstract: This thesis concerns the investigation of direct and inverse resonance results for the Love and the Rayleigh operators, which arise from decoupling the three-dimensional elastic wave equation in the semiclassical limit in the half-space. Direct resonance results in terms of the asymptotic distribution of resonances in the complex plane are obtained for the Love and the Rayleigh operators. An inverse resonance characterization problem is obtained for the Love operator using a class of Jost function and also through a suitable class of Weyl-Tichtmarsh function.