Invited talk at 2023 MATH + X Symposium on Dynamos, Planetary Exploration and General Relativity, Inverse Problems and Machine Learning, Hella, Iceland, 1 June 2023
Semiclassical analysis can be employed to describe surface waves in an elastic half space which is quasi-stratified near its boundary. In the case of an isotropic medium, the surface wave decouples up to principal parts into Love and Rayleigh waves associated to scalar and matrix spectral problems, respectively. Since the mathematical features (such as spectrum, resonances) of these problems can be extracted from the seismograms, we are interested in recovering the Lam e parameters from these data. We generalize spectral methods for Schrodinger operators to the Rayleigh problem, which is essentially not of Schrodinger type; and give comprehensive analysis of the wavenumber resonances, known in seismology as leaking modes.
This is joint work with Maarten V. de Hoop.