Analysis and Probability Seminar

Semiclassical analysis can be employed to describe surface waves in an elastic half space which is quasi-stratified near its boundary. In case of 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 Lamé parameters from these data. We generalize spectral methods for Schrödinger operators to the Rayleigh problem, which is essentially not of Schrödinger type; and give comprehensive analysis of the wavenumber resonances, known in seismology as leaking modes.