QLunch: Alexei Iantchenko

Speaker:  Alexei Iantchenko, Malmö University 

Title: Semiclassical surface-wave imaging and leaking modes in seismology


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 Lam{\'e} parameters from these data. 

We generalize spectral methods for Schr{\"o}dinger operators to the Rayleigh problem, which is essentially not of Schr{\"o}dinger type; and give comprehensive analysis of the wavenumber resonances, known in seismology as leaking modes.