Osculations and diabolical points in seismology and elsewhere

Peter Malischewsky

(Institute of Geosciences, Friedrich-Schiller University, Jena, Germany)

The occurrence of degenerations of the eigenvalues is necessary for the existence of diabolical points. The discussion of these degenerations is mathematically not simple. It is carried out by using the simple model "Layer with Fixed Bottom (LFB)". This model contains an infinite number of degenerations for Rayleigh waves. It is highly probable that a more complicated configuration like a layered elastic halfspace has no degenerations at all but plenty of osculations. But this is not yet mathematically proven up to the end. The leading parameter for the model LFB is Poisson's ratio ν. A picture shows, how a diabolical point with a double conus develops between the fundamental and first higher Rayleigh mode in dependence on frequency and Poisson's ratio for ν = ¼ .