Rayleigh Wave Spectra and Group Velocity Minima, and the resonance of P waves in layered structures

A connection is established between the group velocity of Rayleigh waves, the spectral amplitudes of surface waves generated by a source, and the resonance of vertically travelling P waves. It implies that a minimum in a group velocity curve is reflected in the spectral amplitudes as a maximum. That this is so, appears to have been first noticed by Longuet-Higgins in a study of microseisms. Also when a sharp impedance contrast occurs in a plane-layered model of the crust, the group velocity minimum in the fundamental mode occurs close to a period equal to four times the travel time of P-waves from the surface to the interface. More than one such contrast gives rise in general to more than one minimum. Similar relations hold for the higher modes.