Effective phase velocity of surface waves in layered soil media

In spectral analysis of surface waves,it is very important to consider the effects of higher modes and the source on propagation of surface waves so as to improve the accuracy of calculated soil profile parameters.In order to investigate the effects of higher modes and the source on the effective velocity of surface waves,the analytical expressions of effective phase velocity of horizontal and vertical vibrations as well as the approximate expressions in the far field are derived for horizontally layered elastic media by the thin layer stiffness matrix method.The tendency of the effective phase velocity at both low and high frequencies is analyzed by the rates of energy transmission through layers.Variations of the effective phase velocity with frequency at different positions are obtained for three typical layered systems.The results show that for profiles with shear velocity increasing with depth,the curve of the effective phase velocity versus frequency in the far field approaches to the dispersion of the fundamental mode;for profiles with shear velocity varying irregularly with depth,higher modes have a strong influence on the propagation of surface waves and the effective phase velocities of horizontal and vertical motions are quite different;the effective phase velocities at high frequencies in the far field are approximate to the Rayleigh wave velocity of the first layer.The results indicate that influenced by higher modes and the source,the effective phase velocity is related to frequency as well as the distance from the source.