Surface waves in inversely dispersive media
The dispersion of surface waves in inversely dispersive media where the shear-wave velocity decreases with depth is studied. Theoretical dispersion curves are calculated in the complex wavenumber domain. Excitability and attenuation due to leakage are calculated for each point on the dispersion curves. These additional parameters are critical for a correct understanding of the dispersion properties of surface waves. Mode shapes are included in the study to visualize displacements inside the medium. The results of the study show that, for inversely dispersive media, the Rayleigh-wave assumption is not valid, and other types of interface waves and leaky Lamb waves contribute to the surface wavefield. They also show that, in this case, true theoretical dispersion curves can be approximated by Lamb-wave dispersion curves for a free plate in a vacuum, provided that the stiffness contrast between the top layer and the underlying half-space is large, and also that the shear-wave velocity of the stiff layer is greater than the compressional-wave velocity in the underlying media. The error in the phase velocity resulting from this approximation is investigated and it is shown that the error does not exceed 5% for the fundamental antisymmetric Lamb-wave dispersion curve. Because of the numerical simplicity of calculating its theoretical dispersion curves, the Lamb-wave approximation can provide an effective evaluation method to resolve the thickness and elastic parameters of the stiff top layer. This is exemplified using a set of field data.