Notes on fk analysis of surface waves

The dispersive nature of Rayleigh waves is the basis of many identification procedures to infer the site stiffness profile from surface measurements. This article presents some important aspects related to fk analysis of seismic gathers, which is one of the procedures commonly used to obtain the experimental dispersion curve, focusing on the great influence that the scale of the survey has in the global process. At a short distance from the source, the seismic signal contains information related to different modes of propagation in a composite form. As the wave travels away, the different modal group velocities produce a separation of such information. Hence only if the testing array is sufficiently long is it possible to assume mode separation and to invert the dispersion curve for modal velocities. Otherwise the effects of mode superposition need to be carefully accounted for. To clarify this concept, the results of some numerical simulations are reported, together with some experimental results.