More than a century has passed since Lord Rayleigh (1885) first investigated “the behaviour of waves upon the plane free surface of an infinite homogeneous isotropic elastic solid, their character being such that the disturbance is confined to a superficial region, of thickness comparable to the wave-length.” Rayleigh immediately recognized their importance stating that “it is not improbable that the surface waves here investigated play an important part in earthquakes, and in the collision of elastic bodies.” Since then, surface waves have come to play an important part in many other disciplines as well, including material science, geophysics, nondestructive testing, and engineering site characterization. When used for near-surface site characterization, the objective is usually to determine the shear wave velocity and/or shear damping ratio one-dimensional (1D) profiles for a variety of applications, including earthquake site response, dynamic soil–structure interaction, nondestructive pavement testing, evaluation of ground modification, and so on. <...>