Determination of the frequency equation for three-dimensional Rayleigh waves in vertically inhomogeneous media

The propagation of Rayleigh waves in a three-dimensional medium is investigated. Equations for the propagation of Rayleigh waves in three dimensions with the medium assumed to be vertically inhomogeneous have been derived. We also find the frequency equation for this wave and show that for an inhomogeneous medium, the frequency equation is complex, which naturally leads to the fact that phase properties of the frequency equation as well as the magnitude can be used to determine the properties of the material as highlighted in this paper. We find that inhomogeneity has little effect on the propagation of Rayleigh waves when the soil stiffness G (or modulus of rigidity mu) is 0.6 and above, but it is highly significant when G is less than 0.6, particularly when 0 < G <= 0.4.