The dispersive characteristics of a single elastic layer overlying an elastic half-space are examined in detail for the fundamental and the first and second higher modes of Rayleigh waves. Phase velocity, group velocity, and the ratio of horizontal to vertical surface displacement are computed as functions of dimensionless quantities proportional to period and wave number.

The significant range for the independent variable, B1T/H, proves to be largely independent of the parameters of the structure. The range is 1 to 20 for the fundamental, 0.3 to cutoff for the first higher mode, and 0.2 to cutoff for the second higher mode.

The most important parameter of the structure for Rayleigh wave dispersion is the shear velocity ratio. Variations in the Poisson's ratio in the surface layer and the density contrast may produce substantial effects. Poisson's ratio in the half-space is of least significance.

The dependence on model parameters of the long-period cutoff for the higher modes is determined.

Specific results are given for the following geophysical examples: continental crust, continental ice cap, sedimentary basin, alluvial overburden, and laboratory seismic models.

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