1. A type of seismic surface wave propagated along the free surface of a semi-infinite medium. Particle motion near the surface is elliptical and retrograde (i.e., the particle moves opposite to the direction of propagation at the top of its elliptical path) in the vertical plane containing the direction of propagation; see Figure R-3. Its amplitude decreases exponentially with depth, and the elastic properties to a depth of about one wavelength determine its velocity. For a Poisson ratio of σ=1/4, the Rayleigh-wave velocity is 0.9194 times the S-wave velocity; see Figure R-4. A Rayleigh wave along a free surface can be thought of as a special case of a Stoneley wave (wave travel along an interface). Symbolized R-wave or LR-wave. See Sheriff and Geldart (1995, 49–50). 2. A similar type of wave where the medium is not homogeneous; ground roll, such as encountered in seismic exploration, may involve modes other than a pure Rayleigh wave and is sometimes called a pseudo-Rayleigh wave, although it is usually simply called a Rayleigh wave. Because the elastic constants change with depth in the real Earth, long wavelengths depend on the elastic properties at greater depths than short wavelengths and hence different wavelengths travel at different velocities. This dispersion can be used to calculate the thickness of surface layers. 3. A surface wave in a borehole is sometimes called a Rayleigh wave; see tube wave. Named for John William Strutt, Lord Rayleigh (1842–1919), English physicist.