# Rayleigh Wave

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## Rayleigh wave

[′rā·lē ‚wāv]
(geophysics)
In seismology, a surface wave with a retrograde, elliptical motion at the free surface. Also known as R wave.
(mechanics)
A wave which propagates on the surface of a solid; particle trajectories are ellipses in planes normal to the surface and parallel to the direction of propagation. Also known as surface wave.

## Rayleigh Wave

an elastic disturbance that propagates along the free boundary of a solid body and is attenuated with depth. The existence of such waves was predicted by Lord Rayleigh in 1885.

Rayleigh waves occur on the earth’s surface during earthquakes. Ultrasonic waves used to check the surface layer of various device components and specimens are another example of Rayleigh waves. The thickness of the layer where the waves are localized is (1–2)λ, where λ is the wavelength. At a depth λ the energy density in a wave is ~0.05 of the density at the surface. Particles in Rayleigh waves move in elliptical trajectories whose semimajor axis is perpendicular to the surface of the body and whose semiminor axis is parallel to the direction of wave propagation. The phase velocity of Rayleigh waves is less than the phase velocities of longitudinal and shear waves and is equal to the group velocity.

In anisotropic media the structure and properties of Rayleigh waves depend on the type of anisotropy and the direction of wave propagation. There exist media, such as triclinic crystals, in which Rayleigh waves cannot exist at all. Sometimes, the term “Rayleigh waves” is applied to surface waves of a more general type that arise at the interface between a solid and a liquid or at the boundary of a system of solid or liquid layers with a solid half space.

### REFERENCES

Kol’skii, G. Volny napriazheniia v tverdykh telakh. Moscow, 1955. (Translated from English.)
Landau, L. D., and E. M. Lifshits. Teoriia uprugosti, 3rd ed. Moscow, 1965. (Teoreticheskaia fizika, vol. 7.)
Viktorov, I. A. Fizicheskie osnovy primeneniia ul’trazvukovykh voln Releia i Lemba v tekhnike. Moscow, 1966.
References in periodicals archive ?
The Rayleigh waves are the most important form for the propagation of traffic induced vibration because at the ground level the amplitude of the Rayleigh waves decreases (due to geometric spreading) as the inverse of the square root of the distance from the source, while the amplitude of body waves decrease as the inverse of the square of the distance from the source (Hajek et al.
For determining source locations, four techniques are used: (1) beamforming of the ambient seismic wave field, (62) (2) mapping source distribution by backprojecting observed body waves based on travel time, known as the backprojection method, (63) (3) modeling cross-correlation functions between pairs of stations, and (4) polarization analysis of Rayleigh waves at a station.
Some new theoretical considerations about the ellipticity of Rayleigh waves in the light of site-effect studies in Israel and Mexico.
In other words (and to consider an extreme case), Rayleigh waves generate even in a perfectlyhomogenous medium and their propagation depends on its geomechanical properties ([V.
This correction recovers the true amplitude and phase of the ground motion, allowing the analysis of the true dispersion of Rayleigh waves.
Helmy, "Influences of rotation, magnetic field, initial stress, and gravity on Rayleigh waves in a homogeneous orthotropic elastic half-space," Applied Mathematical Sciences, vol.
Acoustic emission (AE) in a thick structure is dominated by the presence of Rayleigh wave in the far field.
Equation (60) gives the dispersion equation of Rayleigh waves for a granular non-homogeneous medium under the influence of gravity.
Love and Rayleigh waves of short periods (8-12s) in continental trajectories are channelled in the upper crust and are known as [L.
The SASW method is based on the dispersion phenomena of Rayleigh waves in layered media.
The quake initiated, in addition to P waves, a rolling motion called Rayleigh waves that spread through the ocean foot and dry land.

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