Rayleigh wave

Rayleigh wave

Rayleigh waves, also known as the Rayleigh-Lamb Wave or "ground roll", are a type of surface wave. They are associated on the Earth with earthquakes and subterranean movement of magma, or with any other source of seismic energy, such as an explosion or even a sledgehammer impact, and are also the form of ocean waves.

From a condensed matter physics point of view Rayleigh waves are surface acoustic wavesand associated with a huge number of electronic components, the SAW devices, which employ them.SAW devices are mainly used in cellular phones and wireless technology, and theirworldwide yearly production is approximated to lie over 1 billionFact|date=July 2007.


A Rayleigh wave moves across a surface. As it passes, a surface particle moves in a circle or ellipse in the direction of propagation. If one measures particles deeper in the material, the particles move in smaller ellipses, then reach a "no movement" depth, a "node." Below this, harmonics of the Rayleigh wave move particles in regions that alternate elliptical motion with nodes of no-movement. The maximum distance that Rayleigh waves move particles (the amplitude) decreases rapidly with depth in the material.Since Rayleigh waves are surface waves, the strength, or amplitude, of the waves decreases exponentially with the depth of the earthquake. However, since they are confined to the surface, their amplitude decays only as frac{1}{sqrt{r, where r is the distance the wave has traveled from the earthquake. Surface waves therefore decay more slowly with distance than do body waves, which travel in three dimensions. Large earthquakes may generate Rayleigh waves that travel around the Earth several times before dissipating.

The existence of Rayleigh waves was predicted in 1885 by Lord Rayleigh, for whom they were named. They are distinct from other types of seismic waves, such as P-waves and S-waves, which are both body waves, or Love waves, another type of surface wave. Rayleigh waves are generated by the interaction of P- and S- waves at the surface of the earth. The Rayleigh wave travels with a velocity that is lower than the P-, S-, and Love wave velocities. Emanating outward from the epicenter of an earthquake, Rayleigh waves travel along the surface of the earth at about 10 times the speed of sound in air.


Rayleigh waves in the Earth are also dispersive: Rayleigh waves with a higher frequency travel more slowly than those with a lower frequency. This occurs because a Rayleigh wave of lower frequency has a relatively long wavelength. Long wavelength waves "see" more deeply into the Earth than waves with a short wavelength. Since the speed of waves in the Earth increases with increasing depth, the longer wavelength (low frequency) waves can travel faster than the shorter wavelength (high frequency) waves. Rayleigh waves thus often appear "spread out" on seismograms recorded at distant earthquake recording stations.

Earthquake shaking

Due to their higher speed, the P- and S-waves generated by an earthquake arrive before the surface waves. However, the particle motion of surface waves is larger than that of body waves, so the surface waves tend to cause more damage. In the case of Rayleigh waves, the motion is of a rolling nature, similar to an ocean surface wave. The intensity of Rayleigh wave shaking at a particular location is dependent on several factors:

* The size of the earthquake.
* The distance to the earthquake.
* The depth of the earthquake.
* The geologic structure of the crust.
* The focal mechanism of the earthquake.

Local geologic structure can serve to focus or defocus Rayleigh waves, leading to significant differences in shaking over short distances.

Other manifestations


Rayleigh waves are inaudible, yet can be detected by many mammals, birds, insects and spiders. Human beings should be able to detect Rayleigh waves through their Pacinian corpuscles, which are in the joints, although people do not seem to consciously respond to the signals. Some animals seem to use Rayleigh waves to communicate. In particular, some biologists theorize that elephants may use vocalizations to generate Rayleigh waves. Since Rayleigh waves decay slowly, they should be detectable over long distances. [http://biox.stanford.edu/grant/klemperer_r2_iip.html] Note that these Rayleigh waves have a much higher frequency than Rayleigh waves generated by earthquakes.

After the 2004 Indian Ocean Earthquake, some people have speculated that Rayleigh waves served as warning to animals to seek higher ground, allowing them to escape the more slowly-traveling tsunami. At this time, evidence for this is mostly anecdotal. Another animal early warning system may rely on an ability to sense infrasonic waves traveling through the air. [http://www.slate.com/id/2111608]

Non-destructive testing

Rayleigh waves are widely used for material characterization at different scale because they are easily generated and detected on the free surface of the earth or of an object. Since they travel in a very limited portion of the object confined in the vicinity of the free surface and this portion (skin depth) is linked to the frequency of the wave, different frequencies can be used for characterisation at very different scales.Rayleigh waves in the ultrasonic frequency range are used in non-destructive testing applications to help find cracks and other imperfections in materials.Low frequency Rayleigh waves generated during earthquakes are used in seismology to characterise the Earth's interior.In intermediate ranges, Rayleigh wave are used in geophysics and geotechnical engineering for the characterisation of soil deposits. These application are based on the geometric dispersion of Rayleigh waves and on the solution of an inverse problem on the basis of seismic data collected on the ground surface using active sources (falling weights, hammers, small explosions,...) or recording microtremors.

See also

* Seismology
* Longitudinal wave
* S-wave
* P wave
* Lamb wave
* Love wave
* Linear elasticity
* Phonon
* Surface acoustic wave

Further reading

*Aki, K. and Richards, P. G. (2002). "Quantitative seismology" (2nd ed.). University Science Books. ISBN 0-935702-96-2.

*Fowler, C. M. R. (1990). "The solid earth". Cambridge, UK: Cambridge University Press. ISBN 0-521-38590-3.

*Lai, C.G., Wilmanski, K. (Eds.) (2005). "Surface Waves in Geomechanics: Direct and Inverse Modelling for Soils and Rocks"Series: CISM International Centre for Mechanical Sciences , Number 481 , Springer, Wien, ISBN 978-3-211-27740-9

*Viktorov, I.A. (1967) “Rayleigh and Lamb Waves: physical theory and applications”, Plenum Press, New York

*Dilbag Singh and S. K. Tomar "Rayleigh–Lamb waves in a microstretch elastic plate cladded with liquid layers" Journal of Sound and Vibration, Volume 302, Issues 1-2, 17 April 2007, Pages 313-331

External links

* [http://www.uwm.edu/~bketter/Research/Surface_Theory/Rayleigh/rayleigh_index.html Rayleigh wave page]
* [http://www2.polito.it/ricerca/soilmech/sasw/index.html Rayleigh waves and soil characterization]

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