Rayleigh Wave - Wikipedia
Rayleigh Wave - Wikipedia
Rayleigh Wave - Wikipedia
Rayleigh wave
From Wikipedia, the free encyclopedia
Rayleigh waves are a type of surface acoustic wave that travel along the surface of solids. They can be produced
in materials in many ways, such as by a localized impact or by piezoelectric transduction, and are frequently used
in nondestructive testing for detecting defects. They are part of the seismic waves that are produced on the Earth
by earthquakes. When guided in layers they are referred to as Lamb waves, Rayleigh–Lamb waves, or generalized
Rayleigh waves.
Contents
1 Characteristics
1.1 Rayleigh wave dispersion
2 Rayleigh waves in nondestructive testing
3 Rayleigh waves in electronic devices
4 Rayleigh waves in geophysics
4.1 Rayleigh waves from earthquakes
4.2 Rayleigh waves in seismology
5 Other manifestations
5.1 Animals
6 See also
7 Notes
8 Further reading
9 External links
Characteristics
Rayleigh waves are a type of surface wave that travel near the surface of
solids. Rayleigh waves include both longitudinal and transverse motions
that decrease exponentially in amplitude as distance from the surface
increases. There is a phase difference between these component motions.[1]
The existence of Rayleigh waves was predicted in 1885 by Lord Rayleigh,
after whom they were named.[2] In isotropic solids these waves cause the
surface particles to move in ellipses in planes normal to the surface and Picture of a Rayleigh wave.
parallel to the direction of propagation – the major axis of the ellipse is
vertical. At the surface and at shallow depths this motion is retrograde, that is the inplane motion of a particle is
counterclockwise when the wave travels from left to right. At greater depths the particle motion becomes
prograde. In addition, the motion amplitude decays and the eccentricity changes as the depth into the material
increases. The depth of significant displacement in the solid is approximately equal to the acoustic wavelength.
Rayleigh waves are distinct from other types of surface or guided acoustic waves such as Love waves or Lamb
waves, both being types of guided waves supported by a layer, or longitudinal and shear waves, that travel in the
bulk.
Rayleigh waves have a speed slightly less than shear waves by a factor dependent on the elastic constants of the
material.[1] The typical speed of Rayleigh waves in metals is of the order of 2–5 km/s, and the typical Rayleigh
speed in the ground is of the order of 50–300 m/s. For linear elastic materials with positive Poisson ratio ( ),
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the Rayleigh wave speed can be approximated as
.[3] Since Rayleigh waves are confined near the
surface, their inplane amplitude when generated by a point source decays
only as , where is the radial distance. Surface waves therefore decay
more slowly with distance than do bulk waves, which spread out in three
dimensions from a point source. This slow decay is one reason why they
are of particular interest to seismologists; Rayleigh waves can circle the
globe multiple times after a large earthquake and still be measurably large. Comparison of the Rayleigh wave
speed with shear and longitudinal
In seismology, Rayleigh waves (called "ground roll") are the most wave speeds for an isotropic elastic
important type of surface wave, and can be produced (apart from material. The speeds are shown in
earthquakes), for example, by ocean waves, by explosions, by railway dimensionless units.
trains and ground vehicles, or by a sledgehammer impact.[1][4]
Rayleigh wave dispersion
In isotropic, linear elastic materials described by Lame coefficients and
, Rayleigh waves have a speed given by solutions to the equation
The elastic constants often change with depth, due to the changing
properties of the material. This means that the velocity of a Rayleigh wave Dispersion of Rayleigh waves in a
in practice becomes dependent on the wavelength (and therefore thin gold film on glass.[1] (http://kin
frequency), a phenomenon referred to as dispersion. Waves affected by oap.eng.hokudai.ac.jp/index.html)
[1]
dispersion have a different wave train shape. Rayleigh waves on ideal,
homogeneous and flat elastic solids show no dispersion, as stated above. However, if a solid or structure has a
density or sound velocity that varies with depth, Rayleigh waves become dispersive. One example is Rayleigh
waves on the Earth's surface: those 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. The
displacement of long wavelength waves penetrates more deeply into the Earth than short wavelength waves. 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. It is also possible to observe Rayleigh wave
dispersion in thin films or multilayered structures.
Rayleigh waves in nondestructive testing
Rayleigh waves are widely used for materials characterization, to discover the mechanical and structural properties
of the object being tested – like the presence of cracking, and the related shear modulus. This is in common with
other types of surface waves.[6] The Rayleigh waves used for this purpose are in the ultrasonic frequency range.
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They are used at different length scales because they are easily generated and detected on the free surface of solid
objects. Since they are confined in the vicinity of the free surface within a depth (~ the wavelength) linked to the
frequency of the wave, different frequencies can be used for characterization at different length scales.
Rayleigh waves in electronic devices
Rayleigh waves propagating at high ultrasonic frequencies (10–1000 MHz) are used widely in different electronic
devices.[7] In addition to Rayleigh waves, some other types of surface acoustic waves (SAW), e.g. Love waves, are
also used for this purpose. Examples of electronic devices using Rayleigh waves are filters, resonators, oscillators,
sensors of pressure, temperature, humidity, etc. Operation of SAW devices is based on the transformation of the
initial electric signal into a surface wave that, after achieving the required changes to the spectrum of the initial
electric signal as a result of its interaction with different types of surface inhomogeneity,[8] is transformed back into
a modified electric signal. The transformation of the initial electric energy into mechanical energy (in the form of
SAW) and back is usually accomplished via the use of piezoelectric materials for both generation and reception of
Rayleigh waves as well as for their propagation.
Rayleigh waves in geophysics
Rayleigh waves from earthquakes
Because Rayleigh waves are surface waves, the amplitude of such waves generated by an earthquake generally
decreases exponentially with the depth of the hypocenter (focus). However, large earthquakes may generate
Rayleigh waves that travel around the Earth several times before dissipating.
In seismology longitudinal and shear waves are known as Pwaves and Swaves, respectively, and are termed body
waves. Rayleigh waves are generated by the interaction of P and S waves at the surface of the earth, and travel
with a velocity that is lower than the P, S, and Love wave velocities. Rayleigh waves emanating outward from
the epicenter of an earthquake travel along the surface of the earth at about 10 times the speed of sound in air
(0.340 km/s), that is ~3 km/s.
Due to their higher speed, the P and Swaves 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.
The rupture directivity of the earthquake.
Local geologic structure can serve to focus or defocus Rayleigh waves,
leading to significant differences in shaking over short distances.
Rayleigh wave direction
Rayleigh waves in seismology
Low frequency Rayleigh waves generated during earthquakes are used in seismology to characterise the Earth's
interior. In intermediate ranges, Rayleigh waves are used in geophysics and geotechnical engineering for the
characterisation of oil deposits. These applications are based on the geometric dispersion of Rayleigh waves and on
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the solution of an inverse problem on the basis of seismic data collected on the ground surface using active sources
(falling weights, hammers or small explosions, for example) or by recording microtremors. Rayleigh ground waves
are important also for environmental noise and vibration control since they make a major contribution to traffic
induced ground vibrations and the associated structureborne noise in buildings.
Other manifestations
Animals
Low frequency (< 20 Hz) Rayleigh waves are inaudible, yet they can be detected by many mammals, birds, insects
and spiders. Humans should be able to detect such 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.[9] 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 a 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. Other animal early warning systems may rely on an ability to sense infrasonic waves
traveling through the air.[10]
See also
Linear elasticity
Longitudinal wave
Love wave
Pwave
Phonon
Swave
Seismology
Surface acoustic wave
Notes
1. Telford, William Murray; Geldart, L. P.; Robert E. Sheriff (1990). Applied geophysics. Cambridge University Press.
p. 149. ISBN 9780521339384. Retrieved 8 June 2011.
2. http://plms.oxfordjournals.org/content/s117/1/4.full.pdf "On Waves Propagated along the Plane Surface of an
ElasticSolid", Lord Rayleigh, 1885
3. L. B. Freund (1998). Dynamic Fracture Mechanics. Cambridge University Press. p. 83. ISBN 9780521629225.
4. LonguetHiggins, Michael (1950). "A theory of the origin of microseisms". Philosophical Transaction of the Royal
Society of London, series A. 243. pp. 1–35.
5. Landau, L.D.; Lifshitz, E. M. (1986). Theory of Elasticity (3rd ed.). Oxford, England: Butterworth Heinemann. ISBN 0
75062633X.
6. Thompson, Donald O.; Chimenti, Dale E. (1 June 1997). Review of progress in quantitative nondestructive evaluation.
Springer. p. 161. ISBN 9780306455971. Retrieved 8 June 2011.
7. Oliner, A.A.(ed) (1978). Acoustic Surface Waves. Springer. ISBN 3540085750.
8. Biryukov, S.V.; Gulyaev, Y.V.; Krylov, V.V.; Plessky, V.P. (1995). Surface Acoustic Waves in Inhomogeneous Media.
Springer. ISBN 9783642577673.
9. O’ConnellRodwell, C.E.; Arnason, B.T.; Hart, L.A. (14 September 2000). "Seismic properties of Asian elephant
(Elephas maximus) vocalizations and locomotion". J. Acoust. Soc. Am. 108 (6): 3066–3072. doi:10.1121/1.1323460.
PMID 11144599.
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10. Kenneally, Christine (30 December 2004). "Surviving the Tsunami". http://www.slate.com/. Retrieved 26 November
2013. External link in |website= (help)
Further reading
Viktorov, I.A. (2013) "Rayleigh and Lamb Waves: Physical Theory and Applications", Springer; Reprint of
the original 1st 1967 edition by Plenum Press, New York. ISBN 9781489956835.
Aki, K. and Richards, P. G. (2002). Quantitative Seismology (2nd ed.). University Science Books. ISBN 0
935702962.
Fowler, C. M. R. (1990). The Solid Earth. Cambridge, UK: Cambridge University Press. ISBN 0521
385903.
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 9783211277409
Y. Sugawara, O. B. Wright, O. Matsuda, M. Takigahira, Y. Tanaka, S. Tamura and V. E. Gusev, "Watching
ripples on crystals", Phys. Rev. Lett. 88, 185504 (2002) (http://prola.aps.org/abstract/PRL/v88/i18/e185504)
External links
Realtime imaging of Rayleigh waves (http://kinoap.eng.hokudai.ac.jp/ripples.html)
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