Editing Seismic wave (section)

=== Surface waves ===
Seismic surface waves travel along the Earth's surface. They can be classified as a form of [[Surface wave#Mechanical waves|mechanical surface wave]]. Surface waves diminish in amplitude as they get farther from the surface and propagate more slowly than seismic body waves (P and S). Surface waves from very large earthquakes can have globally observable amplitude of several centimeters.<ref>{{cite book|author1=Sammis, C.G.|author2=Henyey, T.L.|title=Geophysics Field Measurements|url=https://books.google.com/books?id=mOaUVakFYwkC&pg=PA12|date=1987|publisher=Academic Press|isbn=978-0-08-086012-1|page=12}}</ref>

==== Rayleigh waves ====
{{Main|Rayleigh wave}} 
Rayleigh waves, also called ground roll, are surface waves that propagate with motions that are similar to those of waves on the surface of water (note, however, that the associated seismic particle motion at shallow depths is typically retrograde, and that the restoring force in Rayleigh and in other seismic waves is elastic, not gravitational as for water waves). The existence of these waves was predicted by John William Strutt, [[Lord Rayleigh]], in 1885.<ref>{{cite journal |last1=Rayleigh |first1=Lord |title=On waves propagated along the plane surface of an elastic solid |journal=Proceedings of the London Mathematical Society |date=1885 |volume=17 |pages=4–11 |url=https://babel.hathitrust.org/cgi/pt?id=uc1.$b671850&view=1up&seq=11}}</ref> They are slower than body waves, e.g., at roughly 90% of the velocity of S waves for typical homogeneous elastic media. In a layered medium (e.g., the crust and [[upper mantle (Earth)|upper mantle]]) the velocity of the Rayleigh waves depends on their frequency and wavelength. See also [[Lamb waves]].

==== Love waves ====
{{Main|Love wave}}
Love waves are horizontally [[Polarization (waves)|polarized]] [[shear wave]]s (SH waves), existing only in the presence of a layered medium.<ref>{{Cite book |last1=Sheriff |first1=R. E. |last2=Geldart |first2=L. P. | year=1995 | title=Exploration Seismology |edition=2nd | publisher=Cambridge University Press | isbn=0-521-46826-4 |page= 52}}</ref> They are named after [[Augustus Edward Hough Love]], a British mathematician who created a mathematical model of the waves in 1911.<ref>{{cite book |last1=Love |first1=A.E.H. |title=Some problems of geodynamics; … |date=1911 |publisher=Cambridge University Press |location=London, England |pages=144–178 |url=https://archive.org/details/cu31924060184367/page/n179/mode/2up}}</ref> They usually travel slightly faster than Rayleigh waves, about 90% of the S wave velocity.

==== Stoneley waves ====
{{Main|Stoneley wave}}
A Stoneley wave is a type of boundary wave (or interface wave) that propagates along a solid-fluid boundary or, under specific conditions, also along a solid-solid boundary. Amplitudes of Stoneley waves have their maximum values at the boundary between the two contacting media and decay exponentially away from the contact. These waves can also be generated along the walls of a fluid-filled [[borehole]], being an important source of coherent noise in [[vertical seismic profile]]s (VSP) and making up the low frequency component of the source in [[sonic logging]].<ref>{{Cite web |url=http://www.glossary.oilfield.slb.com/Display.cfm?Term=Stoneley%20wave |title=Schlumberger Oilfield Glossary. Stoneley wave. |access-date=2012-03-07 |archive-date=2012-02-07 |archive-url=https://web.archive.org/web/20120207002631/http://www.glossary.oilfield.slb.com/Display.cfm?Term=Stoneley%20wave |url-status=dead }}</ref>
The equation for Stoneley waves was first given by Dr. Robert Stoneley (1894–1976), emeritus professor of seismology, Cambridge.<ref>{{cite journal | last = Stoneley | first = R. | title = Elastic waves at the surface of separation of two solids | journal = Proceedings of the Royal Society of London A | volume = 106 | issue = 738 | pages = 416–428 | date = October 1, 1924| doi = 10.1098/rspa.1924.0079 | bibcode = 1924RSPSA.106..416S | doi-access = free }}</ref><ref>[http://www.geolsoc.org.uk/gsl/pid/5825;jsessionid=B80DF900AFFC974028AEFB7138FB1BDF Robert Stoneley, 1929 – 2008.. Obituary of his son with reference to discovery of Stoneley waves.]</ref>

==== Normal modes ====
[[File:Fundametal toroidal oscillation Earth.gif|thumb|right|The sense of motion for toroidal <sub>0</sub>T<sub>1</sub> oscillation for two moments of time.]]
[[File:Fundamental spheroidal oscillation Earth.gif|thumb|right|The scheme of motion for spheroidal <sub>0</sub>S<sub>2</sub> oscillation. Dashed lines give nodal (zero) lines. Arrows give the sense of motion.]]
Free oscillations of the Earth are [[standing wave]]s, the result of interference between two surface waves traveling in opposite directions. Interference of Rayleigh waves results in ''spheroidal oscillation S'' while interference of Love waves gives ''toroidal oscillation T''. The modes of oscillations are specified by three numbers, e.g.,  <sub>n</sub>S<sub>l</sub><sup>m</sup>, where ''l'' is the angular order number (or ''spherical harmonic degree'', see [[Spherical harmonics]] for more details). The number ''m'' is the azimuthal order number. It may take on 2''l''+1 values from −''l'' to +''l''. The number ''n'' is the ''radial order number''. It means the wave with ''n'' zero crossings in radius. For spherically symmetric Earth the period for given ''n'' and ''l'' does not depend on ''m''.

Some examples of spheroidal oscillations are the  "breathing" mode <sub>0</sub>S<sub>0</sub>, which involves an expansion and contraction of the whole Earth, and has a period of about 20 minutes; and the "rugby" mode <sub>0</sub>S<sub>2</sub>, which involves expansions along two alternating directions, and has a period of about 54 minutes. The mode <sub>0</sub>S<sub>1</sub> does not exist because it would require a change in the center of gravity, which would require an external force.<ref name=Shearer2009ch8/>

Of the fundamental toroidal modes, <sub>0</sub>T<sub>1</sub> represents changes in Earth's rotation rate; although this occurs, it is much too slow to be useful in seismology. The mode <sub>0</sub>T<sub>2</sub> describes a twisting of the northern and southern hemispheres relative to each other; it has a period of about 44 minutes.<ref name=Shearer2009ch8/>

The first observations of free oscillations of the Earth were done during the great [[1960 Valdivia earthquake|1960 earthquake in Chile]]. Presently the periods of thousands of modes have been observed. These data are used for constraining large scale structures of the Earth's interior.