Editing Seismic wave

{{Short description|Seismic, volcanic, or explosive energy that travels through Earth's layers}}
{{About|waves that travel through Earth|ocean waves sometimes called "seismic sea waves"|Tsunami}}
{{Geophysics|all}}
{{Earthquakes}}

[[Image:Seismogram.gif|thumb|P wave and S wave from seismograph]]
[[File:Seismic velocity profile.png|thumb|Velocity of seismic waves in Earth versus depth.<ref name=Helffrich>{{cite journal |journal=Nature |year=2002 |volume=412 |issue=2 August |title=The Earth's mantle |author1=G. R. Helffrich |author2=B. J. Wood |pages=501–7 |name-list-style=amp |url=http://rallen.berkeley.edu/teaching/F04_GEO302_PhysChemEarth/Lectures/HellfrichWood2001.pdf |archive-url=https://web.archive.org/web/20160824163306/http://rallen.berkeley.edu/teaching/F04_GEO302_PhysChemEarth/Lectures/HellfrichWood2001.pdf |archive-date=24 August 2016 |url-status=live |publisher=Macmillan Magazines |doi=10.1038/35087500 |pmid=11484043|s2cid=4304379 }}</ref> The negligible ''S''-wave velocity in the outer core occurs because it is liquid, while in the solid inner core the ''S''-wave velocity is non-zero]]

A '''seismic wave''' is a [[mechanical wave]] of [[acoustic wave|acoustic energy]] that travels through the [[Earth]] or another [[planetary body]]. It can result from an [[earthquake]] (or generally, a [[quake (natural phenomenon)|quake]]), [[types of volcanic eruptions|volcanic eruption]], [[magma]] movement, a large [[landslide]] and a large man-made [[explosion]] that produces low-frequency acoustic energy. Seismic waves are studied by [[seismology|seismologists]], who record the waves using [[seismometer]]s, [[hydrophone]]s (in water), or [[accelerometer]]s.  Seismic waves are distinguished from [[seismic noise]] (ambient vibration), which is persistent low-amplitude vibration arising from a variety of natural and anthropogenic sources.
 
The [[signal velocity|propagation velocity]] of a seismic wave depends on [[density]] and [[elasticity (physics)|elasticity]] of the medium as well as the type of wave. Velocity tends to increase with depth through Earth's [[crust (geology)|crust]] and [[mantle (geology)|mantle]], but drops sharply going from the mantle to [[Earth's outer core]].<ref name=Shearer2009intro>{{harvnb|Shearer|2009|loc=Introduction}}</ref>

Earthquakes create distinct types of waves with different velocities. When recorded by a seismic observatory, their different [[phase velocity|travel times]] help scientists locate the quake's [[hypocenter]]. In geophysics, the refraction or reflection of seismic waves is used for research into [[Internal structure of Earth|Earth's internal structure]]. Scientists sometimes generate and measure vibrations to investigate shallow, subsurface structure.

== Types ==
Among the many types of seismic waves, one can make a broad distinction between ''body waves'', which travel through the Earth, and ''surface waves'', which travel at the Earth's surface.<ref name=Shearer2009ch8>{{harvnb|Shearer|2009|loc=Chapter 8}} (Also see [http://mahi.ucsd.edu/shearer/errata.html errata] {{Webarchive|url=https://web.archive.org/web/20131111191407/http://mahi.ucsd.edu/shearer/errata.html |date=2013-11-11 }})</ref>{{rp|48–50}}<ref name="SteinWysession2009">{{cite book|author1=Seth Stein|author2=Michael Wysession|title=An Introduction to Seismology, Earthquakes, and Earth Structure|date=1 April 2009|publisher=John Wiley & Sons|isbn=978-14443-1131-0}}</ref>{{rp|56–57}}
[[File:Overview_Seismic_Waves.jpg|right|thumb|Body waves and surface waves]]
Other modes of wave propagation exist than those described in this article; though of comparatively minor importance for earth-borne waves, they are important in the case of [[asteroseismology]].

* Body waves travel through the interior of the Earth.
* Surface waves travel across the surface. Surface waves decay more slowly with distance than body waves which travel in three dimensions.
* Particle motion of surface waves is larger than that of body waves, so surface waves tend to cause more damage.

=== Body waves ===
Body waves travel through the interior of the Earth along paths controlled by the material properties in terms of [[density]] and [[Young's modulus|modulus]] (stiffness). The density and modulus, in turn, vary according to temperature, composition, and material phase.  This effect resembles the [[refraction]] of [[light wave]]s. Two types of particle motion result in two types of body waves: '''''Primary''''' and '''''Secondary''''' waves.  This distinction was recognized in 1830 by the French mathematician [[Siméon Denis Poisson]].<ref>{{cite journal |last1=Poisson |first1=S. D. |title=Mémoire sur la propagation du mouvement dans les milieux élastiques |journal=Mémoires de l'Académie des Sciences de l'Institut de France |date=1831 |volume=10 |pages=549–605 |url=https://www.biodiversitylibrary.org/item/55253#page/789/mode/1up |trans-title=Memoir on the propagation of motion in elastic media |language=fr}}</ref>
[[File:Seismic wave travel through Earth.png|thumb|Patterns of seismic wave travel through Earth's mantle and core. S waves can not travel through the liquid outer core, so they leave a shadow on Earth's far side. P waves do travel through the core, but P wave refraction bends seismic waves away from P wave shadow zones.]]

==== Primary waves ====
{{Main|P wave}}
Primary waves (P waves) are compressional waves that are [[longitudinal wave|longitudinal]] in nature.  [[P waves]] are pressure waves that travel faster than other waves through the earth to arrive at seismograph stations first, hence the name "Primary". These waves can travel through any type of material, including fluids, and can travel nearly 1.7 times faster than the [[S waves]]. In air, they take the form of sound waves, hence they travel at the [[speed of sound]]. Typical speeds are 330&nbsp;m/s in air, 1450&nbsp;m/s in water and about 5000&nbsp;m/s in [[granite]].

==== Secondary waves ====
{{Main|S wave}}
Secondary waves (S waves) are shear waves that are [[transverse wave|transverse]] in nature. Following an earthquake event, S waves arrive at seismograph stations after the faster-moving P waves and displace the ground perpendicular to the direction of propagation. Depending on the propagational direction, the wave can take on different surface characteristics; for example, in the case of horizontally polarized S waves, the ground moves alternately to one side and then the other. S waves can travel only through solids, as fluids (liquids and gases) do not support [[shear stress]]es. S waves are slower than P waves, and speeds are typically around 60% of that of P waves in any given material. Shear waves can not travel through any liquid medium,<ref>{{cite web|url=http://www.burkemuseum.org/static/earthquakes/cur-seismic.html|title=Seismic Waves|publisher=[[Burke Museum of Natural History and Culture]]|access-date=March 24, 2019}}</ref> so the absence of S waves in earth's outer core suggests a liquid state.

=== 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.

=== P and S waves in Earth's mantle and core ===
When an earthquake occurs, seismographs near the [[epicenter]] are able to record both P and S waves, but those at a greater distance no longer detect the high frequencies of the first S wave.  Since shear waves cannot pass through liquids, this phenomenon was original evidence for the now well-established observation that the Earth has a liquid [[outer core]], as demonstrated by [[Richard Dixon Oldham]].  This kind of observation has also been used to argue, by [[Exploration geophysics|seismic testing]], that the [[Moon]] has a solid core, although recent geodetic studies suggest the core is still molten{{Citation needed|date=January 2010}}.

== Notation ==
[[File:Earthquake wave paths.svg|right|thumb|250px|Earthquake wave paths]]
The naming of seismic waves is usually based on the wave type and its path; due to the theoretically infinite possibilities of travel paths and the different areas of application, a wide variety of nomenclatures have emerged historically, the standardization of which – for example in the ''IASPEI Standard Seismic Phase List'' – is still an ongoing process.<ref name=":0">{{Cite journal |last=Storchak |first=D. A. |last2=Schweitzer |first2=J. |last3=Bormann |first3=P. |date=2003-11-01 |title=The IASPEI Standard Seismic Phase List |url=https://pubs.geoscienceworld.org/srl/article/74/6/761-772/142932 |journal=Seismological Research Letters |language=en |volume=74 |issue=6 |pages=761–772 |doi=10.1785/gssrl.74.6.761 |issn=0895-0695|url-access=subscription }}</ref> The path that a wave takes between the focus and the observation point is often drawn as a ray diagram. Each path is denoted by a set of letters that describe the trajectory and phase through the Earth. In general, an upper case denotes a transmitted wave and a lower case denotes a reflected wave. The two exceptions to this seem to be "g" and "n".<ref name=":0" /><ref>The notation is taken from {{cite book |last1=Bullen |first1=K.E. |title=An introduction to the theory of seismology |last2=Bolt |first2=Bruce A. |date=1985 |publisher=Cambridge University Press |isbn=978-0521283892 |edition=4th |location=Cambridge}} and {{cite book |title=International handbook of earthquake and engineering seismology. |date=2002 |publisher=Academic Press |isbn=9780080489223 |editor-last1=Lee |editor-first1=William H.K. |editor-link=William H. K. Lee |location=Amsterdam |editor-last2=Jennings |editor-first2=Paul |editor-last3=Kisslinger |editor-first3=Carl |editor-last4=Kanamori |editor-first4=Hiroo |display-editors=3}}</ref>
{| class="wikitable"
| c || the wave reflects off the outer core
|-
| d || a wave that has been reflected off a discontinuity at depth d
|-
| g || a wave that only travels through the crust
|-
| i || a wave that reflects off the inner core
|-
| I || a P wave in the inner core
|-
| h || a reflection off a discontinuity in the inner core
|-
| J || an S wave in the inner core
|-
| K || a P wave in the outer core
|-
| L || a Love wave sometimes called LT-Wave (Both caps, while an Lt is different)
|-
| n || a wave that travels along the boundary between the crust and mantle
|-
| P || a P wave in the mantle
|-
| p || a P wave ascending to the surface from the focus
|-
| R || a Rayleigh wave
|-
| S || an S wave in the mantle
|-
| s || an S wave ascending to the surface from the focus
|-
| w || the wave reflects off the bottom of the ocean
|-
| || No letter is used when the wave reflects off of the surfaces
|}

For example:
* '''ScP''' is a wave that begins traveling towards the center of the Earth as an S wave.  Upon reaching the outer core the wave reflects as a P wave.
* '''sPKIKP''' is a wave path that begins traveling towards the surface as an S wave.  At the surface, it reflects as a P wave. The P wave then travels through the outer core, the inner core, the outer core, and the mantle.

== Usefulness of P and S waves in locating an event ==
[[File:Hypocenter Calculation.png|thumb|The hypocenter/epicenter of an earthquake is calculated by using the seismic data of that earthquake from at least three different locations. The hypocenter/epicenter is found at the intersection of three circles centered on three observation stations, here shown in Japan, Australia and the United States. The radius of each circle is calculated from the difference in the arrival times of P and S waves at the corresponding station.]]
In the case of local or nearby earthquakes, the difference in the [[arrival time]]s of the P and S waves can be used to determine the distance to the event. In the case of earthquakes that have occurred at global distances, three or more geographically diverse observing stations (using a common [[clock]]) recording P wave arrivals permits the computation of a unique time and location on the planet for the event. Typically, dozens or even hundreds of P wave arrivals are used to calculate [[hypocenter]]s. The misfit generated by a hypocenter calculation is known as "the residual". Residuals of 0.5 second or less are typical for distant events, residuals of 0.1–0.2 s typical for local events, meaning most reported P arrivals fit the computed hypocenter that well. Typically a location program will start by assuming the event occurred at a depth of about 33&nbsp;km; then it minimizes the residual by adjusting depth. Most events occur at depths shallower than about 40&nbsp;km, but some occur as deep as 700&nbsp;km.
[[Image:Ondes P et S 1d 30 petit.gif|thumb|P and S waves separating with time]]
A quick way to determine the distance from a location to the origin of a seismic wave less than 200&nbsp;km away is to take the difference in arrival time of the P wave and the S wave in [[second]]s and multiply by 8&nbsp;kilometers per second.  Modern seismic arrays use more complicated [[earthquake location]] techniques.

At teleseismic distances, the first arriving P waves have necessarily travelled deep into the mantle, and perhaps have even refracted into the outer core of the planet, before travelling back up to the Earth's surface where the seismographic stations are located. The waves travel more quickly than if they had traveled in a straight line from the earthquake.  This is due to the appreciably increased [[Speed of sound#Three-dimensional solids|velocities]] within the planet, and is termed [[Huygens' Principle]]. [[Density]] in the planet increases with depth, which would slow the waves, but the [[Young's modulus|modulus]] of the rock increases much more, so deeper means faster. Therefore, a longer route can take a shorter time.

The travel time must be calculated very accurately in order to compute a precise hypocenter. Since P waves move at many kilometers per second, being off on travel-time calculation by even a half second can mean an error of many kilometers in terms of distance.  In practice, P arrivals from many stations are used and the errors cancel out, so the computed epicenter is likely to be quite accurate, on the order of 10–50&nbsp;km or so around the world.  Dense arrays of nearby sensors such as those that exist in California can provide accuracy of roughly a kilometer, and much greater accuracy is possible when timing is measured directly by [[cross-correlation]] of [[seismogram]] waveforms.

==See also==
*[[Adams–Williamson equation]]
*[[Helioseismology]]
*[[Reflection seismology]]

== References ==
{{Reflist}}

== Sources ==
{{Refbegin}}
*{{cite book|first1=Peter M. |last1=Shearer|title=Introduction to Seismology|year=2009|publisher=Cambridge University Press|isbn=978-0-521-88210-1 }}
{{Refend}}

== External links ==
{{Wikibooks |Historical Geology|Seismic waves}}
*[http://www.kuleuven.be/bwm/edt EDT: A MATLAB Website for seismic wave propagation]

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[[Category:Seismology]]
[[Category:Surface waves]]