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{{Short description|Type of seismic wave}}
{{hatnote|This article is on the type of seismic wave. For the term used in electrocardiography, see [[P wave (electrocardiography)]]. P wave can also refer to a type 
of electronic wave function in atomic physics; see [[atomic orbital]].}}
{{Earthquakes}}
[[Image:Onde compression impulsion 1d 30 petit.gif|thumb|upright=1.4|Plane P wave]]
[[Image:Ondes compression 2d 20 petit.gif|thumb|upright=1.4|Representation of the propagation of a P wave on a 2D grid (empirical shape){{clarify|date=November 2017}}]]

A '''P wave''' ('''primary wave''' or '''pressure wave''') is one of the two main types of elastic [[Body wave (seismology)|body waves]], called [[seismic waves]] in seismology. P waves travel faster than other seismic waves and hence are the first signal from an earthquake to arrive at any affected location or at a [[seismograph]]. P waves [[Continuum mechanics|may be transmitted through]] gases, liquids, or solids.

==Nomenclature==
The name ''P wave'' can stand for either '''pressure wave''' (as it is formed from alternating [[compression (physical)|compression]]s and [[rarefaction]]s) or '''primary wave''' (as it has high velocity and is therefore the first wave to be recorded by a seismograph).<ref name="John">{{cite book|last=Milsom|first=J.|title=Field Geophysics|publisher=John Wiley and Sons|year=2003|series=The geological field guide series|volume=25|page=232|isbn=978-0-470-84347-5|url=https://books.google.com/books?id=T7CKj8bqVlwC&pg=PA179|access-date=2010-02-25}}</ref> The name ''[[S wave]]'' represents another seismic wave propagation mode, standing for secondary or shear wave, a usually more destructive wave than the primary wave.

==Seismic waves in the Earth==
{{See also|Core-mantle boundary|Mohorovičić discontinuity|Low-velocity zone|Lehmann discontinuity}}
[[File:Speeds of seismic waves.svg|thumb|upright=1.4|Velocity of seismic waves in the Earth versus depth.<ref name=Helffrich>{{cite journal |journal=Nature |year=2002 |volume=412 |issue=2 August |pages=501–7 |title=The Earth's Mantle |author=GR Helffrich & BJ Wood |url=http://www.phys.uu.nl/~sommer/master/Structure%20and%20Evolution/articles%20for%20presentation/9.pdf | 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.]]

Primary and secondary waves are body waves that travel within the Earth. The motion and behavior of both P and S waves in the Earth are monitored to probe the interior [[structure of the Earth]]. Discontinuities in velocity as a function of depth are indicative of changes in phase or composition. Differences in arrival times of waves originating in a seismic event like an earthquake as a result of waves taking different paths allow mapping of the Earth's inner structure.<ref name="Negendank">
{{cite book |author=Rubinstein |first=Justin L. |title=New Frontiers in Integrated Solid Earth Sciences |last2=Shelly |first2=D. R. |last3=Ellsworth |first3=W. L. |publisher=Springer |year=2009 |isbn=978-90-481-2736-8 |editor=Cloetingh |editor-first=S. |page=287 ''ff'' |chapter=Non-volcanic tremor: A window into the roots of fault zones |quote=The analysis of seismic waves provides a direct high-resolution means for studying the internal structure of the Earth... |editor-last2=Negendank |editor-first2=Jorg |chapter-url=https://books.google.com/books?id=7AIPPoWf3KIC&pg=PA287}}
</ref><ref name="Fowler">
{{cite book |author=Fowler |first=C. M. R. |title=The solid earth: an introduction to global geophysics |publisher=Cambridge University Press |year=2005 |isbn=978-0-521-58409-8 |edition=2nd |page=100 |chapter=§4.1 Waves through the Earth |quote=Seismology is the study of the passage of elastic waves through the Earth. It is arguably the most powerful method available for studying the structure of the interior of the Earth, especially the crust and mantle. |chapter-url=https://books.google.com/books?id=PifkAotvTroC&pg=PA100}}
</ref>

===P wave shadow zone===
[[Image:Earthquake wave shadow zone.svg|thumb|upright=1.4|P wave shadow zone (from [[USGS]])]]
Almost all the information available on the structure of the Earth's deep interior is derived from observations of the travel times, [[Reflection (physics)|reflection]]s, [[refraction]]s and phase transitions of seismic body waves, or [[normal modes]]. P waves travel through the fluid layers of the [[Internal structure of Earth|Earth's interior]], and yet they are refracted slightly when they pass through the transition between the semisolid [[mantle (geology)|mantle]] and the liquid [[Internal structure of Earth#Core|outer core]]. As a result, there is a P wave "[[shadow zone]]" between 103° and 142°<ref>Lowrie, William. ''The Fundamentals of Geophysics''. Cambridge University Press, 1997, p. 149.</ref> from the earthquake's focus, where the initial P waves are not registered on seismometers. In contrast, S waves do not travel through liquids.

===As an earthquake warning===

Advance earthquake warning is possible by detecting the nondestructive primary waves that travel more quickly through the Earth's crust than do the destructive [[S wave|secondary]] and [[Rayleigh wave]]s.

The amount of warning depends on the delay between the arrival of the P wave and other destructive waves, generally on the order of seconds up to about 60 to 90 seconds for deep, distant, large quakes such as the [[2011 Tohoku earthquake and tsunami|2011 Tohoku earthquake]]. The effectiveness of a warning depends on accurate detection of the P waves and rejection of [[ground vibrations]] caused by local activity (such as trucks or construction). [[Earthquake early warning]] systems can be automated to allow for immediate safety actions, such as issuing alerts, stopping elevators at the nearest floors, and switching off utilities.

==Propagation==

===Velocity===
In [[isotropic]] and homogeneous solids, a P&nbsp;wave travels in a straight line [[Longitudinal wave|longitudinally]]; thus, the particles in the solid vibrate along the axis of propagation (the direction of motion) of the wave energy. The velocity of P&nbsp;waves in that kind of medium is given by
<math display="block">v_\mathrm{p} \; = \; \sqrt{ \frac{\, K + \tfrac{4}{3} \mu \;}{\rho} } \; = \; \sqrt{ \frac{\, \lambda + 2 \mu \;}{\rho} } </math>
where {{mvar|K}} is the [[bulk modulus]] (the modulus of incompressibility), {{mvar|μ}} is the [[shear modulus]] (modulus of rigidity, sometimes denoted as {{mvar|G}} and also called the second [[Lamé parameters|Lamé parameter]]), {{mvar|ρ}} is the [[density]] of the material through which the wave propagates, and {{mvar|λ}} is the first [[Lamé parameters|Lamé parameter]].

In typical situations in the interior of the Earth, the density {{mvar|ρ}} usually varies much less than {{mvar|K}} or {{mvar|μ}}, so the velocity is mostly "controlled" by these two parameters.

The [[elastic moduli]] [[P wave modulus]], <math>M</math>, is defined so that <math display="inline">\, M = K + \tfrac{4}{3} \mu \,</math> and thereby
<math display="block">v_\mathrm{p} = \sqrt{ \frac{\, M \;}{\rho} } </math>

Typical values for P&nbsp;wave velocity in earthquakes are in the range 5 to 8&nbsp;km/s. The precise speed varies according to the region of the Earth's interior, from less than 6&nbsp;km/s in the Earth's crust to 13.5&nbsp;km/s in the lower mantle, and 11&nbsp;km/s through the inner core.<ref>
{{cite journal
 |last1=Dziewonski |first1=Adam M.
 |last2=Anderson |first2=Don L.
 |year=1981
 |title=Preliminary reference Earth model
 |journal=Physics of the Earth and Planetary Interiors
 |volume=25 |issue=4 |pages=297–356
 |doi=10.1016/0031-9201(81)90046-7
 |bibcode=1981PEPI...25..297D
}}
</ref>

{| class="wikitable sortable collapsible"
|+ Velocity in common rock types<ref>
{{cite web
 |title=Acoustic Logging
 |date=2011-12-12
 |department=Geophysics
 |publisher=U.S. [[Environmental Protection Agency]]
 |url=http://www.epa.gov/esd/cmb/GeophysicsWebsite/pages/reference/methods/Borehole_Geophysical_Methods/Logging_Techniques_and_Tools/Acoustic_Logging.htm
 |access-date=2015-02-03
}}
</ref>
|-
! scope="col" | Rock Type
! scope="col" | Velocity [m/s]
! scope="col" | Velocity [ft/s]
|-
| Unconsolidated [[sandstone]] || 4,600–5,200 || 15,000–17,000 
|-
| Consolidated sandstone || 5,800 || 19,000
|-
| [[Shale]] || 1,800–4,900 || 6,000–16,000
|-
| [[Limestone]] || 5,800–6,400 || 19,000–21,000
|-
| [[Dolomite (rock)|Dolomite]] || 6,400–7,300 || 21,000–24,000
|-
| [[Anhydrite]] || 6,100 || 20,000
|-
| [[Granite]] || 5,800–6,100 || 19,000–20,000
|-
| [[Gabbro]] || 7,200 || 23,600
|-
|}

Geologist [[Francis Birch (geophysicist)|Francis Birch]] discovered a relationship between the velocity of P&nbsp;waves and the density of the material the waves are traveling in:
<math display="block"> v_\mathrm{p} = a ( \bar{M} ) + b \, \rho </math>
which later became known as [[Birch's law]]. (The symbol {{math|''a''()}} is an empirically tabulated function, and {{mvar|b}} is a constant.)

==See also==
* [[Earthquake warning system]]
* [[Lamb waves]]
* [[Love wave]]
* [[S wave]]
* [[Surface wave]]

==References==
<references/>
* {{cite web|url=https://earthquake.usgs.gov/learning/glossary.php|publisher=United States Geological Survey"|title=Photo Glossary of Earthquakes|access-date=March 8, 2009|url-status=dead|archive-url=https://web.archive.org/web/20090227061801/http://earthquake.usgs.gov/learning/glossary.php|archive-date=February 27, 2009}}

==External links==
*[https://www.youtube.com/watch?v=2rYjlVPU9U4 Animation of a P wave]
*[http://www.fxsolver.com/browse/formulas/P-wave+Velocity P-wave velocity calculator]
*[https://web.archive.org/web/20051004065509/http://www.eas.purdue.edu/~braile/edumod/waves/WaveDemo.htm Purdue's catalog of animated illustrations of seismic waves]
*[http://bingweb.binghamton.edu/%7Ejbarker/animations.html Animations illustrating simple wave propagation concepts by Jeffrey S. Barker ]
*[https://web.archive.org/web/20141013181425/http://internationalscienceindex.org/publications/10327/bayesian-networks-for-earthquake-magnitude-classification-in-a-early-warning-system/ Bayesian Networks for Earthquake Magnitude Classification in a (sic) Early Warning System]

{{DEFAULTSORT:P Wave}}
[[Category:Waves]]
[[Category:Fluid dynamics]]
[[Category:Seismology measurement]]
[[Category:Seismology]]