P-wave

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 wavefunction in atomic physics; see atomic orbital.

Plane P-wave

Representation of the propagation of a P-wave on a 2d grid (empirical shape)

P-waves are a type of elastic wave, also called seismic waves, that can travel through gases (as sound waves), solids and liquids, including the Earth. P-waves are produced by earthquakes and recorded by seismographs. The name P-wave stands either for primary wave, as it has the highest velocity and is therefore the first to be recorded; or pressure wave,^[1] as it is formed from alternating compressions and rarefactions.

In isotropic and homogeneous solids, the mode of propagation of a P-wave is always longitudinal; thus, the particles in the solid have vibrations along or parallel to the travel direction of the wave energy.

Velocity

The velocity of P-waves in a homogeneous isotropic medium is given by

$v_p= \sqrt{ \frac {K+\frac{4}{3}\mu} {\rho}}= \sqrt{ \frac{\lambda+2\mu}{\rho}}$

where K is the bulk modulus (the modulus of incompressibility), μ is the shear modulus (modulus of rigidity, sometimes denoted as G and also called the second Lamé parameter), ρ is the density of the material through which the wave propagates, and λ is the first Lamé parameter.

Of these, density shows the least variation, so the velocity is mostly controlled by K and μ.

The elastic moduli P-wave modulus, M, is defined so that M = K + 4μ / 3 and thereby

$v_p = \sqrt{M/\rho}.\$

Typical values for P-wave velocity in earthquakes are in the range 5 to 8 km/s.^[2] The precise speed varies according to the region of the Earth's interior, from less than 6 km/s in the Earth's crust to 13 km/s through the core.^[3]

Seismic waves in the Earth

See also: Core-mantle boundary, Mohorovičić discontinuity, LVZ, and Lehmann discontinuity

Velocity of seismic waves in the Earth versus depth.^[4] 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.

The seismic waves of both P-type and S-type 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.^[5][6]

P-wave shadow zone

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, reflections, refractions and phase transitions of seismic body waves, or normal modes. Body waves travel through the fluid layers of the Earth's interior, but P-waves are refracted slightly when they pass through the transition between the semisolid mantle and the liquid outer core. As a result, there is a P-wave "shadow zone" between 105° and 143°^[7] from the earthquake's focus, where the initial P-waves are not registered on seismometers. In contrast, S-waves do not travel through liquids, rather, they are attenuated.

As an earthquake warning

Earthquake advance warning is possible by detecting the non-destructive primary waves that travel more quickly through the Earth's crust than do the destructive secondary and Rayleigh waves, in the same way that lightning flashes reaches our eyes before we hear the thunder during a storm. The amount of advance 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 60–90 seconds for deep, distant, large quakes such as Tokyo would have received before the 2011 Tohoku earthquake and tsunami. The effectiveness of advance warning depends on accurate detection of the P-waves and rejection of ground vibrations caused by local activity (such as trucks or construction) otherwise false-positive warnings will result. Technology currently in use known as the QuakeGuard system employs this technique to automate emergency response procedures that protect against loss of life and reduce property damage.^[8]

See also

• S-Wave
• Lamb waves
• Longitudinal wave
• Love wave
• Surface wave
• Earthquake Early Warning (Japan)

References

1. ^ Milsom, J. (2003). Field Geophysics. The geological field guide series. 25. John Wiley and Sons. pp. 232. ISBN 9780470843475. http://books.google.com/?id=T7CKj8bqVlwC&pg=PA179&dq=%22P-wave%22+pressure+wave+geophysics&cd=3#v=onepage&q=&f=false. Retrieved 2010-02-25. 
2. ^ http://hypertextbook.com/facts/2001/PamelaSpiegel.shtml
3. ^ http://earthquake.usgs.gov/learn/topics/seismology/keeping_track.php
4. ^ GR Helffrich & BJ Wood (2002). "The Earth's Mantle". Nature (Macmillan Magazines) 412 (2 August): 501; Figure 1. doi:10.1038/35087500. http://www.phys.uu.nl/~sommer/master/Structure%20and%20Evolution/articles%20for%20presentation/9.pdf. 
5. ^ Justin L Rubinstein, DR Shelly & WL Ellsworth (2009). "Non-volcanic tremor: A window into the roots of fault zones". In S. Cloetingh, Jorg Negendank. New Frontiers in Integrated Solid Earth Sciences. Springer. p. 287 ff. ISBN 904812736X. http://books.google.com/books?id=7AIPPoWf3KIC&pg=PA287. "The analysis of seismic waves provides a direct high-resolution means for studying the internal structure of the Earth..." 
6. ^ CMR Fowler (2005). "§4.1 Waves through the Earth". The solid earth: an introduction to global geophysics (2nd ed.). Cambridge University Press. p. 100. ISBN 0521584094. http://books.google.com/books?id=PifkAotvTroC&pg=PA100. "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." 
7. ^ Lowrie, William. The Fundamentals of Geophysics. Cambridge University Press, 1997, p. 149.
8. ^ "Earthquake P-wave Pre-Detection and Disaster Mitigation Technology". 1999. http://www.seismicwarning.com/web/technology/waveseparation.php. 

• "Photo Glossary of Earthquakes". U.S. Geological Survey". http://earthquake.usgs.gov/learning/glossary.php. Retrieved March 8, 2009. 

External links

• Purdue's catalog of animated illustrations of seismic waves
• Animations illustrating simple wave propagation concepts by Jeffrey S. Barker
• Detection of P-waves and Rejection of Environmental Noise for Accurate Earthquake Early Warning