A P wave (primary wave or pressure wave) is one of the two main types of elastic

body waves Body may refer to: In science * Physical body, an object in physics that represents a large amount, has mass or takes up space * Body (biology), the physical material of an organism * Body plan, the physical features shared by a group of animal ...

, 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 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 compressions and

rarefaction Rarefaction is the reduction of an item's density, the opposite of compression. Like compression, which can travel in waves ( sound waves, for instance), rarefaction waves also exist in nature. A common rarefaction wave is the area of low relat ...

s) or primary wave (as it has high velocity and is therefore the first wave to be recorded by a seismograph). The name ''

S wave __NOTOC__ In seismology and other areas involving elastic waves, S waves, secondary waves, or shear waves (sometimes called elastic S waves) are a type of Linear elasticity#Elastic wave, elastic wave and are one of the two main types of elastic ...

'' represents another seismic wave propagation mode, standing for secondary or shear wave.

Seismic waves in the Earth

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.

P-wave shadow zone

Almost all the information available on the structure of the Earth's deep interior is derived from observations of the travel times, reflections,

refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomen ...

s and phase transitions of seismic body waves, or

normal modes A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies ...

. P waves travel through the fluid layers of the

Earth's interior The internal structure of Earth is the solid portion of the Earth, excluding its atmosphere and hydrosphere. The structure consists of an outer silicate solid crust, a highly viscous asthenosphere and solid mantle, a liquid outer core whose ...

, and yet they are refracted slightly when they pass through the transition between the semisolid

mantle A mantle is a piece of clothing, a type of cloak. Several other meanings are derived from that. Mantle may refer to: *Mantle (clothing), a cloak-like garment worn mainly by women as fashionable outerwear **Mantle (vesture), an Eastern Orthodox ve ...

and the liquid outer core. As a result, there is a P-wave "

shadow zone A seismic shadow zone is an area of the Earth's surface where seismographs cannot detect direct P waves and/or S waves from an earthquake. This is due to liquid layers or structures within the Earth's surface. The most recognized shadow zone is ...

" between 103° and 142° 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 secondary and Rayleigh waves. 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 Eleven or 11 may refer to: *11 (number), the natural number following 10 and preceding 12 * one of the years 11 BC, AD 11, 1911, 2011, or any year ending in 11 Literature * ''Eleven'' (novel), a 2006 novel by British author David Llewellyn *''E ...

. 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

isotropic Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence '' anisotropy''. ''Anisotropy'' is also used to describ ...

and homogeneous solids, a P wave travels in a straight line 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 waves in that kind of medium is given by

v_\mathrm \; = \; \sqrt \; = \; \sqrt

where is the

bulk modulus The bulk modulus (K or B) of a substance is a measure of how resistant to compression the substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume. Other moduli descri ...

(the modulus of incompressibility), is the shear modulus (modulus of rigidity, sometimes denoted as and also called the second Lamé parameter), is the

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...

of the material through which the wave propagates, and is the first Lamé parameter. In typical situations in the interior of the Earth, the density usually varies much less than or , so the velocity is mostly "controlled" by these two parameters. The elastic moduli P-wave modulus,

M

, is defined so that

\, M = K + \tfrac \mu \,

and thereby

v_\mathrm = \sqrt

Typical values for P wave velocity in earthquakes are in the range 5 to 8 km/s. 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 13.5 km/s in the lower mantle, and 11 km/s through the inner core. Geologist Francis Birch discovered a relationship between the velocity of P waves and the density of the material the waves are traveling in:

v_\mathrm = a ( \bar ) + b \, \rho

which later became known as

Birch's law Birch's law, discovered by the geophysicist Francis Birch, establishes a linear relation between compressional wave velocity and density of rocks and minerals: : v_\mathrm = a( \bar M ) + b \rho where \, \bar M \, is the mean atomic mass in fo ...

. (The symbol is an empirically tabulated function, and is a constant.)

References

External links

Animation of a P waveP-wave velocity calculator
*[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 Early Warning System] {{DEFAULTSORT:P-Wave Waves Fluid dynamics Seismology measurement Seismology da:P-bølger