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

seismic waves 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 ...

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

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 The internal structure of Earth are the layers 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 flow g ...

. 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 transmission medium, 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 commo ...

s and phase transitions of seismic body waves, or normal modes. P waves travel through the fluid layers of the Earth's interior, and yet they are refracted slightly when they pass through the transition between the semisolid mantle and the liquid

outer core Earth's outer core is a fluid layer about thick, composed of mostly iron and nickel that lies above Earth's solid Earth's inner core, inner core and below its Earth's mantle, mantle. The outer core begins approximately beneath Earth's surface ...

. As a result, there is a P wave " shadow zone" 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 wave Rayleigh waves are a type of surface acoustic wave that travel along the surface of solids. They can be produced in materials in many ways, such as by a localized impact or by Piezoelectricity, piezo-electric Interdigital transducer, transduction, ...

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. 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 In physics and geometry, isotropy () is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence '' anisotropy''. ''Anisotropy'' is also ...

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 or k) of a substance is a measure of the resistance of a substance to bulk compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume. Other mo ...

(the modulus of incompressibility), is the

shear modulus In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the Elasticity (physics), elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear s ...

(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 ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

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. (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 (sic) Early Warning System] {{DEFAULTSORT:P Wave Waves Fluid dynamics Seismology measurement Seismology