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
A seismic wave is a wave of acoustic energy that travels through the Earth. It can result from an earthquake, volcanic eruption, magma movement, a large landslide, and a large man-made explosion that produces low-frequency acoustic energy. S ...
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
A seismometer is an instrument that responds to ground noises and shaking such as caused by earthquakes, volcanic eruptions, and explosions. They are usually combined with a timing device and a recording device to form a seismograph. The output ...
. 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
compression
Compression may refer to:
Physical science
*Compression (physics), size reduction due to forces
*Compression member, a structural element such as a column
*Compressibility, susceptibility to compression
*Gas compression
*Compression ratio, of a c ...
s 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 relativ ...
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
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In seismology and other areas involving elastic waves, S waves, secondary waves, or shear waves (sometimes called elastic S waves) are a type of elastic wave and are one of the two main types of elastic body waves, so named because th ...
'' represents another seismic wave propagation mode, standing for secondary or shear wave.
Seismic waves in the Earth
![Speeds of seismic waves](https://upload.wikimedia.org/wikipedia/commons/b/be/Speeds_of_seismic_waves.PNG)
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 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 whos ...
. 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.
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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,
reflection Reflection or reflexion may refer to:
Science and technology
* Reflection (physics), a common wave phenomenon
** Specular reflection, reflection from a smooth surface
*** Mirror image, a reflection in a mirror or in water
** Signal reflection, in ...
s,
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 phenomeno ...
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 wh ...
, 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
Earth's outer core is a fluid layer about thick, composed of mostly iron and nickel that lies above Earth's solid inner core and below its mantle. The outer core begins approximately beneath Earth's surface at the core-mantle boundary and e ...
. 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
Secondary may refer to: Science and nature
* Secondary emission, of particles
** Secondary electrons, electrons generated as ionization products
* The secondary winding, or the electrical or electronic circuit connected to the secondary winding i ...
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 piezo-electric transduction, and are frequently used in non-destructiv ...
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
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
*''El ...
. The effectiveness of a warning depends on accurate detection of the P waves and rejection of
ground vibrations Ground vibrations is a technical term that is being used to describe mostly man-made vibrations of the ground, in contrast to natural vibrations of the Earth studied by seismology. For example, vibrations caused by explosions, construction works, ra ...
caused by local activity (such as trucks or construction).
Earthquake early warning
An earthquake warning system or earthquake early warning system is a system of accelerometers, seismometers, communication, computers, and alarms that is devised for notifying adjoining regions of a substantial earthquake while it is in progress ...
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
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 describe ...
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
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 describe ...
(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 elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain:
:G \ \stackrel ...
(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. Mathematical ...
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
An elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is ...
P-wave modulus There are two kinds of seismic body waves in solids, ''pressure waves'' (P-waves) and ''shear waves.'' In linear elasticity, the P-wave modulus M, also known as the longitudinal modulus, or the constrained modulus, is one of the elastic moduli avail ...
,
, is defined so that
and thereby
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.
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Geologist
Francis Birch discovered a relationship between the velocity of P waves and the density of the material the waves are traveling in:
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.)
See also
*
Earthquake warning system
An earthquake warning system or earthquake early warning system is a system of accelerometers, seismometers, communication, computers, and alarms that is devised for notifying adjoining regions of a substantial earthquake while it is in progress ...
*
Lamb waves Lamb waves propagate in solid plates or spheres. They are elastic waves whose particle motion lies in the plane that contains the direction of wave propagation and the direction perpendicular to the plate. In 1917, the English mathematician Horace L ...
*
Love wave
In elastodynamics, Love waves, named after Augustus Edward Hough Love, are horizontally polarized surface waves. The Love wave is a result of the interference of many shear waves (S-waves) guided by an elastic layer, which is ''welded'' to an e ...
*
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 elastic wave and are one of the two main types of elastic body waves, so named because th ...
*
Surface wave
In physics, a surface wave is a mechanical wave that propagates along the Interface (chemistry), interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occu ...
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]
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Waves
Fluid dynamics
Seismology measurement
Seismology
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