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 body wave, called seismic waves in seismology, that travel through a continuum and are the first waves from an earthquake to arrive at a seismograph. The continuum is made up of gases (as sound waves), liquids, or solids, including the Earth. P-waves can be produced by earthquakes and recorded by seismographs. 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 the highest velocity and is therefore the first wave to be recorded.

In isotropic and homogeneous solids, the mode of propagation of a P-wave is always longitudinal; thus, the particles in the solid vibrate along the axis of propagation (the direction of motion) 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), $\mu$ is the shear modulus (modulus of rigidity, sometimes denoted as G and also called the second Lamé parameter), $\rho$ is the density of the material through which the wave propagates, and $\lambda$ 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 $M = K + 4\mu/3$ and thereby

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

Typical values for P-wave velocity in earthquakes are in the range 5 to 8 km/s. 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.

Velocity of Common Rock Types

Rocktype	Velocity [m/s]	Velocity [ft/s]
Unconsolidated Sandstone	4600 - 5200	15000 - 17000
Consolidated Sandstone	5800	19000
Shale	1800 - 4900	6000 -16000
Limestone	5800 - 6400	19000 - 21000
Dolomite	6400 - 7300	21000 - 24000
Anhydrite	6100	20000
Granite	5800 - 6100	19000 - 20000
Gabbro	7200	23600

Geologist Francis Birch discovered a relationship between the velocity of P waves and the density of the material the waves are traveling in:

$V_p = a (\bar{ M}) + b \rho$.

Which later became known as Birch's law.

Seismic waves in the Earth

See also: Core-mantle boundary, Mohorovičić discontinuity, Low-velocity zone, and Lehmann discontinuity

Velocity of seismic waves in the Earth versus depth. 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-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.

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, and yet 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 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, 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 reach 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) as otherwise false-positive warnings will result. Earthquake Early Warning systems can be automated to allow for immediate safety actions such as issuing alerts, stopping elevators at the nearest floors or switching gas utilities off.

See also

• Earthquake Early Warning (Japan)
• Lamb waves
• Love wave
• Surface wave

External links

• Animation of a P-Wave
• P-Wave velocity calculator
• 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 Warningda:P-bølger