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Plane P we
Representation of the propagation of a P we on a 2D grid (empirical shape)[clarification needed]
A P we (primary we or pressure we) is one of the two main types of elastic body wes, called seismic wes in seismology. P wes trel faster than other seismic wes and hence are the first signal from an earthquake to arrive at any affected location or at a seismograph. P wes may be transmitted through gases, liquids, or solids.
Nomenclature[edit]The name P we can stand for either pressure we (as it is formed from alternating compressions and rarefactions) or primary we (as it has high velocity and is therefore the first we to be recorded by a seismograph).[1] The name S we represents another seismic we propagation mode, standing for secondary or shear we, a usually more destructive we than the primary we.
Seismic wes in the Earth[edit] See also: Core-mantle boundary, Mohorovičić discontinuity, Low-velocity zone, and Lehmann discontinuity
Velocity of seismic wes in the Earth versus depth.[2] The negligible S we velocity in the outer core occurs because it is liquid, while in the solid inner core the S we velocity is non-zero.
Primary and secondary wes are body wes that trel within the Earth. The motion and behior of both P and S wes 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 wes originating in a seismic event like an earthquake as a result of wes taking different paths allow mapping of the Earth's inner structure.[3][4]
P we shadow zone[edit]
P we shadow zone (from USGS)
Almost all the information ailable on the structure of the Earth's deep interior is derived from observations of the trel times, reflections, refractions and phase transitions of seismic body wes, or normal modes. P wes trel 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. As a result, there is a P we "shadow zone" between 103° and 142°[5] from the earthquake's focus, where the initial P wes are not registered on seismometers. In contrast, S wes do not trel through liquids.
As an earthquake warning[edit]Advance earthquake warning is possible by detecting the nondestructive primary wes that trel more quickly through the Earth's crust than do the destructive secondary and Rayleigh wes.
The amount of warning depends on the delay between the arrival of the P we and other destructive wes, 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 wes 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[edit] Velocity[edit]In isotropic and homogeneous solids, a P we trels in a straight line longitudinally; thus, the particles in the solid vibrate along the axis of propagation (the direction of motion) of the we energy. The velocity of P wes in that kind of medium is given by v p = K + 4 3 μ ρ = λ + 2 μ ρ {\displaystyle v_{\mathrm {p} }\;=\;{\sqrt {\frac {\,K+{\tfrac {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 we propagates, and λ is the first Lamé parameter.
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 we propagates, and λ is the first Lamé parameter.
In typical situations in the interior of the Earth, the density ρ usually varies much less than K or μ, so the velocity is mostly "controlled" by these two parameters.
The elastic moduli P we modulus, M {\displaystyle M} , is defined so that M = K + 4 3 μ {\textstyle \,M=K+{\tfrac {4}{3}}\mu \,} and thereby v p = M ρ {\displaystyle v_{\mathrm {p} }={\sqrt {\frac {\,M\;}{\rho }}}}
, is defined so that
M
=
K
+
4
3
μ
{\textstyle \,M=K+{\tfrac {4}{3}}\mu \,}
and thereby
v
p
=
M
ρ
{\displaystyle v_{\mathrm {p} }={\sqrt {\frac {\,M\;}{\rho }}}}
Typical values for P we 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.[6]
Velocity in common rock types[7] Rock Type Velocity [m/s] Velocity [ft/s] Unconsolidated sandstone 4,600–5,200 15,000–17,000 Consolidated sandstone 5,800 19,000 Shale 1,800–4,900 6,000–16,000 Limestone 5,800–6,400 19,000–21,000 Dolomite 6,400–7,300 21,000–24,000 Anhydrite 6,100 20,000 Granite 5,800–6,100 19,000–20,000 Gabbro 7,200 23,600Geologist Francis Birch discovered a relationship between the velocity of P wes and the density of the material the wes are treling in: v p = a ( M ¯ ) + b ρ {\displaystyle v_{\mathrm {p} }=a({\bar {M}})+b\,\rho } which later became known as Birch's law. (The symbol a() is an empirically tabulated function, and b is a constant.)
See also[edit] Earthquake warning system Lamb wes Love we S we Surface we References[edit] ^ Milsom, J. (2003). Field Geophysics. The geological field guide series. Vol. 25. John Wiley and Sons. p. 232. ISBN 978-0-470-84347-5. Retrieved 2010-02-25. ^ GR Helffrich & BJ Wood (2002). "The Earth's Mantle" (PDF). Nature. 412 (2 August): 501–7. doi:10.1038/35087500. PMID 11484043. S2CID 4304379. ^ Rubinstein, Justin L.; Shelly, D. R.; Ellsworth, W. L. (2009). "Non-volcanic tremor: A window into the roots of fault zones". In Cloetingh, S.; Negendank, Jorg (eds.). New Frontiers in Integrated Solid Earth Sciences. Springer. p. 287 ff. ISBN 978-90-481-2736-8. The analysis of seismic wes provides a direct high-resolution means for studying the internal structure of the Earth... ^ Fowler, C. M. R. (2005). "§4.1 Wes through the Earth". The solid earth: an introduction to global geophysics (2nd ed.). Cambridge University Press. p. 100. ISBN 978-0-521-58409-8. Seismology is the study of the passage of elastic wes through the Earth. It is arguably the most powerful method ailable for studying the structure of the interior of the Earth, especially the crust and mantle. ^ Lowrie, William. The Fundamentals of Geophysics. Cambridge University Press, 1997, p. 149. ^ Dziewonski, Adam M.; Anderson, Don L. (1981). "Preliminary reference Earth model". Physics of the Earth and Planetary Interiors. 25 (4): 297–356. Bibcode:1981PEPI...25..297D. doi:10.1016/0031-9201(81)90046-7. ^ "Acoustic Logging". Geophysics. U.S. Environmental Protection Agency. 2011-12-12. Archived from the original on October 22, 2011. Retrieved 2015-02-03. "Photo Glossary of Earthquakes". United States Geological Survey". Archived from the original on February 27, 2009. Retrieved March 8, 2009. External links[edit] Animation of a P we P-we velocity calculator Purdue's catalog of animated illustrations of seismic wes Animations illustrating simple we propagation concepts by Jeffrey S. Barker Archived 2017-05-10 at the Wayback Machine Bayesian Networks for Earthquake Magnitude Classification in a (sic) Early Warning System
which later became known as Birch's law. (The symbol a() is an empirically tabulated function, and b is a constant.)