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A P wave (primary wave or pressure wave) is one of the two main types of elastic body waves, 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.
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). [1] 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.
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. [3] [4]
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. 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. As a result, there is a P wave "shadow zone" between 103° and 142° [5] from the earthquake's focus, where the initial P waves are not registered on seismometers. In contrast, S waves do not travel through liquids.
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. 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.
In isotropic 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 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 wave 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 wave modulus, , 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. [6]
| 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 | 23,600 |
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. (The symbol a() is an empirically tabulated function, and b is a constant.)
Seismology is the scientific study of earthquakes and the generation and propagation of elastic waves through the Earth or other planetary bodies. It also includes studies of earthquake environmental effects such as tsunamis as well as diverse seismic sources such as volcanic, tectonic, glacial, fluvial, oceanic microseism, atmospheric, and artificial processes such as explosions and human activities. A related field that uses geology to infer information regarding past earthquakes is paleoseismology. A recording of Earth motion as a function of time, created by a seismograph is called a seismogram. A seismologist is a scientist works in basic or applied seismology.
A seismic wave is a mechanical wave of acoustic energy that travels through the Earth or another planetary body. 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. Seismic waves are studied by seismologists, who record the waves using seismometers, hydrophones, or accelerometers. Seismic waves are distinguished from seismic noise, which is persistent low-amplitude vibration arising from a variety of natural and anthropogenic sources.
Longitudinal waves are waves in which the vibration of the medium is parallel to the direction the wave travels and displacement of the medium is in the same direction of the wave propagation. Mechanical longitudinal waves are also called compressional or compression waves, because they produce compression and rarefaction when travelling through a medium, and pressure waves, because they produce increases and decreases in pressure. A wave along the length of a stretched Slinky toy, where the distance between coils increases and decreases, is a good visualization. Real-world examples include sound waves and seismic P-waves.
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. More simply, the speed of sound is how fast vibrations travel. At 20 °C (68 °F), the speed of sound in air is about 343 m/s, or 1 km in 2.91 s or one mile in 4.69 s. It depends strongly on temperature as well as the medium through which a sound wave is propagating.
Isostasy or isostatic equilibrium is the state of gravitational equilibrium between Earth's crust and mantle such that the crust "floats" at an elevation that depends on its thickness and density. This concept is invoked to explain how different topographic heights can exist at Earth's surface. Although originally defined in terms of continental crust and mantle, it has subsequently been interpreted in terms of lithosphere and asthenosphere, particularly with respect to oceanic island volcanoes, such as the Hawaiian Islands.
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:
In geophysics and reflection seismology, amplitude versus offset (AVO) or amplitude variation with offset is the general term for referring to the dependency of the seismic attribute, amplitude, with the distance between the source and receiver. AVO analysis is a technique that geophysicists can execute on seismic data to determine a rock's fluid content, porosity, density or seismic velocity, shear wave information, fluid indicators.
In seismology and other areas involving elastic waves, S waves, secondary waves, or shear waves are a type of elastic wave and are one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves.
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 elastic half space on one side while bordering a vacuum on the other side. In seismology, Love waves (also known as Q waves (Quer: German for lateral)) are surface seismic waves that cause horizontal shifting of the Earth during an earthquake. Augustus Edward Hough Love predicted the existence of Love waves mathematically in 1911. They form a distinct class, different from other types of seismic waves, such as P-waves and S-waves (both body waves), or Rayleigh waves (another type of surface wave). Love waves travel with a lower velocity than P- or S- waves, but faster than Rayleigh waves. These waves are observed only when there is a low velocity layer overlying a high velocity layer/ sub–layers.
Seismic anisotropy is the directional dependence of the velocity of seismic waves in a medium (rock) within the Earth.
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 due to the core-mantle boundary where P waves are refracted and S waves are stopped at the liquid outer core; however, any liquid boundary or body can create a shadow zone. For example, magma reservoirs with a high enough percent melt can create seismic shadow zones.
Acoustic waves are a type of energy propagation that travels through a medium, such as air, water, or solid objects, by means of adiabatic compression and expansion. Key quantities describing these waves include acoustic pressure, particle velocity, particle displacement, and acoustic intensity. The speed of acoustic waves depends on the medium's properties, such as density and elasticity, with sound traveling at approximately 343 meters per second in air, 1480 meters per second in water, and varying speeds in solids. Examples of acoustic waves include audible sound from speakers, seismic waves causing ground vibrations, and ultrasound used for medical imaging. Understanding acoustic waves is crucial in fields like acoustics, physics, engineering, and medicine, with applications in sound design, noise reduction, and diagnostic imaging.
There are two kinds of seismic body waves in solids, pressure waves (P-waves) and shear waves. In linear elasticity, the P-wave modulus, also known as the longitudinal modulus, or the constrained modulus, is one of the elastic moduli available to describe isotropic homogeneous materials.
The Cauchy number (Ca) is a dimensionless number in continuum mechanics used in the study of compressible flows. It is named after the French mathematician Augustin Louis Cauchy. When the compressibility is important the elastic forces must be considered along with inertial forces for dynamic similarity. Thus, the Cauchy Number is defined as the ratio between inertial and the compressibility force in a flow and can be expressed as
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-destructive testing for detecting defects. Rayleigh waves are part of the seismic waves that are produced on the Earth by earthquakes. When guided in layers they are referred to as Lamb waves, Rayleigh–Lamb waves, or generalized Rayleigh waves.
Shear wave splitting, also called seismic birefringence, is the phenomenon that occurs when a polarized shear wave enters an anisotropic medium. The incident shear wave splits into two polarized shear waves. Shear wave splitting is typically used as a tool for testing the anisotropy of an area of interest. These measurements reflect the degree of anisotropy and lead to a better understanding of the area's crack density and orientation or crystal alignment. We can think of the anisotropy of a particular area as a black box and the shear wave splitting measurements as a way of looking at what is in the box.
The Adams–Williamson equation, named after Leason H. Adams and E. D. Williamson, is an equation used to determine density as a function of radius, more commonly used to determine the relation between the velocities of seismic waves and the density of the Earth's interior. Given the average density of rocks at the Earth's surface and profiles of the P-wave and S-wave speeds as function of depth, it can predict how density increases with depth. It assumes that the compression is adiabatic and that the Earth is spherically symmetric, homogeneous, and in hydrostatic equilibrium. It can also be applied to spherical shells with that property. It is an important part of models of the Earth's interior such as the Preliminary reference Earth model (PREM).
Gassmann's equations are a set of two equations describing the isotropic elastic constants of an ensemble consisting of an isotropic, homogeneous porous medium with a fully connected pore space, saturated by a compressible fluid at pressure equilibrium.
Seismic site effects are related to the amplification of seismic waves in superficial geological layers. The surface ground motion may be strongly amplified if the geological conditions are unfavorable. Therefore, the study of local site effects is an important part of the assessment of strong ground motions, seismic hazard and engineering seismology in general. Damage due to an earthquake may thus be aggravated as in the case of the 1985 Mexico City earthquake. For alluvial basins, we may shake a bowl of jelly to model the phenomenon at a small scale.
A one-way wave equation is a first-order partial differential equation describing one wave traveling in a direction defined by the vector wave velocity. It contrasts with the second-order two-way wave equation describing a standing wavefield resulting from superposition of two waves in opposite directions. In the one-dimensional case it is also known as a transport equation, and it allows wave propagation to be calculated without the mathematical complication of solving a 2nd order differential equation. Due to the fact that in the last decades no general solution to the 3D one-way wave equation could be found, numerous approximation methods based on the 1D one-way wave equation are used for 3D seismic and other geophysical calculations, see also the section § Three-dimensional case.
The analysis of seismic waves provides a direct high-resolution means for studying the internal structure of the Earth...
Seismology is the study of the passage of elastic waves through the Earth. It is arguably the most powerful method available for studying the structure of the interior of the Earth, especially the crust and mantle.
