Seismic wave
Seismic waves are waves of energy that travel through the core of the earth or other elastic bodies, for example as a result of an earthquake, explosion, or some other process that imparts low-frequency acoustic energy. Seismic waves are studied by seismologists and geophysicists. Seismic wavefields are measured by a seismograph, geophone, hydrophone (in water), or accelerometer.
The propagation velocity of the waves depends on density and elasticity of the medium. Velocity tends to increase with depth, and ranges from approximately 2 to 8 km/s in the Earth's crust up to 13 km/s in the deep mantle.
Earthquakes create various types of waves with different velocities; when reaching seismic observatories, their different travel time enables the scientists to locate the epicenter. In geophysics the refraction or reflection of seismic waves is used for research of the Earth's interior, and artificial vibrations to investigate subsurface structures.
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Types of seismic waves
There are two types of seismic waves, body waves and surface waves. Other modes of wave propagation exist than those described in this article, but they are of comparatively minor importance for earth-borne waves, although they are important in the case of stellar helioseismology.
Body waves
Body waves travel through the interior of the Earth. They follow raypaths refracted by the varying density and modulus (stiffness) of the Earth's interior. The density and modulus, in turn, vary according to temperature, composition, and phase. This effect is similar to the refraction of light waves.
P-waves
P waves (primary waves) are longitudinal or compressional waves. In solids, these waves generally travel almost twice as fast as S waves and can travel through any type of material. In air, these pressure waves take the form of sound waves, hence they travel at the speed of sound. Typical speeds are 330 m/s in air, 1450 m/s in water and about 5000 m/s in granite.
S-waves
S waves (secondary waves) are transverse or shear waves, which means that the ground is displaced perpendicularly to the direction of propagation. In the case of horizontally polarized S waves, the ground moves alternately to one side and then the other. S waves can travel only through solids, as fluids (liquids and gases) do not support shear stresses. Their speed is about 60% of that of P waves in a given material. S waves arrive second in a seismic station because of their slower speed.
Surface waves
Surface waves are analogous to water waves and travel along the Earth's surface. They travel slower than body waves. Because of their low frequency, long duration, and large amplitude, they can be the most destructive type of seismic wave. There are two types of surface waves: Rayleigh waves and Love waves.
Rayleigh waves
Rayleigh waves, also called ground roll, are surface waves that travel as ripples with motions that are similar to those of waves on the surface of water (note, however, that the associated particle motion at shallow depths is retrograde, and that the restoring force in Rayleigh and in other seismic waves is elastic, not gravitational as for water waves). The existence of these waves was predicted by John William Strutt, Lord Rayleigh, in 1885. They are slower than body waves, roughly 90% of the velocity of S waves for typical homogeneous elastic media.
Love waves
Love waves are surface waves that cause circular shearing of the ground. They are named after A.E.H. Love, a British mathematician who created a mathematical model of the waves in 1911. They usually travel slightly faster than Rayleigh waves, about 90% of the S wave velocity. They are the slowest and have the largest amplitude.
P and S waves in Earth's mantle and core
When an earthquake occurs, seismographs near the epicenter are able to record both P and S waves, but those at a greater distance no longer detect the high frequencies of the first S wave. Since shear waves cannot pass through liquids, this phenomenon was original evidence for the now well-established observation that the Earth has a liquid outer core, as demonstrated by Richard Dixon Oldham. This kind of observation has also been used to argue, by seismic testing, that the Moon has a solid core, although recent geodetic studies suggest the core is still molten.
Notation
The path that a wave takes between the focus and the observation point is often drawn as a ray diagram. An example of this is shown in a figure above. When reflections are taken into account there are an infinite number of paths that a wave can take. Each path is denoted by a set of letters that describe the trajectory and phase through the Earth. In general an upper case denotes a transmitted wave and a lower case denotes a reflected wave. The two exceptions to this seem to be "g" and "n". The notation is taken from [1] and [2].
| c | the wave reflects off the outer core |
| d | a wave that has been reflected off a discontinuity at depth d |
| g | a wave that only travels through the crust |
| i | a wave that reflects off the inner core |
| I | a P-wave in the inner core |
| h | a reflection off a discontinuity in the inner core |
| J | an S wave in the inner core |
| K | a P-wave in the outer core |
| L | a Love wave sometimes called LT-Wave (Both caps, while an Lt is different) |
| n | a wave that travels along the boundary between the crust and mantle |
| P | a P wave in the mantle |
| p | a P wave ascending to the surface from the focus |
| R | a Rayleigh wave |
| S | an S wave in the mantle |
| s | an S wave ascending to the surface from the focus |
| w | the wave reflects off the bottom of the ocean |
| No letter is used when the wave reflects off of the surface |
For example:
- ScP is a wave that begins traveling towards the center of the Earth as an S wave. Upon reaching the outer core the wave reflects as a P wave.
- sPKIKP is wave path that begins traveling towards the surface as an S-wave. At the surface it reflects as a P-wave. The P-wave then travels through the outer core, the inner core, the outer core, and the mantle.
Usefulness of P and S waves in locating an event
In the case of local or nearby earthquakes, the difference in the arrival times of the P and S waves can be used to determine the distance to the event. In the case of earthquakes that have occurred at global distances, four or more geographically diverse observing stations (using a common clock) recording P-wave arrivals permits the computation of a unique time and location on the planet for the event. Typically, dozens or even hundreds of P-wave arrivals are used to calculate hypocenters. The misfit generated by a hypocenter calculation is known as "the residual". Residuals of 0.5 second or less are typical for distant events, residuals of 0.1-0.2 s typical for local events, meaning most reported P arrivals fit the computed hypocenter that well. Typically a location program will start by assuming the event occurred at a depth of about 33 km; then it minimizes the residual by adjusting depth. Most events occur at depths shallower than about 40 km, but some occur as deep as 700 km.
A quick way to determine the distance from a location to the origin of a seismic wave less than 200 km away is to take the difference in arrival time of the P wave and the S wave in seconds and multiply by 8 kilometers per second. Modern seismic arrays use more complicated earthquake location techniques.
At teleseismic distances, the first arriving P waves have necessarily travelled deep into the mantle, and perhaps have even refracted into the outer core of the planet, before travelling back up to the Earth's surface where the seismographic stations are located. The waves travel more quickly than if they had traveled in a straight line from the earthquake. This is due to the appreciably increased velocities within the planet, and is termed Huygens' Principle. Density in the planet increases with depth, which would slow the waves, but the modulus of the rock increases much more, so deeper means faster. Therefore, a longer route can take a shorter time.
The travel time must be calculated very accurately in order to compute a precise hypocenter. Since P waves move at many kilometers per second, being off on travel-time calculation by even a half second can mean an error of many kilometers in terms of distance. In practice, P arrivals from many stations are used and the errors cancel out, so the computed epicenter likely to be quite accurate, on the order of 10–50 km or so around the world. Dense arrays of nearby sensors such as those that exist in California can provide accuracy of roughly a kilometer, and much greater accuracy is possible when timing is measured directly by cross-correlation of seismogram waveforms.
External links
- EDT: A MATLAB toolbox for seismic wave propagation
- Illustrated discussion of seismic waves - Purdue.edu