Seismic wave
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Image:Pswaves.jpg Image:Earthquake wave paths.gif Image:Seismogram.gif
A seismic wave is a wave that travels through the Earth, often as the result of an earthquake or explosion. Seismic waves are studied by seismologists, and measured by a seismograph or seismometer.
- Body waves travel through the interior of the Earth. They follow curved paths because of the varying density and composition of the Earth's interior. This effect is similar to the refraction of light waves. Body waves transmit the preliminary tremors of an earthquake but have little destructive effect. Body waves are divided into two types: primary (P-waves) and secondary (S-waves}.
- P waves are longitudinal or compressional waves, which means that the ground is alternately compressed and dilated in the direction of propagation. These waves generally travel twice as fast as S waves and can travel through any type of material. As pressure waves 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. P waves are sometimes called "elastic P waves".
- S waves are transverse or shear waves, which means that the ground is displaced perpendicularly to the direction of propagation, 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 58% of that of P waves in a given material. S waves are sometimes called "elastic S waves".
- Surface waves are analogous to water waves and travel over the Earth's surface. They travel more slowly than body waves. Because of their low frequency, they are more likely than body waves to stimulate resonance in buildings, and are therefore the most destructive type of seismic wave. There are two types of surface waves: Rayleigh waves and Love waves.
- Rayleigh waves, also called ground roll, are surface waves that travel as ripples similar to those on the surface of water. The existence of these waves was predicted by John William Strutt, Lord Rayleigh, in 1885. They are slower than body waves and can readily be seen during an earthquake in an open space like a parking lot where the cars move up and down with the waves.
- Love waves are surface waves that cause horizontal 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 are usually slightly faster than Rayleigh waves.
A quick way to determine the distance from a location to the origin of a seismic wave is to take the difference of arrival time from the P wave to the S wave in seconds and multiply by 8 kilometers per second. Modern seismic arrays use special earthquake location techniques.
Other modes of wave propagation exist than those described in this article, but they are of comparatively minor importance.
An excellent audience demonstration for seismic waves is shown in slinky seismology.
Use of P and S waves in Seismography
An earthquake induces a pressure wave (called the P wave) and shear waves (called S waves). P and S are also known as the primary and secondary waves.
P waves can be likened to sound waves which alternately compress and rarify (by a small amount) the density of rock. The S wave is akin to the ripples on a pond when a stone is dropped into it, or the movement of a rope when the end of it is shaken. (As noted below, liquids cannot conduct shear waves, but solid materials such as rock can.)
P waves travel much faster than S waves. P waves can also travel deep into the earth, not only in the crust, but also beyond the mantle into the liquid outer core and even the solid inner core. The S wave is a surface wave that propagates in the Earth's crust and upper mantle.
When an earthquake occurs, seismographs near the epicenter are able to record both P and S waves, but those on the other side of the Earth can record only P waves. This is due to the fact that shear waves cannot pass through liquids. This was how Oldham proved that the Earth had a liquid core. The moon and Mars have been proven by seismic testing to have solid cores, because they conduct shear waves.
Before the advent of precise electronic clocks and modern high-speed electronic communications, P and S waves were the principal method of determining the location of distant events. Today, P and S arrivals are used to locate only nearby (or "local") events. In the case of teleseismic events, or earthquakes detected at distances of several thousand kilometers or more, S waves are generally ignored today, for the purposes of epicenter calculation. However they may be used to provide a better estimate of event magnitude, for some events.
In the case of very large earthquakes, both P wave amplitude and long-period amplitude are used to accurately estimate the magnitude of an event. But routinely, in the case of most events, only the maximum P wave amplitude is used to calculate magnitude.
The P arrival is selected as the first observed impulse or movement on a seismogram, and is ideally timed to 0.1 second, or at least a second. Typically the shock waves generated by an earthquake propagate at different intensities at different compass directions from the event. However, by averaging the reported P-wave amplitudes from many seismograph stations, a very good estimate of the total energy released by an earthquake, or its "magnitude", can be calculated.
An earthquake can also generate other more esoteric types of waves, known as Love waves, Rayleigh waves, and so on, which travel in the crust and upper mantle. But for the purpose of epicenter calculation, the P waves are the most important. The P wave are typically the only ones used in calculations, at least at global distances.
A compressional P wave can also bounce repeatedly inside the earth's outer liquid core before it reaches the surface of the earth. If it bounces seven times, the P wave is referred to as PKKKKKKKP, or P7KP. Each "K" assigned represents a bounce of the shock wave deep inside the planet. The travel time for P7KP is about 75 minutes, and the detected signal is typically very small. Usually it's just one small isolated blip or tiny bump on a seismogram. However if one has calculated where the event occurred, and when, then it is possible to calculate where P7KP should be, and sometimes it is possible to see it. P7KP and similar "K" waves are essentially echoes from deep inside the planet. Earthquakes which generate a lot of energy vertically (such as those occurring in the Hindu Kush mountains of Afghanistan and the Everest area) can provide good P7KP signals. Such signals have been used by seismologists to analyze the detailed structure of the core. They can also be used to detect relatively minor density differences within the solid mantle, particularly from events where the time is known precisely, as in the case of most underground nuclear detonations.
The compressional shock waves from an earthquake travel much faster through the planet than sound does in air. Deep inside the Earth, a P wave can be travelling at about Mach 20 or 25. The deeper the pressure wave moves into the mantle, or core, the denser is the material it encounters. Thus, the faster it moves, because more dense materials conduct pressure waves better, i.e. faster. (Just as sound moves through steel appreciably faster than it does through air.)
Locating an event
In the case of local or nearby earthquakes, the difference in the arrival times of the P and S waves is used to determine the distance to the event. In the case of earthquakes that have occurred at global distances, typically (just) three or more P-wave arrivals permits the computation of a unique location on the planet. Typically, dozens or even hundreds of P-wave arrivals are used to calculate epicenters. The error generated by an epicenter calculation is known as "the residual". Residuals of 0.5 second or less are typical, meaning most reported P arrivals fit the computed epicenter 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. Many events occur at a depth of about 33 km, or near the bottom of the Earth's crust, but some occur as deep as 600 km.
At teleseismic distances, detected P waves have necessarily travelled deep into the mantle, and perhaps have even refracted into the outer core of the planet, before reaching the Earth's surface and a seismograph station. They arrive first—even though they have travelled much further than other compressional (P) waves which have travelled more-or-less straight-line or surface paths. This is due to the appreciably increased velocities within the planet. Density in the planet increases with depth, so deeper means faster. Therefore, a longer route can take a shorter time.
The travel times of P waves from their source to recording equipment at a seismograph station can be accurately calculated only by using fifth-degree polynomials, such as
y = ax5 + bx4 + cx³ + dx² + ex + f
However, cubic polynomials y = ax³ + bx² + cx + d, or a series of "cubic splines" (cubic equations which fit a particular range) can also provide good estimates of travel time versus distance (in terms of surface distance, which is easily calculated, given latitude and longitude). Quadratic equations aren't accurate enough, because they cannot be made to fit travel times, except for very short intervals. The nature of a cubic spline is to give a "good fit" for a cubic equation, of travel time versus distance, for a particular range of distance. Two, three or more cubic splines (equations) may have to be used in order to derive a good estimate. Since the density keeps changing with depth (according to distance, which implies the path of the first arrival), a series of splines must be used. However, for a wide range of distances, fifth-degree polynomials fit distance vs travel time data very accurately, if the appropriate constants a, b, c, d, e and f are chosen. Thus, a more simple calculation can be done. In practice, the calculation is trivial, and requires only iterating to obtain the lowest possible residual.
The travel time must be calculated very accurately in order to compute a precise epicenter. 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 km or so.) Dense arrays of nearby sensors such as those that exist in California can provide accuracy of roughly a kilometer.
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