Editing Seismic wave (section)

== Usefulness of P and S waves in locating an event ==
[[File:Hypocenter Calculation.png|thumb|The hypocenter/epicenter of an earthquake is calculated by using the seismic data of that earthquake from at least three different locations. The hypocenter/epicenter is found at the intersection of three circles centered on three observation stations, here shown in Japan, Australia and the United States. The radius of each circle is calculated from the difference in the arrival times of P and S waves at the corresponding station.]]
In the case of local or nearby earthquakes, the difference in the [[arrival time]]s 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, three 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 [[hypocenter]]s. 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&nbsp;km; then it minimizes the residual by adjusting depth. Most events occur at depths shallower than about 40&nbsp;km, but some occur as deep as 700&nbsp;km.
[[Image:Ondes P et S 1d 30 petit.gif|thumb|P and S waves separating with time]]
A quick way to determine the distance from a location to the origin of a seismic wave less than 200&nbsp;km away is to take the difference in arrival time of the P wave and the S wave in [[second]]s and multiply by 8&nbsp;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 [[Speed of sound#Three-dimensional solids|velocities]] within the planet, and is termed [[Huygens' Principle]]. [[Density]] in the planet increases with depth, which would slow the waves, but the [[Young's modulus|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 is likely to be quite accurate, on the order of 10–50&nbsp;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.