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[At 4:31 A.M. (local time) on Monday, January 17, 1994, a magnitude 6.8 earthquake woke nearly everyone in southern California. The earthquake epicenter was beneath the San Fernando Valley, 20 miles west-northwest of downtown Los Angeles, near the community of Northridge. At the Northridge Fashion Center, near the earthquake epicenter, the second and third floors of Bullocks Department Store collapsed onto the bottom story.]
Locating Epicenters

When an earthquake occurs, one of the first questions is "where was it?" The location may tell us what fault it was on and where damage (if any) most likely occurred. Unfortunately, the earth is not transparent and we can't just see or photograph the earthquake disturbance like meteorologists can photograph clouds. When an earthquake occurs, it generates an expanding wave-front from the earthquake hypocenter at a speed of several kilometers per second.

We observe earthquakes with a network of seismometers on the earth's surface. The ground motion at each seismometer is amplified and recorded electronically at a central recording site. As the wave-front expands from the earthquake, it reaches more distant seismic stations. When an earthquake occurs, we observe the times at which the wave-front passes each station. Determining the earthquake source is calculated from these wave arrival times.

The procedure is simple to state: 1. Guess a location, depth and origin time. 2. Compare the predicted arrival times of the wave from your guessed location with the observed times at each station. 3. Move the location a little in the direction that reduces the difference between the observed and calculated times. 4. Repeat this procedure, each time getting closer to the actual earthquake location and fitting the observed times a little better. 5. Quit when your adjustments have become small enough and when they fit to the observed wave arrival times close enough.

Mathematically, the problem is solved by setting up a system of linear equations, one for each station. The equations express the difference between the observed arrival times and those calculated from the previous (or initial) hypocenter, in terms of small steps in the 3 hypocentral coordinates and the origin time. We must also have a mathematical model of the crustal velocities (in kilometers per second) under the seismic network to calculate the travel times of waves from an earthquake at a given depth to a station at a given distance. The system of linear equations is solved by the method of least squares which minimizes the sum of the squares of the differences between the observed and calculated arrival times. The process begins with an initial guessed hypocenter, performs several hypocentral adjustments each found by a least squares solution to the equations, and iterates to a hypocenter that best fits the observed set of wave arrival times at the stations of the seismic network.