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, 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 wavefront 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 wavefront expands from the earthquake, it reaches more distant seismic stations. When an earthquake occurs, we observe the times at which the wavefront passes each station. We must find the unknown earthquake source knowing these wave arrival times. Here is a map of U.S. Geological Survey seismic stations in the San Francisco Bay Area and 6 seismograms from an earthquake:

We want to find the location, depth and origin time of an earthquake whose waves arrive at the times measured on each seismograms. We want a straightforward and general procedure that we can also program in a computer. The procedure is simple to state: guess a location, depth and origin time; compare the predicted arrival times of the wave from your guessed location with the observed times at each station; then move the location a little in the direction that reduces the difference between the observed and calculated times. Then repeat this procedure, each time getting closer to the actual earthquake location and fitting the observed times a little better. Quit when your adjustments have become small enough and when the fit to the observed wave arrival times is close enough.

You can try to fit an earthquake location on the map just to see how the procedure goes. Note that the earthquake arrives first on station C, so C is a good first guess for the location. Many earthquakes in California occur between 2 and 12 kilometers depth and we will guess a 6 kilometer depth. The origin time should be a few seconds before the time of the wave at the first station. Let's guess an origin time of 10 seconds, measured on the same clock that made the time scale at the bottom of the figure and timed the seismograms. Then we can list the tentative travel times by subtracting the origin time from the observed arrival times:

station....................... A B C D E F

observed time.......... 16.5 17.8 11.3 15.2 22.3 18.3

tentative travel time... 6.5 7.8 1.3 5.2 12.3 8.3

Note the scale at the left of the figure. It shows travel times for waves from an earthquake at a depth of 6 kilometers. The scale starts at 1.3 seconds because the wave reaches the surface 1.3 seconds after the earthquake origin time. You can make a tracing of the scale and move the earthquake on the map until the tentative travel times match the travel times from the scale. Where do you think the earthquake was? Are the times for each station systematically early or late, requiring a shift in the origin time?

The earthquake was near station C. The depth was about 6 km and the origin time was about 10 seconds. (We guessed very well!) A real magnitude 3.4 earthquake occurred at this location on April 29, 1992. It was felt by many people who were sitting or at rest.

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.

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#### How are earthquakes recorded? How are earthquakes measured? How is the magnitude of an earthquake determined?

Earthquakes are recorded by a seismographic network. Each seismic station in the network measures the movement of the ground at that site. The slip of one block of rock over another in an earthquake releases energy that makes the ground vibrate. That vibration pushes the adjoining piece of ground and causes it to vibrate, and thus the energy travels out from the earthquake hypocenter in a wave...

link#### Moment magnitude, Richter scale - what are the different magnitude scales, and why are there so many?

Earthquake size, as measured by the Richter Scale is a well known, but not well understood, concept. The idea of a logarithmic earthquake magnitude scale was first developed by Charles Richter in the 1930's for measuring the size of earthquakes occurring in southern California using relatively high-frequency data from nearby seismograph stations. This magnitude scale was referred to as ML, with...

link#### What is the difference between earthquake magnitude and earthquake intensity? What is the Modified Mercalli Intensity Scale?

Magnitude scales, like the moment magnitude, measure the size of the earthquake at its source. An earthquake has one magnitude. The magnitude does not depend on where the measurement is made. Often, several slightly different magnitudes are reported for an earthquake. This happens because the relation between the seismic measurements and the magnitude is complex and different procedures will often...

link#### How do you determine the magnitude for an earthquake that occurred prior to the creation of the magnitude scale?

For earthquakes that occurred between about 1890 (when modern seismographs came into use) and 1935 when Charles Richter developed the magnitude scale, people went back to the old records and compared the seismograms from those days with similar records for later earthquakes. For earthquakes prior to about 1890, magnitudes have been estimated by looking at the physical effects (such as amount of...

link#### What was the duration of the earthquake? Why don't you report the duration of each earthquake? How does the duration affect the magnitude?

The duration of an earthquake is related to its magnitude but not in a perfectly strict sense. There are two ways to think about the duration of an earthquake. The first is the length of time it takes for the fault to rupture and the second is the length of time shaking is felt at any given point (e.g. when someone says "I felt it shake for 10 seconds" they are making a statement about the...

link#### How can an earthquake have a negative magnitude?

Magnitude calculations are based on a logarithmic scale, so a ten-fold drop in amplitude decreases the magnitude by 1.If an amplitude of 20 millimetres as measured on a seismic signal corresponds to a magnitude 2 earthquake, then:10 times less (2 millimetres) corresponds to a magnitude of 1;100 times less (0.2 millimetres) corresponds to magnitude 0;1000 times less (0.02 millimetres) corresponds...

link#### How can an earthquake have a negative magnitude?

#### What does it mean that the earthquake occurred at a depth of 0 km? How can an earthquake have a negative depth; that would mean it’s in the air. What is the geoid, and what does it have to do with earthquake depth?

An earthquake cannot physically occur at a depth of 0 km or -1km (above the surface of the earth). In order for an earthquake to occur, two blocks of crust must slip past one another, and it is impossible for this to happen at or above the surface of the earth. So why do we report that the earthquake occurred at a depth of 0 km or event as a negative depth sometimes? First of all, the depth of an...

link#### Seismometers, seismographs, seismograms - what's the difference? How do they work?

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link#### Seismometers, seismographs, seismograms - what's the difference? How do they work?

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link#### How can I make my own seismometer?

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link#### What was the first instrument that actually recorded an earthquake?

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link#### What is a Geoid? Why do we use it and where does its shape come from?

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