## How Do We Measure and Locate Earthquakes?

Most news reports about earthquakes provide information on the size and location of an earthquake. What does this information mean, and how do we obtain it? What’s the difference between a large earthquake and a minor one? How do seismologists locate an epicentre? To answer these questions we must ﬁrst understand how a seismometer works and how to read the information it provides.

### Seismometers and the Record of an Earthquake

Researchers use an instrument, called a seismometer (or seismograph), to systematically measure the ground motion from an earthquake. Seismologists now use two basic conﬁgurations of seismometers, one for measuring vertical (up-and-down) ground motion and the other for measuring horizontal (backand-forth) ground motion.

The basic operation of a seismometer. |

A mechanical vertical-motion seismometer consists of a heavy weight (like a pendulum) suspended from a spring (figure above a). The spring connects to a sturdy frame that has been bolted to the ground. A pen extends sideways from the weight and touches a vertical revolving cylinder of paper that has been connected to the seismometer frame. If the ground is steady, it traces out a straight reference line as the cylinder turns under it. But when an earthquake wave arrives and causes the ground surface to move up and down, it makes the seismometer frame also move up and down. The weight, however, because of its inertia (the tendency of an object at rest to remain at rest), remains ﬁxed in space. As a consequence, the revolving paper roll moves up and down under the pen and the position of the pen moves relatively away from the reference line. The apparent deﬂection of the pen, therefore, represents the up-and-down movement. As the paper cylinder revolves under the pen, the pen traces out the curves that resemble waves. A mechanical horizontal-motion seismometer works on the same principle, except that the paper cylinder is horizontal and the weight hangs from a wire (figure above b). Sideways back-and-forth movement of the cylinder and the frame relative to the pen causes the pen to trace out waves.

Modern seismometers work on the same principle, except the weight is a magnet that moves relative to a wire coil, producing an electric signal that can be recorded digitally. These seismometers are so sensitive that they can record ground movements of a millionth of a millimetre (only ten times the diameter of an atom) movements that people can’t feel. Typically, the instruments are placed in a vault on bedrock in sheltered areas, away from trafﬁc and other urban noise (figure above c). The entire conﬁguration comprises a seismometer station.

The nature of seismogram. |

An earthquake record produced by a seismometer is called a seismogram (figure above a, b). At ﬁrst glance, a typical seismogram looks like a messy squiggle of lines, but to a seismologist it contains a wealth of information. The horizontal axis represents time, and the vertical axis represents the amplitude (the size) of the seismic waves. The instant at which an earthquake wave appears at a seismometer station is the “arrival time” of the wave. The ﬁrst squiggles on the record represent P-waves, because P-waves travel the fastest. Next come the S-waves, and ﬁnally the surface waves (R-waves and L-waves). Typically, the surface waves have the largest amplitude and arrive over a relatively long interval of time.

### Finding the Epicenter

The method for locating an earthquake epicentre. |

How do we ﬁnd the location of an earthquake’s epicentre? The key to this problem comes from measuring the difference between the time that the P-wave arrives and the time that the S-wave arrives at a seismometer station. P-waves and S-waves pass through the interior of the Earth at different velocities. The delay between P-wave and S-wave arrival times increases as the distance from the epicentre increases (figure above a). To picture why, imagine a car race. If one car travels faster than another, the distance between them increases as the race proceeds.

We can represent the time delay between P- and S-waves on a graph whose horizontal axis indicates distance from the epicentre and whose vertical axis indicates time. A curve on the graph is called a travel-time curve it shows how the time for an earthquake wave to move from its origin to a seismometer station increases as the distance between the epicentre and the seismometer station increases (figure above b).

To use a graph of travel-time curves for determining the distance to an epicentre, start by measuring the time difference between the P- and S-waves on your seismogram; this is called the S

P (pronounced “S minus P”) time. Then draw a line segment on a piece of tracing paper to represent this amount of time, at the scale used for the vertical axis of the graph. Orient the line segment parallel to the time axis and move it back and forth until one end lies on the P-wave curve and the other end lies on the S-wave curve (this gives the S

P time). Extend the line down to the horizontal axis, and simply read off the distance to the epicentre from the seismic station.

The analysis of one seismogram tells you only the distance between the epicentre and the seismometer station; it does not tell you in which direction from the station the epicentre lies. To determine the map position of the epicentre, we use a method called triangulation, which requires plotting the distance from the epicentre to three stations. For example, say you know that the epicentre lies 2,000 km from Station 1, 4,000 km from Station 2, and 6,000 km from Station 3. On a map, draw a circle around each station, such that the radius of the circle is the distance between the station and the epicentre, at the scale of the map. The epicentre lies at the intersection of the three circles, for this is the only point at which the epicentre has the appropriate measured distance from all three stations (figure above c).

*Credits: Stephen Marshak (Essentials of Geology)*