Math in the Natural Sciences

Math in Geology

How do geologists measure the intensity of earthquakes?

Geologists measure the intensity of earthquakes in order to compare and judge potential damage. One of the first standard ways to measure intensity was developed in 1902 by Italian seismologist Giuseppe Mercalli (1850–1914) and is called the Mercalli Intensity Scale (it was later modified and renamed the Modified Mercalli Intensity Scale). The numbers, in Roman numerals from I to XII, represent the subjective measurement of an earthquake’s strength based on its effects on local populations and structures. For example, Roman numeral V on the scale represents a quake felt by nearly everyone, with some dishes and windows broken, unstable objects overturned, and disturbances of trees, poles, and other tall objects sometimes noticed.


A devastating tsunami struck Indonesia in 2004. Scientists are using mathematics to study tsunamis and develop a more effective advance-warning system that could save lives.

But scientists wanted a more solid, less subjective scale. One of the first scales developed to measure the true magnitude was invented by American seismologist Charles Francis Richter (1900–1985) and German-born seismologist Beno Gutenberg (1889–1960). In 1935 these scientists borrowed the idea of magnitude from astronomers (stellar brightness is measured by magnitude), defining earthquake magnitude as how fast the ground moved as measured on a particular seismograph a specific distance from the quake’s epicenter.

The Richter Scale is not a physical scale like a ruler, but rather a mathematical construct—it is not linear, but logarithmic. Thus, an increase in each whole number on the scale represents a ten-fold increase in power. Its numbers represent the maximum amplitude of seismic waves that occur 62 miles (100 kilometers) from the epicenter of an earthquake. Because seismographs are usually not located at this exact interval, the magnitudes are deduced using the arrival of specific waves of energy given off when an earthquake occurs.

Although the Richter Scale is mentioned most often in the media when a quake occurs, there is a more precise scale in use today that is based on the mathematics of motions caused by the earthquake. Called moment magnitude, this method uses a physical quantity related to the total energy released in the quake, which is called a moment. Seismologists can also deduce moment magnitude from a fault’s geometry in the field or a seismogram reading. Scientists occasionally use moment magnitude when describing an earthquake event to the public, but because the concept is so difficult to explain the number is often translated into the Richter Scale.


This is a web preview of the "The Handy Math Answer Book" app. Many features only work on your mobile device. If you like what you see, we hope you will consider buying. Get the App