# earthquake magnitudes

A typical earthquake begins when bent rock stops sticking and starts slipping. The unbending of the rock releases energy, much as releasing a coiled spring does. This energy spreads out from the place where the earthquake began in the form of waves. Ideally, there should be a way of describing the “strength” of an earthquake in terms of the energy released, independent of the location of the observer.

Instruments that record the waves made by earthquakes are called seismographs. Each contains a mass that is free to move. Because of inertia, the mass tends to stay where it is when the ground and the rest of the seismograph move during an earthquake. A pendulum is a simple example. The relative movement of the mass in relation to everything else is magnified (by levers, in the simplest case) and makes a record, for example, by moving a pen that is marking moving paper. The farther the ground moves, the greater the back and forth movement of the pen.

Although earthquake detecting devices have been built for more than a thousand years, it was not until the last half of the 19th century that instruments comparable to modern seismographs were widely deployed. Many of these devices were installed in California.

In 1931 the Seismological Laboratory in Pasadena, California decided to publish an annual list of local earthquakes. The list, however, contained two or three hundred earthquakes, and it was felt it would be too scary for general consumption without some indication that most of the quakes were small. Intensity estimates were not available because the data came from seismographs, not from observers on the ground. So Charles Richter decided to define some “rational,” as he described it, way of describing the size of these earthquakes. The method he chose resembled one used by K. Wadati in Japan.

As a basis for his comparisons, Richter decided to use the how far the earthquake made the pen of a seismograph move. As a standard seismograph he chose a particular type that all the stations in southern California had: torsion seismographs with an 0.8 second period and a magnification of 2,800. The scale would have to be logarithmic; Richter chose log to the base 10.

To provide a set point on the scale, Richter decided an earthquake would be magnitude one if it made the pen of one of his seismographs, located 100 kilometers from the quake, move a maximum of one-thousandth of a millimeter. This value was chosen to ensure that any earthquake a person could feel would have a positive magnitude. Given the above assumptions, the magnitude of any quake can be described by the log10 of the ratio of the maximum trace amplitude of that quake (at a distance of 100 km) to the maximum trace amplitude of the magnitude one quake, i.e., one-thousandth of a millimeter. So a pen movement of one millimeter indicated a magnitude three earthquake–if the quake was 100 km away.

Since earthquakes do not conveniently occur at 100-km distances from seismographs, Richter devised an empirical method for correcting the trace amplitude for distance.

Richter’s original scale of earthquake magnitudes had a number of limitations. Almost all California earthquakes are shallow, so the scale got by without taking into account the depth of an earthquake. Only relatively local quakes were on the list, so the scale didn’t need to deal with distant quakes. But for its purpose, the original scale was a great success, and that success prompted Richter, Beno Gutenberg, and many other workers to devise more general measures of magnitude. The more sophisticated scales now used take into account differences in the types of waves generated by earthquakes; Mb magnitudes reflect waves that have traveled through great depths, and MS magnitudes, waves that travel along the surface (the symbol for magnitudes on Richter’s scale is ML). The new scales (including many used only in a particular area) have been defined so that their values are consistent with those of the original scale, and these too are popularly called magnitudes “on the Richter scale.”

Each whole number step in the Richter scale represents a ten-fold increase in magnitude, but roughly a 32-fold increase in released energy. The annual frequency of big earthquakes, at least in a recent 47-year period, has been as follows:

Earthquakes per Year
MS
Magnitudes
Number
8.5–8.9 0.3
8.0–8.4 1.1
7.5–7.9 3.1
7.0–7.4 15
6.5–6.9 56
6.0–6.4 210

Unlike the Mercalli scale, the Richter scale has no defined “highest reading.” But in fact the highest readings recorded on the Mb scale have been about 6.5–6.8, and on the MS scale, about 8.3–8.7. This limit reflects the way earthquakes occur; the rock breaks before any more energy could be stored.  Higher magnitudes have probably occurred, but due to other causes: when a large asteroid slams into the Earth.

There is a problem: all the magnitude scales described so far underestimate the size of very large earthquakes because their definitions assume all earthquakes generate the same mixture of waves. In very large earthquakes the rock ruptures across a very large underground surface, and the resulting waves have a greater proportion of waves with very long periods than smaller earthquakes do. So workers looked for a way of describing earthquake size that reflect even more closely the geological reality.

## Seismic Moment

By analyzing the waveforms recorded by a number of seismographs, each seeing the earthquake from a different angle, researchers can reconstruct what happened where the earthquake occurred, such as the direction and tilt of the fault and the direction the rock moved. From these they can calculate a quantity called the seismic moment, the product of the fault surface area over which movement occurred, the strength of the rock, and the average displacement. A new magnitude scale (symbol, MW) has been defined based on the seismic moment. Unlike the other scales, the MW scale takes into account the geometrical relationships between the fault's orientation and the observers.

Magnitudes based on seismic moment give a truer picture of large earthquakes than the other scales do; the 1960 Chile quake, for example, was MS 8.5 but MW 9.6; the 1964 Alaska earthquake, MS 8.3, but MW 9.2.

## want more?

B. Gutenberg and C. F. Richter.
Seismicity of the Earth and Associated Phenomenon. 2nd Ed.
Princeton: Princeton University Press, 1954.

Susan Elizabeth Hough.
Richter's Scale: Measure of an Earthquake, Measure of a Man.
Princeton University Press, 2007.

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