June 2008

Measurement: Breaking the Richter habit

It is not easy weaning the public off its favorite numbers. At least not in the U.S., which still avoids the metric system along with fellow travelers Myanmar and Liberia, it is not.

Therefore, it is newsworthy to note the media left off the term "Richter scale" more often than not in their descriptions of the earthquake in Sichuan Province, China, in May.

"The quake had a magnitude of 7.9," was a typical observation. That is not to say that such venerated news sources as the BBC did not say, "The recent quake near Chengdu, China, was 7.9 on the Richter scale." Because, they did say just that. 

In fact, there is no 7.9 on the Richter scale. Technically the Richter scale does not go beyond 6.8 because the upper reaches of the mathematics that define the Richter scale are such that all the quakes rather glom together at that point, and one can no longer discriminate between quake strengths.

Thomas C. Hanks and Hiroo Kanamori introduced the moment magnitude scale in 1979 as a successor to the Richter scale, and it is the tool seismologists now use to compare the energy released by earthquakes.

Its main advantage is it does not saturate at the upper end. There is no particular value beyond which all large earthquakes have virtually the same magnitude.

For this reason, moment magnitude is now the most often used estimate of large earthquake magnitudes.

The symbol for the moment magnitude scale is Mw, with the subscript w meaning mechanical work accomplished. The United States Geological Survey does not use this scale for earthquakes with a magnitude of less than 3.5.

The moment magnitude, Mw, is a dimensionless number.

measurement

... where M0 is the seismic moment, which we get from seismograms. The denominator N•m (Newton•meters) is to note we should take the measurement of the seismic moment in those units before taking the logarithm.

Charles Richter and Beno Gutenberg of the California Institute of Technology developed the Richter scale-local magnitude ML-in 1935 to study a particular area of interest in California.

The number used only data from a particular instrument-the Wood-Anderson torsion seismometer.

Richter originally reported values to the nearest quarter of a unit, but decimal numbers came later.

His motivation for creating the local magnitude scale was to separate the vastly larger number of smaller earthquakes from the few larger earthquakes observed in California at the time.

His inspiration was the "apparent magnitude" scale used in astronomy to describe the brightness of stars and other celestial objects.

Richter arbitrarily chose a magnitude 0 event to be an earthquake that would show a maximum combined horizontal displacement of one micrometer on a seismograph recorded using a Wood-Anderson torsion seismometer 100 kilometers (62 miles) from the earthquake epicenter.

Because of the limitations of the Wood-Anderson meter, the original ML does not calculate for events larger than about 6.8, though over the years there have been ad hoc add-ons.