Why are there so many magnitudes?

Seismologists have several different methods for determining the size of an earthquake - some based on body waves (which travel deep within the structure of the earth), some based on surface waves (which primarily travel along the uppermost layers of the earth), and some based on completely different methodologies.

Here is a brief description of four of the most common methodologies.

ML - "Local Magnitude" determined for local earthquakes (usually 600 km, or less from the recording station), originally developed by Charles Richter circa 1935 for classification of earthquakes in southern California. ML is defined as

where a is the maximum trace amplitude recorded by a standard instrument (the Wood Anderson Torsion seismometer) at a given distance and ao is amplitude for an earthquake of zero magnitude at the same distance. ML has been used most successfully in California, although it is in use in some other regions as well.

Ms - "Surface Wave Magnitude" used for shallow (depth < 70km) earthquakes at teleseismic distances (20-180 degrees) using the 20-second Rayleigh wave for the determination. Ms is defined:

where A is maximum displacement, T is the period of the displacement, and s is a correction term for the distance of the station and the depth of the earthquake. Ms was developed by Gutenberg and Richter in 1936 as an extension to local magnitude at greater distances.

mb - "Body Wave Magnitude" which uses the amplitude of the P-wave train, the first arriving body wave, in the magnitude calculation. It is used at teleseismic distances from 16 to about 100 degrees, where this waveform starts to graze and then enter the core of the earth, changing its character. mb is defined in analogous fashion to Ms, with different correction factors.

Each of these magnitudes uses different parts of the seismogram over a different range of frequencies. While effort has been made to calibrate these scales so that they agree with one another, their definitions were limited by the type of instrumentation which existed during their development. For example, ML begins to "saturate" around magnitude 6.5. That is, ML does not properly estimate the size of larger events. In response to this, a new magnitude scale has been developed:

Mw - "Moment Magnitude" is the latest concept in magnitude determination. Unlike the other methods above, which are all based on the maximum amplitude of ground movement at the station, Mw is based on the seismic moment at the source, or hypocenter, of the earthquake. It may be calculated for local earthquakes all the way out to events occurring half way around the world. These are typically determined for local events of about 3.5 and larger magnitude, and teleseismic events of about magnitude 5.5. Smaller events typically don't generate enough energy to provide a sufficently strong signal to perform the determination.