The moment magnitude scale was introduced in 1979 by Thomas C. Hanks and Hiroo Kanamori as a successor to the Richter scale and is used by seismologists to compare the energy released by earthquakes.[1] The moment magnitude $ M_\mathrm{w} $ is a dimensionless number defined by

$ M_\mathrm{w} = {2 \over 3}\left(\log_{10} \frac{M_0}{\mathrm{N}\cdot \mathrm{m}} - 9.1\right) = {2 \over 3}\left(\log_{10} \frac{M_0}{\mathrm{dyn}\cdot \mathrm{cm}} - 16.1\right) $

where $ M_0 $ is the seismic moment. The division by N m has the effect of indicating that the seismic moment is to be expressed in newton meters before the logarithm is taken; see ISO 31-0.

An increase of 1 step on this logarithmic scale corresponds to a 101.5 = 31.6 times increase in the amount of energy released, and an increase of 2 steps corresponds to a 10³ = 1000 times increase in energy.

The constants in the equation are chosen so that estimates of moment magnitude roughly agree with estimates using other scales, such as the Local Magnitude scale, ML, commonly called the Richter magnitude scale. One advantage of the moment magnitude scale is that, unlike other magnitude scales, it does not saturate at the upper end. That is, there is no particular value beyond which all large earthquakes have about the same magnitude. For this reason, moment magnitude is now the most often used estimate of large earthquake magnitudes.[2] The symbol for the moment magnitude scale is $ M_\mathrm{w} $, 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.


  1. Hanks, Thomas C.; Kanamori, Hiroo (05/1979). "Moment magnitude scale". Journal of Geophysical Research 84 (B5): 2348–2350. doi:10.1029/JB084iB05p02348. Retrieved on 2007-10-06.</cite>  </li>
  2. Boyle, Alan (May 12, 2008). "Quakes by the numbers". MSNBC. Retrieved on 2008-05-12. “That original scale has been tweaked through the decades, and nowadays calling it the "Richter scale" is an anachronism. The most common measure is known simply as the moment magnitude scale.” </li></ol>
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