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Moment magnitude scale

The moment magnitude scale (a successor to the Richter scale), was introduced in 1979 by Tom Hanks and Hiroo Kanamori and is used by seismologists to compare the energy released by earthquakes. The moment magnitude $M W$ is defined by the equation

$M_W = {2 \over 3}(\log_{10} M_0 - 16.1),\,$

where $M 0$ is the seismic moment measured in dyne-centimeters (dyn·cm = 10⁻⁷N·m). In SI-units the formula is:

$M_W = {2 \over 3}(\log_{10} M_{0,\mathrm{SI}} - 9.1).\,$

The constants in the equation are chosen so that estimates of moment magnitude roughly agree with estimates using other scales such as 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. The USGS does not use this scale for earthquakes with a magnitude of less than 3.5.

Energy

The energy is 1/2000 times the moment:

$M_W = {2 \over 3}(\log_{10} E_{\mathrm{SI}} - 4.8).\,$

Using 1 Mt TNT = 4 PJ = J:

$M_W = {2 \over 3}(\log_{10} E_{\mathrm{Mt}} + 10.8).\,$

Using EMt (equivalent Mt) to compare ground shaking, we multiply the number of Mt by 1000/15, based on the observation that a 1 kton explosion is approximately equivalent to a magnitude 4 earthquake:

$M_W = {2 \over 3}(\log_{10} E_{\mathrm{EMt}} + 9).\,$

From this formula, one can determine that for each step on the magnitude scale, approximately 32 times as much energy is required.

Thus a magnitude 6.0 earthquake is approximately equivalent to a 1 Mton explosion, etc. (actually 1.01 Mton, see [1])

External links

Categories: Seismology

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03-10-2013 05:06:04
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