Moment magnitude scale
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The moment magnitude scale was introduced in 1979 by Tom Hanks and Hiroo Kanamori as a successor to the Richter scale and is used by seismologists to compare the energy released by earthquakes. The moment magnitude [M_\mathrm] is a dimensionless number defined by
- [M_\mathrm = \left(\log_ \frac\cdot \mathrm} - 9.1\right) = \left(\log_ \frac\cdot \mathrm} - 16.1\right),]
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 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.
Comparison with radiated seismic energy
Potential energy is stored in the crust in the form of built-up strain. During an earthquake, this stored energy is transformed and results in
- cracks and deformation in rocks,
- heat,
- radiated seismic energy [E_\mathrm].
- [E_\mathrm = M_0 \cdot 10^ = M_0 \cdot 1.6\times 10^]
- [M_\mathrm = \log_ \frac}\cdot \mathrm} - 2.9]
Comparison with nuclear detonations
The energy released by nuclear weapons is traditionally expressed in terms of the energy stored in a kiloton or megaton of the conventional explosive trinitrotoluene (TNT). The often quoted rule of thumb that a 1 kt TNT explosion is roughly equivalent to a magnitude 4 earthquake leads to the equation
- [M_\mathrm = \log_ \frac}}} = \log_ \frac}}} + 4 = \log_ \frac}}} + 6].
Such comparison figures are not very meaningful. Like with earthquakes, during an underground explosion of a nuclear weapon, only a small fraction of the total amount of energy transformed ends up being radiated as seismic waves. Therefore a seismic efficiency has to be chosen for a bomb that is quoted as a comparison. Using the conventional specific energy of TNT (4.184 MJ/kg), the above formula implies the assumption that about 0.5% of the bomb's energy is converted into radiated seismic energy [E_\mathrm]. For real underground nuclear tests, the actual seismic efficiency achieved varies significantly and depends on the site and design parameters of the test.
See also
- Geophysics
- List of earthquakes
- Other seismic scales
External links
References
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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Modern scales | ||||||||||||||||
| Intensity scales | ||||||||||||||||
| European Macroseismic Scale (EMS) | INQUA | Medvedev-Sponheuer-Karnik (MSK) | Modified Mercalli (MM) | Shindo | ||||||||||||||||
| Magnitude scales | ||||||||||||||||
| Local magnitude (Richter scale) | Moment magnitude | ||||||||||||||||
| Historical scales | ||||||||||||||||
| Mercalli-Cancani-Sieberg (MCS) | Mercalli-Wood-Neuman (MWN) | Omori | Rossi-Forel | ||||||||||||||||
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