Moment magnitude scale

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 $M_{\mathrm {w} }$ 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.

An increase of 1 step on this logarithmic scale corresponds to a 10^1.5 = 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 $E_{\mathrm {s} }$.

The seismic moment $M_{0}$ is a measure of the total amount of energy that is transformed during an earthquake. Only a small fraction of the seismic moment $M_{0}$ is converted into radiated seismic energy $E_{\mathrm {s} }$, which is what seismographs register. Using the estimate

$E_{\mathrm {s} }=M_{0}\cdot 10^{-4.8}=M_{0}\cdot 1.6\times 10^{-5}$

Choy and Boatwright defined in 1995 the energy magnitude

$M_{\mathrm {e} }={2 \over 3}\log _{10}{\frac {E_{\mathrm {s} }}{\mathrm {N} \cdot \mathrm {m} }}-2.9$

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

$M_{\mathrm {n} }={2 \over 3}\log _{10}{\frac {m_{\mathrm {TNT} }}{\mbox{kg}}}={2 \over 3}\log _{10}{\frac {m_{\mathrm {TNT} }}{\mbox{kt}}}+4={2 \over 3}\log _{10}{\frac {m_{\mathrm {TNT} }}{\mbox{Mt}}}+6$.

where $m_{\mathrm {TNT} }$ is the mass of the explosive TNT that is quoted for comparison.

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 $E_{\mathrm {s} }$. 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

• USGS: What is moment magnitude?

References

• Hanks TC, Kanamori H (1979). "A moment magnitude scale". Journal of Geophysical Research. 84 (B5): 2348–50.
• Choy GL, Boatwright JL (1995). "Global patterns of radiated seismic energy and apparent stress". Journal of Geophysical Research. 100 (B9): 18205–28.