Moment magnitude scale

Moment magnitude scale

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Moment magnitude scale

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 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 Local Magnitude scale, M_L, 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.

Radiated seismic energy
Nuclear explosions
See also
External links
References
Sources

Radiated seismic energy

Potential energy is stored in the crust in the form of built-up stress. 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

Nuclear explosions

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).

Many academics refer to a 1 kt TNT explosion being roughly equivalent to a magnitude 4 earthquake (an often quoted rule of thumb in seismology), which in turn 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. As 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.