The
moment magnitude scale (abbreviated as
MMS; denoted as
M_\mathrm{w},
where
_{w} indicates work accomplished) is used by
seismologists to measure the size of
earthquakes in terms of the energy released. The
magnitude is based on the
moment of the
earthquake, which is equal to the rigidity of the Earth multiplied
by the average amount of slip on the
fault and the size of the area that slipped.
The scale was developed in the 1970s to succeed the 1930sera
Richter magnitude scale,
M_\mathrm{L}. Even though the formulae are different, the new scale
retains the familiar continuum of magnitude values defined by the
older one. The MMS is now the scale used to estimate magnitudes for
all modern large earthquakes by the
United States Geological
Survey.
Like the Richter scale, the MMS is
logarithmic; on the scale, an earthquake
one number higher is approximately thirtyone times (the square
root of 1,000) more powerful (for example, 7.0 is about thirtyone
times the power of 6.0).
Comparison to Richter scale
In 1935,
Charles Richter developed the
local magnitude (M_\mathrm{L}) scale
(also known as the Richter scale) with
the goal of quantifying mediumsized earthquakes (between magnitude
3.0 and 7.0) in Southern California. This scale was based on the responses of
seismographs and their distance from the
epicentre. Because of this, there is an upper limit on the highest
measurable magnitude; all large earthquakes will have a local
magnitude of around 7. The local magnitude's estimate of earthquake
size is also unreliable for measurements taken at a distance of
more than about 350 miles (600 km) from the earthquake's
epicenter.
The moment
magnitude (M_\mathrm{w}) scale was introduced in 1979 by Caltech
seismologists Thomas
C. Hanks and
Hiroo Kanamori to address these
shortcomings while maintaining consistency. Thus, for mediumsized
earthquakes, the moment magnitude values should be similar to
Richter values. That is, a magnitude 5.0 earthquake will be about a
5.0 on both scales. This scale was based on the physical properties
of the earthquake, specifically the
seismic moment (M_0). Unlike other scales,
the moment magnitude scale does not saturate at the upper end;
there is no upper limit to the possible measurable magnitudes.
However, this has the sideeffect of lowenergy earthquakes
clustering together.
Moment magnitude is now the most common estimate of both medium and
large earthquake magnitudes, but is rarely used for smaller quakes.
For example, the
United
States Geological Survey does not use this scale for
earthquakes with a magnitude of less than 3.5,
which is the great majority of quakes. For these smaller quakes,
other magnitude scales similar to the Richter scale are used.
Neither scale measures the
earthquake intensity, which is the
perceptible moving, shaking, and local damages experienced during a
quake. The shaking intensity at a given spot depends on many
factors, such as soil types, soil sublayers, depth, type of
displacement, and range from the epicenter (not counting the
complications of building engineering and architectural factors).
Rather, they are used to estimate only the total energy released by
the quake.
The following table compares magnitudes towards the upper end of
the Richter Scale for major Californian earthquakes.{{Table
type=class="wikitable sortable" 
hdrs=Date 
M_0\times10^{25} 
M_\mathrm{L} 
M_\mathrm{w} 
row1=19330311 2 6.3 6.2 
row2=19400519 30 6.4 7.0 
row3=19410701 0.9 5.9 6.0 
row4=19421021 9 6.5 6.6 
row5=19460315 1 6.3 6.0 
row6=19470410 7 6.2 6.5 
row7=19481204 1 6.5 6.0 
row8=19520721 200 7.2 7.5 
row9=19540319 4 6.2 6.4}}
Equation
The symbol for the moment magnitude scale is M_\mathrm{w}, with the
subscript _{w} meaning mechanical work accomplished. The moment
magnitude M_\mathrm{w} is a dimensionless number defined by
 M_\mathrm{w} = {2 \over 3}\log_{10}\left(M_0\right)  10.7
where M_0 is the seismic moment in
dyne centimetres (10^{7} Nm). The
constant values in the equation are chosen to achieve consistency
with the magnitude values produced by earlier scales, most
importantly the Local Moment (or "Richter") scale.
As with the Richter scale, 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
10^{3} = 1000 times increase in energy.
Radiated seismic energy
Potential energy is stored in the crust in the form of builtup
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\cdot10^{4.8}=M_0\cdot1.6\times10^{5}.
Choy and Boatwright defined in 1995 the energy
magnitude
 M_\mathrm{e} = {2\over
3}\log_{10}\left(E_\mathrm{s}\right)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{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.
See also
Notes
References
External links
