The **moment magnitude scale** (abbreviated as **MMS**; denoted as **M _{W}** or

**M**) is used by seismologists to measure the size of earthquakes in terms of the energy released.

## Contents

- The Richter scale a former measure of earthquake magnitude
- The modified Richter scale
- Correcting weaknesses of the modified Richter scale
- Recent research
- Definition
- Comparative energy released by two earthquakes
- Radiated seismic energy
- Nuclear explosions
- Comparison with Richter scale
- References

The scale was developed in the 1970s to succeed the 1930s-era Richter magnitude scale (M_{L}). Even though the formulas are different, the new scale retains a similar continuum of magnitude values to that defined by the older one. As with the Richter magnitude scale, an increase of one step on this logarithmic scale corresponds to a 10^{1.5} (about 32) times increase in the amount of energy released, and an increase of two steps corresponds to a 10^{3} (1,000) times increase in energy. Thus, an earthquake of M_{W} of 7.0 releases about 32 times as much energy as one of 6.0 and 1,000 times that of 5.0.

The magnitude is based on the seismic 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.

Since January 2002, the MMS has been the scale used by the United States Geological Survey to calculate and report magnitudes for all modern large earthquakes.

Popular press reports of earthquake magnitude usually fail to distinguish between magnitude scales, and are often reported as "Richter magnitudes" when the reported magnitude is a moment magnitude (or a surface-wave or body-wave magnitude). Because the scales are intended to report the same results within their applicable conditions, the confusion is minor.

## The Richter scale: a former measure of earthquake magnitude

In 1935, Charles Richter and Beno Gutenberg developed the local magnitude ( _{L} scale was simple to use and corresponded well with the damage which was observed, it was extremely useful for engineering earthquake-resistant structures, and gained common acceptance.

## The modified Richter scale

The Richter scale was not effective for characterizing some classes of quakes. As a result, Beno Gutenberg expanded Richter's work to consider earthquakes detected at distant locations. For such large distances the higher frequency vibrations are attenuated and seismic surface waves (Rayleigh and Love waves) are dominated by waves with a period of 20 seconds (which corresponds to a wavelength of about 60 km). Their magnitude was assigned a surface wave magnitude scale (M_{S}). Gutenberg also combined compressional P-waves and the transverse S-waves (which he termed "body waves") to create a body-wave magnitude scale (M_{b}), measured for periods between 1 and 10 seconds. Ultimately Gutenberg and Richter collaborated to produce a combined scale which was able to estimate the energy released by an earthquake in terms of Gutenberg's surface wave magnitude scale (M_{S}).

## Correcting weaknesses of the modified Richter scale

The Richter Scale, as modified, was successfully applied to characterize localities. This enabled local building codes to establish standards for buildings which were earthquake resistant. However a series of quakes were poorly handled by the modified Richter scale. This series of "great earthquakes", included faults that broke along a line of up to 1000 km. Examples include the 1957 Andreanof Islands earthquake and the 1960 Chilean quake, both of which broke faults approaching 1000 km. The M_{S} scale was unable to characterize these "great earthquakes" accurately.

The difficulties with use of M_{S} in characterizing the quake resulted from the size of these earthquakes. Great quakes produced 20 s waves such that M_{S} was comparable to normal quakes, but also produced very long period waves (more than 200 s) which carried large amounts of energy. As a result, use of the modified Richter scale methodology to estimate earthquake energy was deficient at high energies.

In 1972, Keiiti Aki, a professor of Geophysics at the Massachusetts Institute of Technology, introduced elastic dislocation theory to improve understanding of the earthquake mechanism. This theory proposed that the energy release from a quake is proportional to the surface area that breaks free, the average distance that the fault is displaced, and the rigidity of the material adjacent to the fault. This is found to correlate well with the seismologic readings from long-period seismographs. Hence the moment magnitude scale (M_{W}) represented a major step forward in characterizing earthquakes.

## Recent research

Recent research related to the moment magnitude scale has included:

## Definition

The symbol for the moment magnitude scale is

where ^{−7} N⋅m). The constant values in the equation are chosen to achieve consistency with the magnitude values produced by earlier scales, such as the Local Magnitude and the Surface Wave magnitude.

## Comparative energy released by two earthquakes

As with the Richter scale, an increase of one step on this logarithmic scale corresponds to a 10^{1.5} ≈ 32 times increase in the amount of energy released, and an increase of two steps corresponds to a 10^{3} = 1000 times increase in energy. Thus, an earthquake of M_{W} of 7.0 contains 1000 times as much energy as one of 5.0 and about 32 times that of 6.0.

The following formula, obtained by solving the previous equation for

For example, an earthquake with a moment magnitude of 7.0 is 5.62 times greater than a quake with moment magnitude 6.5.

## 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

The seismic moment

Choy and Boatwright defined in 1995 the *energy magnitude*

where

## 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).

A rule of thumb equivalence from seismology used in the study of nuclear proliferation asserts that a one kiloton nuclear explosion creates a seismic signal with a magnitude of approximately 4.0. This in turn leads to the equation

where

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 released ends up being radiated as seismic waves. Therefore, a seismic efficiency needs to be chosen for the bomb that is being quoted in this comparison. Using the conventional specific energy of TNT (4.184 MJ/kg), the above formula implies that about 0.5% of the bomb's energy is converted into radiated seismic energy

## Comparison with Richter scale

The moment magnitude (

The concept of seismic moment was introduced in 1966, but it took 13 years before the

Moment magnitude is now the most common measure for medium to large earthquake magnitudes, but breaks down 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.

Magnitude scales differ from earthquake intensity, which is the perceptible shaking, and local damage 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, magnitude scales are used to estimate with one number the size of the quake.

The following table compares magnitudes towards the upper end of the Richter Scale for major Californian earthquakes.