[3] It has become the standard scale used by seismological authorities like the United States Geological Survey[4] for reporting large earthquakes (typically M > 4), replacing the local magnitude (ML ) and surface-wave magnitude (Ms ) scales.
[6] Charles F. Richter then worked out how to adjust for epicentral distance (and some other factors) so that the logarithm of the amplitude of the seismograph trace could be used as a measure of "magnitude" that was internally consistent and corresponded roughly with estimates of an earthquake's energy.
An early step was to determine how different systems of forces might generate seismic waves equivalent to those observed from earthquakes.
[16] A double couple can be viewed as "equivalent to a pressure and tension acting simultaneously at right angles".
[citation needed] In 1923 Hiroshi Nakano showed that certain aspects of seismic waves could be explained in terms of a double couple model.
[20] In principle these models could be distinguished by differences in the radiation patterns of their S waves, but the quality of the observational data was inadequate for that.
[21] The debate ended when Maruyama (1963), Haskell (1964), and Burridge and Knopoff (1964) showed that if earthquake ruptures are modeled as dislocations the pattern of seismic radiation can always be matched with an equivalent pattern derived from a double couple,[citation needed] but not from a single couple.
[22] This was confirmed as better and more plentiful data coming from the World-Wide Standard Seismograph Network (WWSSN) permitted closer analysis of seismic waves.
[24] While slippage along a fault was theorized as the cause of earthquakes (other theories included movement of magma, or sudden changes of volume due to phase changes[25]), observing this at depth was not possible, and understanding what could be learned about the source mechanism from the seismic waves requires an understanding of the source mechanism.
[26] More generally applied to problems of stress in materials,[27] an extension by F. Nabarro in 1951 was recognized by the Russian geophysicist A. V. Vvedenskaya as applicable to earthquake faulting.
[30] Numerous other researchers worked out other details,[31] culminating in a general solution in 1964 by Burridge and Knopoff, which established the relationship between double couples and the theory of elastic rebound, and provided the basis for relating an earthquake's physical features to seismic moment.
[32] Seismic moment – symbol M0 – is a measure of the fault slip and area involved in the earthquake.
[33] (More precisely, it is the scalar magnitude of the second-order moment tensor that describes the force components of the double-couple.
[34]) Seismic moment is measured in units of Newton meters (N·m) or Joules, or (in the older CGS system) dyne-centimeters (dyn-cm).
First, he used data from distant stations of the WWSSN to analyze long-period (200 second) seismic waves (wavelength of about 1,000 kilometers) to determine the magnitude of the earthquake's equivalent double couple.
[38] In particular, he derived an equation that relates an earthquake's seismic moment to its physical parameters: with μ being the rigidity (or resistance to moving) of a fault with a surface area of S over an average dislocation (distance) of ū.
[40] Seismic moment is a measure of the work (more precisely, the torque) that results in inelastic (permanent) displacement or distortion of the Earth's crust.
However, the power or potential destructiveness of an earthquake depends (among other factors) on how much of the total energy is converted into seismic waves.
[42] This is typically 10% or less of the total energy, the rest being expended in fracturing rock or overcoming friction (generating heat).
[46] Most earthquake magnitude scales suffered from the fact that they only provided a comparison of the amplitude of waves produced at a standard distance and frequency band; it was difficult to relate these magnitudes to a physical property of the earthquake.
Unfortunately, the duration of many very large earthquakes was longer than 20 seconds, the period of the surface waves used in the measurement of Ms .
Moment magnitude is now the most common measure of earthquake size for medium to large earthquake magnitudes,[48][scientific citation needed] but in practice, seismic moment (M0 ), the seismological parameter it is based on, is not measured routinely 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,[citation needed] which includes the great majority of quakes.
[49][4] The symbol for the moment magnitude scale is Mw , with the subscript "w" meaning mechanical work accomplished.
is the average of the absolute shear stresses on the fault before and after the earthquake (e.g., equation 3 of Venkataraman & Kanamori 2004) and
Currently, there is no technology to measure absolute stresses at all depths of interest, nor method to estimate it accurately, and
can now be computed more directly and robustly than in the 1970s, introducing a separate magnitude associated to radiated energy was warranted.
Under these assumptions, the following formula, obtained by solving for M0 the equation defining Mw , allows one to assess the ratio
To make the significance of the magnitude value plausible, the seismic energy released during the earthquake is sometimes compared to the effect of the conventional chemical explosive TNT.
[56] Various ways of determining moment magnitude have been developed, and several subtypes of the Mw scale can be used to indicate the basis used.