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. Hiroo Kanamori (金森 博雄 Kanamori Hiroo; October 17, 1936 — is a Japanese Seismologist who has made fundamental contributions The Richter magnitude scale, or more correctly local magnitude M L scale assigns a single number to quantify the amount of seismic energy released Seismology (from Greek grc σεισμός seismos, "earthquake" and grc -λογία -logia) is the scientific study of Earthquakes An earthquake is the result of a sudden release of energy in the Earth 's crust that creates Seismic waves Earthquakes are recorded with a Seismometer [1] The moment magnitude Mw 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 M0 is the seismic moment. In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units Seismic moment is a quantity used by Earthquake Seismologists to measure the size of an earthquake 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. ISO 31-0 is the introductory part of international standard ISO 31 on quantities and units.

An increase of 1 step on this logarithmic scale corresponds to a 101. Definition and base Logarithmic scales are either defined for ratios of the underlying quantity or one has to agree to measure 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, ML, commonly called the Richter magnitude scale. The Richter magnitude scale, or more correctly local magnitude M L scale assigns a single number to quantify the amount of seismic energy released 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 Mw, with the subscript w meaning mechanical work accomplished. In Physics, mechanical work is the amount of Energy transferred by a Force. The United States Geological Survey does not use this scale for earthquakes with a magnitude of less than 3. The United States Geological Survey ( USGS) is a scientific agency of the United States government. An earthquake is the result of a sudden release of energy in the Earth 's crust that creates Seismic waves Earthquakes are recorded with a Seismometer 5.

## Contents

Potential energy is stored in the crust in the form of built-up stress. Stress is a measure of the average amount of Force exerted per unit Area. During an earthquake, this stored energy is transformed and results in

• cracks and deformation in rocks,
• heat,

The seismic moment M0 is a measure of the total amount of energy that is transformed during an earthquake. Only a small fraction of the seismic moment M0 is converted into radiated seismic energy Es, which is what seismographs register. Seismometers (from Greek Seism - "the shakes" - and Metro - "I measure" are instruments that measure and record motions of the ground including 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). A nuclear weapon is an explosive device that derives its destructive force from Nuclear reactions either fission or a combination of fission and fusion. Units of mass There are three similar units of Mass called the ton: Long ton (simply ton in countries such as the United Trinitrotoluene ( TNT) is a Chemical compound with the formula C6H2(NO23CH3

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

$M_\mathrm{n} = {2 \over 3}\log_{10} \frac{m_{\mathrm{TNT}}}{\mbox{kg}} = {2 \over 3}\log_{10} \frac{m_{\mathrm{TNT}}}{\mbox{kt}} + 4 = {2 \over 3}\log_{10} \frac{m_{\mathrm{TNT}}}{\mbox{Mt}} + 6$. A rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation

where mTNT 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. A convention is a set of agreed, stipulated or generally accepted Standards norms social norms or criteria, often taking the form of Specific energy is defined as the Energy per unit Mass: J/kg or in basic SI units m2/s2 184 MJ/kg), the above formula implies the assumption that about 0. 5% of the bomb's energy is converted into radiated seismic energy Es. For real underground nuclear tests, the actual seismic efficiency achieved varies significantly and depends on the site and design parameters of the test.