# Seismic moment

Seismic moment is a quantity used by seismologists to measure the size of an earthquake. The scalar seismic moment ${\displaystyle M_{0}}$ is defined by the equation ${\displaystyle M_{0}=\mu AD}$, where

• ${\displaystyle \mu }$ is the shear modulus of the rocks involved in the earthquake (in Pa, or N/m2)
• ${\displaystyle A}$ is the area of the rupture along the geologic fault where the earthquake occurred (in m2), and
• ${\displaystyle D}$ is the average slip (displacement offset between the two sides of the fault) on ${\displaystyle A}$ (in m).

${\displaystyle M_{0}}$ thus has dimensions of torque, measured in Newton meters. The connection between seismic moment and a torque is natural in the representation of seismic sources as a pair of force couples. Seismic moment is not a measure of energy. The relations between seismic moment, potential energy drop and radiated energy are indirect and approximative.

The seismic moment of an earthquake is typically estimated using whatever information is available to constrain its factors. For modern earthquakes, moment is usually estimated from ground motion recordings of earthquakes known as seismograms. For earthquakes that occurred in times before modern instruments were available, moment may be estimated from geologic estimates of the size of the fault rupture and the slip.

Seismic moment is the basis of the moment magnitude scale introduced by Hiroo Kanamori, which is often used to compare the size of different earthquakes and is especially useful for comparing the sizes of large (great) earthquakes.

The seismic moment is not restricted to earthquakes. For a more general seismic source described by a seismic moment tensor ${\displaystyle M_{ij}}$ (a symmetric tensor, but not necessarily a double couple tensor), the seismic moment is

${\displaystyle M_{0}={\frac {1}{\sqrt {2}}}(M_{ij}^{2})^{1/2}}$