Assuming earthquakes as shear rupture, Aki (1966) defined seismic moment as
$$M_0=\mu*\bar D*A$$
where \(\mu\) is the shear modulus or rigidity of rocks near the rupture area, \(\bar D\) is the average slip or displacement, and \(A\) is the rupture area. The metric system’s unit of \(M_0\) is Newton-meter.
Seismic moment is the most stable scale for measuring the size/strength of an earthquake. Unlike the Richter magnitude scale, the seismic moment does not saturate with increasing magnitude and is used by Hanks and Kanamori (1979) to define the moment magnitude (\(M_w\)) scale.
Seismic moment rate is defined as
$$\dot {M_0}=\mu*\bar S*A$$
where \(\bar S\) is the average slip rate for the fault.