Seismic Moment and Moment Magnitude

Seismic moment is a quantity that combines the area of the rupture and the amount of fault offset with a measure of the strength of the rocks - the shear modulus m.
Seismic Moment = m x (Rupture Area) x (Fault Offset)Usually we measure the moment directly from seismograms, since the size of the very long-period waves generated by an earthquake is proportional to the seismic moment. The physical units of seismic moment are force x distance, or dyne-cm.
For scientific studies, the moment is the measure we use since it has fewer limitations than the magnitudes, which often reach a maximum value (we call that magnitude saturation).
To compare seismic moment with magnitude, M_w , we use a formula constructed by Hiroo Kanamori of the California Institute of Seismology:
M_w = 2 / 3 * log(Seismic Moment) - 10.73where the units of the moment are in dyne-cm.