Moment magnitude ($M_w$)

A logarithmic measure of earthquake size based on seismic moment. A commonly used SI relation is $M_w=\frac{2}{3}[{\log }_{10}(M_0/(\mathrm{N}\mathrm{m}))-9.1]$. Because seismic moment integrates fault slip over the fault plane and includes the shear modulus, a peak slip value cannot replace the area integral.