Defining the scalar moment of a seismic source with a general moment tensor

We compare several published definitions of the scalar moment Mo, a measure of the size of a seismic disturbance derived from the second-order seismic moment tensor M (with eigenvalues m(1) greater than or equal to m(3) greater than or equal to m(2)). While arbitrary, a useful definition is in terms of a total moment, M-0(T) = M-I + M-D, where M-I = \M\, with M = (m(1) + m(2) + m(3))/3, is the isotropic moment, and M-D = max(\m(j) - M\; j = 1, 2, 3), is the deviatoric moment. This definition is consistent with other definitions of M-0 if M is a double couple. This definition also gives physically appealing and simple results for the explosion and crack sources. Furthermore, our definitions of M-0(T), M-I and M-D are in accord with the parameterization of the moment tensor into a deviatoric part (represented by T which lies in [-1,1]) and a volumetric part (represented by k which lies in [-1,1]) proposed by Hudson et nl. (1989).