David Bowers and John A. Hudson
Defining the scalar moment of a seismic source with a general moment tensor
Bulletin of the Seismological Society of America (October 1999), 89(5):1390-1394

Abstract:
We compare several published definitions of the scalar moment M ₀ , a measure of the size of a seismic disturbance derived from the second-order seismic moment tensor M (with eigenvalues m ₁ > or = m ₃ > or = m ₂ ). While arbitrary, a useful definition is in terms of a total moment, M ^T ₀ = 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 ^T ₀ , 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 al. (1989).