On seismological moments and magnitudes

My approach to seismology over the years has always been from the point of view of applied mathematics, as exemplified broadly by the work of the late Sir Harold Jeffreys and Professor K. E. Bullen. Both stresses the development of mathematics in the context of physical systems and of modeling, with an eye always on the side of inference. Seismology provided for them and still provides today the almost perfect paradigm; the problem is the resolution of the detailed consitution of the Earth and its geologically short-term dynamics. The latter part, includes, of course, seismic-risk estimation. The last 20 years have seen the construction of a brilliant theoretical  formalism for linear inverse problems in seismology , although, oddly enough, the current popular Earth models do not take account it. It is interesting too that the narrow opinion, prevelent a decade ago, to the effect that the traditional seismic body-wave approaches to structural definition were superceded, has been largely abandoned under today's banner of tomography-as though the Oldham-Jeffreys-Gutenbery inversions were not tomography.