The fits that were obtained for both global earthquakes and those of Southern California both indicated peaks at about M 1.1. In thermodynamics if two bodies had the same peak in their radiation spectrum we would consider them to be at the same temperature and it they were in contact with each other we would conclude that they were in thermal equilibrium. So we need to consider the possibility that the earthquake faults are in some kind of thermal equilibrium. This would imply that the faults can exchange energy in some manner.
With respect to the unexpected deviations from the distributions for Southern California it may also be that there is some coupling among the faults or the statistics may be affected to some extent by absorption by the medium. The seismologists make assumptions about the nature of the location of the earthquake, that of the location of the seismograph and the path connecting them. In optics the medium can absorb some of the radiation and we think of it as a filter. The same may be true with the Earth acting as a filter. It is less likely that a discrete spectrum is present in the earthquake data.