Spatial distribution of earthquakes: the four-point moment function

The four-point moment function of the spatial distribution of shallow earthquake hypocentres is studied for the Central California (USGS) catalogue. We consider the numbers of hypocentre quadruplets which have a maximum hypocentre separation less than certain limits. Each of these numbers is proportional to the reciprocal of the volume of the tetrahedron formed by the lines connecting the four points. There is some evidence that for a catalogue of long time duration, this moment is independent of the form (or maximum dimension) of the tetrahedron once the volume is fixed. The results seem to rule out the conventional model of earthquake hypocentres occurring on a single isolated plane or on several planes. The study of four-point and lower-order moments provides a numerical basis for the comparison of different models of fault geometries.