Spatial distribution of earthquakes: the three-point moment function

Summary. The three-point moment of the spatial distribution of shallow earthquakes is determined for one local and one world-wide catalogue. We compare the numbers of hypocentre triplets forming a particular triangle in a real catalogue and in a randomized (simulated Poissonian) catalogue, which has the same boundaries and depth distribution of hypocentres as the real catalogue. The ratio of these quantities seems fairly well approximated by the reciprocal of the surface area of the triangle. There is good evidence that this ratio is independent of the form of the triangle once the surface area is fixed. These results, similar to those from the two-point spatial moments, indicate lack of any intrinsic scale of distance or triples configuration for distances between hypocentres ranging from a few kilometres up to 1000 km. The results, together with similar ones from two- and four-point moment studies, place limits on the possible models of earthquake fault geometries.