FIGURE 4. Distance versus earthquake linear density for a time-randomized catalogue.

Distances are measured between ten random earthquakes from the mainshock data set and random catalogue earthquakes, producing 346 earthquake pairs. Unlike the aftershock data, there is no systematic decay of density with distance. The sum of squared residuals is lowest when the data are fitted with the relationship that linear earthquake density is constant (solid line), as opposed to linear density equals r (dashed line), which would correspond to hypocentres being located randomly in two dimensions, or r² (dashed-dotted line), which would correspond to random locations in a volume (see equation (3)). The fits are done from 0 to 100 km, which completely covers the range of aftershock data analysed in this paper.