Spatial Analysis of Volcanoes at Convergent Margins on Earth

One of the most obvious patterns seen on the surface of the terrestrial planets is the distribution of volcanoes. On Earth, most volcanoes are distributed in volcanic “arcs” that signal the primary relationship between subduction and volcanism. The distributions of major composite volcanoes in volcanic arcs are thought to reflect the primary magmatic pathways from source to surface. Understanding these patterns therefore may allow fundamental controls on the organization of magmatic plumbing in arcs to be identified. Using a control dataset from the Central Volcanic Zone of the Andes (de Silva and Francis, 1991; Springer-Verlag) we have examined several popular approaches to spatial analysis of volcano distribution in several volcanic arcs (Aleutian, Alaskan, Central American, Northern and Southern volcanic zones of the Andes). Restricting our analysis to major volcanoes of similar age, we find that while clustering is visually obvious in many volcanic arcs it has been rejected as a primary signal by previous analytical efforts (e.g. Bremont d'Ars et al (1995)). We show that the fractal box or grid counting method used previously does not detect clusters and statistical methods such as the Kernel Density Analysis or Single-link Cluster Analysis are better suited for cluster detection. Utilizing both ARC GIS and Matlab to conduct density analyses in combination with statistical software SPlus for the appropriate hypothesis testing methods such as the pooled variance t-test, the Welch Modified two sample t-test, and the f-test we find evidence of clustering in four volcanic arcs whose crustal thickness is greater than or equal to 40 kilometres (Central America, CVZ, NVZ, SVZ). We suggest that clustering is the surface manifestation of upper crustal diffusion of primary magmatic pathways, which in other places manifests as a single volcano. The inter-cluster distance is a thus reflection of primary magmatic pathways and thus equivalent to inter-volcano distance. With this recognition in hand a more realistic analysis of volcano-spacing has been undertaken. We find a weak correlation between median volcano/cluster distance and crustal thickness when the crust is no thicker than 40 kilometres. At values of 40 kilometres and greater, there is instead a strong inverse correlation between crustal thickness and median spacing. With p-values all less than 0.05 and a 95% confidence interval, the two-sided two-sample t-tests show that there is a significant difference between the mean volcano/cluster distance for the CVZ and the mean distance for all other arc systems implicating a strong influence of the over thickened (70 to 80 km) crust in that region.