Statistical self-similarity of magmatism and volcanism

Magmatism and volcanism exhibit spatial and temporal clustering on a wide range of scales. Using the spatial pair-correlation function, the number of pairs of magmatic or volcanic events whose separation is between r-1/2Δr and r+1/2Δr per unit area, we quantify the spatial clustering of magmatism and volcanism in several data sets. Statistically self-similar clustering characterized by power law spatial pair-correlation functions is observed. The temporal pair-correlation function is used to identify self-similar temporal clustering of magmatism and volcanism in the Radiometric Age Data Bank of 11,986 dated intrusive and extrusive rocks in the North American Cordillera. The clustering of magmatism and volcanism in space and time in this data set is found to be statistically self-similar and identical to those of distributed seismicity. The frequency-size distributions of eruption volume and areal extent of basaltic flows are also found to be self-similar with power laws analogous to the Gutenburg-Richter distribution for earthquakes. In an attempt to understand the origin of statistical self-similarity in magmatism and volcanism we present one end-member model in which the ascent of magma through a disordered crust of variable macroscopic permeability is modeled with a cellular-automaton model to create a distribution of magma supply regions which erupt with equal probability per unit time. The model exhibits statistical self-similarity similar to that observed in the real data sets.