Statistical self-similarity of magmatism and volcanism

Magmatism and volcanism exhibit spatial and temporal clustering on a wide r ange of scales. Using the spatial pair-correlation function the number of p airs of magmatic or volcanic events whose separation is between r - 1/2 Del ta r and r + 1/2 Delta r 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 i s 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 Am erican Cordillera. The clustering of magmatism and volcanism in space and t ime in this data set is found to be statistically self-similar and identica l to those of distributed seismicity. The frequency-size distributions of e ruption volume and areal extent of basaltic flows are also found to be self -similar with power laws analogous to the Gutenburg-Richter distribution fo r earthquakes. In an attempt to understand the origin of statistical self-s imilarity in magmatism and volcanism we present one end-member model in whi ch the ascent of magma through a disordered crust of variable macroscopic p ermeability is modeled with a cellular-automaton model to create a distribu tion of magma supply regions which erupt with equal probability per unit ti me. The model exhibits statistical self-similarity similar to that observed in the real data sets.