Fractal hierarchies of magma transport in Hawaii and critical self- organization of tremor

A hierarchical model of magma transport in Hawaii is developed from the seismic records of deep (30-60 km) and intermediate-depth (5-15 km) harmonic tremor between January 1, 1962, and December 31, 1983. A tremor model of magma transport is developed from mass balances of percolation that are proportional to tremor durations. It gives reasonable magma fractions and residence times for a vertical drift velocity of 4 km yr^-1 and yields patterns of intermittency that are in accord with singularity analyses of the 22-year time series record. It is suggested that spatiotemporal universality extends from small to large scales in Hawaiian and other magmatic systems. The apparent universal scaling of frequencies may be more than 15 decades in time (1 s to about 60 m.y.) and 10 decades in length (0.1 mm to 10³ km). -from Authors