Earthquake size distribution: power-law with exponent beta = 1/2 ?

Yan Y. Kagan

Published 2010, SCEC Contribution #1418

We propose that the widely observed and universal Gutenberg-Richter relation is a mathematical consequence of the critical branching nature of earthquake process in a brittle fracture environment. These arguments, though preliminary, are confirmed by recent investigations of the seismic moment distribution in global earthquake catalogs and by the results on the distribution in crystals of dislocation avalanche sizes. We consider possible systematic and random errors in determining earthquake size, especially its seismic moment. These effects increase the estimate of the parameter beta of the power-law distribution of earthquake sizes. In particular, we find that estimated beta-values may be inflated by 1-3% because relative moment uncertainties decrease with increasing earthquake size. Moreover, earthquake clustering greatly influences the beta-parameter. If clusters (aftershock sequences) are taken as the entity to be studied, then the exponent value for their size distribution would decrease by 5-10%. The complexity of any earthquake source also inflates the estimated beta-value by at least 3-7%. The centroid depth distribution also should influence the beta-value, an approximate calculation suggests that the exponent value may be increased by 2-6%. Taking all these effects into account, we propose that the recently obtained beta-value of 0.63 could be reduced to about 0.52--0.56: near the universal constant value (1/2) predicted by theoretical arguments. We also consider possible consequences of the universal beta-value and its relevance for theoretical and practical understanding of earthquake occurrence in various tectonic and Earth structure environments. Using comparative crystal deformation results may help us understand the generation of seismic tremors and slow earthquakes and illuminate the transition from brittle fracture to plastic flow.

Key Words
power law, seismic moment, magnitude, Gutenberg-Richter relation, plastic flow, plastic deformation, brittle deformation, equations, fracturing, deformation, depth, aftershocks, size distribution, errors, transition zones, mathematical methods, focus, catalogs, earthquakes, uncertainty

Kagan, Y. Y. (2010). Earthquake size distribution: power-law with exponent beta = 1/2 ?. Tectonophysics, 490( 1-2), 103-114. doi: 10.1016/j.tecto.2010.04.034.