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We propose that the widely observed and universal Gutenberg-Richter relationis a mathematical consequence of the critical branching nature of earthquakeprocess in a brittle fracture environment. These arguments, though preliminary,are confirmed by recent investigations of the seismic moment distribution inglobal earthquake catalogs and by the results on the distribution in crystalsof dislocation avalanche sizes. We consider possible systematic and randomerrors in determining earthquake size, especially its seismic moment. Theseeffects increase the estimate of the parameter beta of the power-lawdistribution of earthquake sizes. In particular, we find that estimatedbeta-values may be inflated by 1-3% because relative moment uncertaintiesdecrease with increasing earthquake size. Moreover, earthquake clusteringgreatly influences the beta-parameter. If clusters (aftershock sequences) aretaken as the entity to be studied, then the exponent value for their sizedistribution would decrease by 5-10%. The complexity of any earthquake sourcealso inflates the estimated beta-value by at least 3-7%. The centroid depthdistribution also should influence the beta-value, an approximate calculationsuggests that the exponent value may be increased by 2-6%. Taking all theseeffects into account, we propose that the recently obtained beta-value of 0.63could be reduced to about 0.52--0.56: near the universal constant value (1/2)predicted by theoretical arguments. We also consider possible consequences ofthe universal beta-value and its relevance for theoretical and practicalunderstanding of earthquake occurrence in various tectonic and Earth structureenvironments. Using comparative crystal deformation results may help usunderstand the generation of seismic tremors and slow earthquakes andilluminate the transition from brittle fracture to plastic flow.

Earthquake Size Distribution: Power-Law with Exponent Beta = 1/2?