Why is Gutenberg-Richter scaling applicable, why are b-values nearly constant?

Turcotte, D L - Department of Geology, University of California, One Shields Ave., Davis, CA
Shcherbakov, R - Center for Computational Science and Engineering, University of California, Davis, CA

The near universal applicability of the Gutenberg-Richter (GR) frequency-magnitude scaling of earthquakes is quite remarkable. Even more remarkable is the constancy of the scaling exponent, the b-value (also identified as a fractal dimension D = 2b). Many explanations for this scaling have been given but uncertainties remain. The first question is whether the scaling is applicable to earthquakes on a single fault or to an ensemble of faults. We will argue that the former is the case and it is the fractal distribution of faults that leads to GR scaling. An explanation for the fractal distribution of faults is comminution tectonics. All fractal (power-law) distributions in nature must have upper and lower bounds. The upper and lower bounds on GR scaling will be discussed. The applicability of GR scaling has important implications for probabilistic earthquake hazard assessment. Under many circumstances the probability of large earthquakes can be obtained from the occurrence of smaller earthquakes using GR scaling. The implication of this approach will be discussed. The question of the relationship of characteristic earthquakes to GR scaling will be considered. In terms of statistical physics, the background seismicity associated with GR scaling appears to play the role of thermal fluctuations. A major question is why the background seismicity does not change significantly during the earthquake cycle of characteristic earthquakes.

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