The size-frequency distribution of many geological and geophysical variables, in relation to fractures, faulting and seismicity, is well described by a statistical distribution of the power law type which is characterized by its exponent. For earthquake magnitudes, the exponent is the well-known b-parameter of the Gutenberg-Richter scaling law. In this paper we:

  • provide a strict statistical derivation of the distribution law of earthquake magnitudes,
  • show that the maximum likelihood estimator of the b-parameter is unbiased,
  • demonstrate that the maximum likelihood estimator is invariant to the value chosen as the minimum magnitude threshold in so far as it is larger than the magnitude of completeness of the earthquake catalogue, and
  • provide a new estimator based on the minimization of the Kolmogorov-Smirnov statistic and provide a strategy for detecting and mapping the spatio-temporal variation of the b-parameter in seismic swarms.

The findings are illustrated with simulated data and a case study with real data.

Eulogio Pardo-Igúzquiza, Peter A. Dowd, Inference of the Gutenberg-Richter b-value: New insights and results, Tectonophysics, Volume 890,
2024, https://doi.org/10.1016/j.tecto.2024.230486

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