<p>Measurements of the fractal dimensions and entropy of the spatial distribution of seismic sources are seen to correlate with measurements of the Gutenberg–Richter <i>b</i>-value, but, although this parameter is related to the fractal dimension of the rupture areas distribution and to the entropy of the magnitude distribution, there is no specific mechanism to relate it to epi- or hypocentral source distributions. A plausible relation between the <i>b</i>-value and the spatial source distributions is proposed and tested through Monte Carlo simulation on a cellular automaton model based on the premise that the probability of an earthquake occurring at a particular point in space is proportional to the stress at that point. Results showing the appropriate correlations are robust and not critically dependent on the values of the parameters of the model.</p>

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A relation between the G-R b-value and spatial fractal dimensions and entropy

  • F. A. Nava

摘要

Measurements of the fractal dimensions and entropy of the spatial distribution of seismic sources are seen to correlate with measurements of the Gutenberg–Richter b-value, but, although this parameter is related to the fractal dimension of the rupture areas distribution and to the entropy of the magnitude distribution, there is no specific mechanism to relate it to epi- or hypocentral source distributions. A plausible relation between the b-value and the spatial source distributions is proposed and tested through Monte Carlo simulation on a cellular automaton model based on the premise that the probability of an earthquake occurring at a particular point in space is proportional to the stress at that point. Results showing the appropriate correlations are robust and not critically dependent on the values of the parameters of the model.