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Nonextensive models for earthquakes.

R Silva¹, G S França, C S Vilar

¹Observatório Nacional, Rua Gal. José Cristino 77, 20921-400 Rio de Janeiro, Rio de Janeiro, Brazil. rsilva@uern.br,rsilva@on.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 12, 2006

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This study revises the fragment-asperity model using Tsallis statistics, yielding a new earthquake energy-distribution function (EDF) that differs from prior work. The revised EDF shows significant differences in energy density, despite similar nonextensive parameters.

Area of Science:

Geophysics
Statistical Physics

Background:

The fragment-asperity interaction model is crucial for understanding earthquake dynamics.
Tsallis nonextensive statistics offers a framework for analyzing complex systems like earthquakes.

Purpose of the Study:

To revisit and refine the fragment-asperity interaction model.
To introduce a new scale relating earthquake energy and fragment size.
To derive and validate a novel energy-distribution function (EDF).

Main Methods:

Application of Tsallis nonextensive statistics with a modified definition of mean values.
Introduction of a scale factor (epsilon proportional to r3) linking earthquake energy and fragment size.
Validation of the derived EDF using seismic data from NEIC and Revista Brasileira de Geofísica catalogs.

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Main Results:

A new energy-distribution function (EDF) was deduced, differing significantly from previous models.
The nonextensive parameter (q) values were found to be similar across both models.
Physical quantities like energy density showed substantial differences (several orders of magnitude) between the models.

Conclusions:

The revised fragment-asperity model provides a distinct EDF with implications for earthquake energy calculations.
While the nonextensive parameter remains consistent, other physical properties are sensitive to the model's specifics.
Further research is needed to fully explore the implications of the new EDF for seismology.