Introduction to nonlinear geophysics, chaos and fractals: Transitions characterizing seismic and volcanic events need other methods when linear physics is not adapted to represent the processes; specific development on the Gutenberg-Richter law | INSTITUT DE PHYSIQUE DU GLOBE DE PARIS

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  Introduction to nonlinear geophysics, chaos and fractals: Transitions characterizing seismic and volcanic events need other methods when linear physics is not adapted to represent the processes; specific development on the Gutenberg-Richter law

Type de publication:

Journal Article

Auteurs:

Sailhac, P.

Source:

Cahiers du Centre Européen de Géodynamique et de Séismologie, Volume 14, p.121-161 (1997)

Numéro d'appel:

PUB

Mots-clés:

entropy, fragility map, Géomagnétisme ; Fourier transform, geophysical applications, multifractal analysis, scaling laws, scaling rules, seismicity, tools for chaos, UMR 7577

Résumé:

A definition of the chaos in dynamical systems and the limitations of the Fourier transform are given. Following is an introduction to useful tools for chaos and self-organised systems (Lyapunov Exponents, Poincaré Section, Return Map, Time Delay Embedding, Fractal Dimension, Hölder Exponents and Multifractal Analysis) with exemples of Geophysical applications. Then the approach is applied specifically to seismicity : scaling laws, scaling rules in rock fracture, information entropy linked with seismic events, and multifractal spectra ; possible implications of multifractal analysis for fragility maps and earthquake localisation forecasting is given