E-Book Overview
This book deals with the application of fractal and nonlinear time-series analysis to seismicity and earthquakes within the framework of earthquake prediction research. Emphasis is on theoretical foundations as well as practical implementation and pitfalls to enable readers to conduct their own analyses. The theoretical parts include introductions to fractals and multifractals, the relation between fractal dimension and entropy, the Hurst phenomenon, basic ideas of low-dimensional chaotic dynamics and a roadmap of nonlinear time-series analysis. Practical implementation is discussed in each case and synthetic data sets are analyzed. Fractal methods are applied to landslide and seismicity patterns in space and time, nonlinear analysis is carried out for radon and strain data as well as earthquake intervals. Due to the comprehensive coverage of theoretical background and step-by-step applications, readers of all levels will benefit from this book.
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Lecture Notes in Earth Sciences E&tors: S Bhattacharj1, Brooklyn G M. Friedman, Brooklyn and Troy H. J. Neugebauer, Bonn A. Sedacher, Tueblngen and Yale
77
Christian Goltz
Fractal and Chaotic Properties of Earthquakes
Springer
Author Dr. Christian Goltz Klel University, Institute of Geophysics Leibnizstraf3e 15, D-24118 Klel, Germany
E-mail: goltz @physlk. uni-kiel, de
"For all Lecture Notes in Earth Sciences published till now please see final pages of the book"
Cataloging-ln-Pubhcatlon data applied for D i e D e u t s c h e B i b l i o t h e k - CIP-Einheitsaufnahme
Goltz, C h r i s t i a n : Fractal and chaotic properties o f earthquakes / Christian Goltz. Berlin ; H e i d e l b e r g ; N e w York ; Barcelona ; Budapest ; H o n g K o n g ; L o n d o n ; Milan ; Paris ; Singapore ; Tokyo : Springer, 1998 (Lecture notes in earth sciences ; 77) ISBN 3-540-64893-3
ISSN 0930-0317 ISBN 3-540-64893-3 Sprmger-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recatation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of thas publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9. 1965, m its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Sprmger-Verlag Berhn Heidelberg 1997 Printed in Germany Typesetting Camera ready by author SPIN" 10677150 32/3142-543210 - Pnnted on acid-free paper
Table of Contents
1.
Introduction
..............................................
1
P a r t I. E a r t h q u a k e s a n d F r a c t a l s .
Fractal Concepts 2.1 2.2
......................................... Introduction ........................................... Some I m p o r t a n t F r a c t a l D i m e n s i o n s . . . . . . . . . . . . . . . . . . . . . . 2.2.1 E u c l i d e a n a n d Similarity D i m e n s i o n . . . . . . . . . . . . . . . . 2.2.2 Hansdorff D i m e n s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 C a p a c i t y D i m e n s i o n Do . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 I n f o r m a t i o n D i m e n s i o n D1 . . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 C o r r e l a t i o n D i m e n s i o n D2 . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.6 Generalised D i m e n s i o n s a n d Multifractals . . . . . . . . . . . 2.2.7 D e v i a t i o n s from Ideal Fractals . . . . . . . . . . . . . . . . . . . . .
5 5 6 7 7 8 10 12 15 17
3.
A S