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This book contains state-of-the-art continuous wavelet analysis of one and more dimensional (geophysical) signals. Special attention is given to the reconaissance of specific properties of a signal. It also contains an extension of standard wavelet approximation to the application of so-called second generation wavelets for efficient representation of signals at various scales even on the sphere and more complex geometries. Furthermore, the book discusses the application of harmonic (spherical) wavelets in potential field analysis with emphasis on the gravity field of the Earth. Many examples are given for practical application of these tools; to support the text exercises and demonstrations are available on the Web.
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Lecture Notes in Earth Sciences Editors: S. Bhattacharj1, Brooklyn G. M. Friedman, Brooklyn and Troy H J Neugebauer, Bonn A Sedacher, Tueblngen and Yale
90
Roland Klees Roger Haagmans (Eds.)
Wavelets in the Geosciences With 102 Figures and 3 Tables
Springer
Editors Prof Dr. Roland Klees Roger Haagmans Delft Umverslty of Technology Delft Institute of Earth-Oriented Space Research (DEOS) Thijssewegl 1, 2629 JA Delft, The Netherlands
From January 1st, 2000 on, Mr. Haagmans wdl have the following address. Roger Haagmans Agricultural University of Norway Department of Mapping Sciences P.O Box 5034, 1432 As, Norway Cataloging-m-Pubhcation data applied for Die Deutsche Blbhothek - CIP-Emheltsaufnahme Wavelets 111the geosclences " with 3 tables / Roland Klees ; Roger Haagmans (ed) - Berlin, Heidelberg, New York, Barcelona ; Hong Kong, London, Milan ; Pans ; Singapore ; Tokyo Springer, 2000 (Lecture notes in earth sciences ; 90) ISBN 3-540-66951-5
"For all Lecture Notes in Earth Sciences published till now please see final pages of the book" ISSN 0930-0317 ISBN 3-540-66951-5 Springer-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 fights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or m any other way, and storage in data banks Duplication of this pubhcation or parts thereof ~s permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law © Sprxnger-Verlag Berlin Heidelberg 2000 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. m th~s publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore tree for general use. Typesetting: Camera ready by author Printed on acid-free paper SPIN: 10723309
32/3142-543210
Preface
This book is a collection of the Lecture Notes of the School of Wavelets in the Geosciences held in Delft (The Netherlands) from 4-9 October 1998. The objective of the school was to provide the necessary information for understanding the potential and limitations of the application of wavelets in the geosciences. Three lectures were given by outstanding scientists in the field of wavelet theory and applications: D r . Matthias Holschneider, Laboratoire de Geomagnetisme, Institut de Physique du Globe De Paris, France; Dr. Wire Sweldens, Mathematical Sciences Research Centre, Lucent Technologies, Bell Laboratories, Murray Hill, N J, U.S.A.; Prof. Dr. Willi Freeden, Geomathematics Group, Department of Mathematics, University of Kaiserslautern, Germany. The lectures have been supplemented by intensive computer exercises. The school has been very successful due to the engagement and the excellent presentations of the