Inverse Problems Basics, Theory and Applications in Geophysics
The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract
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Mathias Richter
Inverse Problems Basics, Theory and Applications in Geophysics
Lecture Notes in Geosystems Mathematics and Computing
Series editors W. Freeden, Kaiserslautern Z. Nashed, Orlando O. Scherzer, Vienna
More information about this series at http://www.springer.com/series/15481
Mathias Richter
Inverse Problems Basics, Theory and Applications in Geophysics
Mathias Richter FakultRat fRur Elektrotechnik und Informationstechnik UniversitRat der Bundeswehr MRunchen Neubiberg, Germany
Lecture Notes in Geosystems Mathematics and Computing ISBN 978-3-319-48383-2 ISBN 978-3-319-48384-9 (eBook) DOI 10.1007/978-3-319-48384-9 Library of Congress Control Number: 2016960201 © Springer International Publishing AG 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this 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 free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser (www.birkhauser-science.com) The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
The term “inverse problem” has no acknowledged mathematical definition; its meaning relies on notions from physics. One assumes that there is a known mapping T W U ! W; which models a physical law or a physical device. Here, U is a set of “causes” and W is a set of “effects.” The computation of an effect T.u/ for a given cause u is called a direct problem. Finding a cause u 2 U, which entails a given effect w 2 W, is called an inverse problem. Solving an inverse problem thus means to ask for the solution of an equation T.u/ D w. Maybe a certain effect w 2 W is desirable and one is looking for some u 2 U to produce it. An inverse problem of this kind is called a control problem. In the following, it will be assumed that an effect is actually observed and that its cause has to be found. An inverse problem of this kind is called an identification problem. It arises, when an interesting physical quantity is not directly amenable to measurements, but can
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