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Geophysical Data Analysis:

Discrete Inverse Theor y

Academic Press is an imprint of Elsevier

225 Wyman Street, Waltham, MA 02451, USA

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Third edition 2012

Copyright

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Elsevier Inc. 2012, 1989, 1984. All rights reserved.

No part of this publication may be reproduced, stored in a retrieval system or transmitted in

any form or by any means electronic, mechanical, photocopying, recording, or otherwise

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No responsibility is assumed by the publisher for any injury and/or damage to persons or

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herein. Because of rapid advances in the medical sciences, in particular, independent

verification of diagnoses and drug dosages should be made.

Library of Congress Cataloging-in-Publication Data

Menke, William.

Geophysical data analysis : discrete inverse theory / William Menke. – MatLab ed., 3rd ed.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-12-397160-9 (hardback)

1. Geophysics–Measurement. 2. Oceanography–Measurement. 3. Inverse problems

(Differential equations)–Numerical solutions. I. Title.

QC802.A1M46 2012

551–dc23

2012000457

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

For information on all Academic Press publications

visit our web site at store.elsevier.com

Printed and bound in China

1213141516 10987654321

ISBN: 978-0-12-397160-9

Preface

For now we see through a glass, darkly, but then ...

Paul of Tarsus

Every researcher in the applied sciences who has analyzed data has practiced

inverse theory. Inverse theory is simply the set of methods used to extract useful

inferences about the world from physical measurements. The fitting of a straight

line to data involves a simple application of inverse theory. Tomography,

popularized by the physician’s CT and MRI scanners, uses it on a more sophis-

ticated level.

The study of inverse theory, however, is more than the cataloging of

methods of data analysis. It is an attempt to organize these techniques, to bring

out their underlying similarities and pin down their differences, and to deal with

the fundamental question of the limits of information that can be gleaned from

any given data set.

Physical properties fall into two general classes: those that can be described

by disc rete parameters (e.g., the mass of the earth or the position of the atoms in

a protein molecu le) and those that must be described by continuous functions

(e.g., temperature over the face of the earth or electri c field intensity in a capac-

itor). Inverse theory employs different mathematical techniques for these two

classes of parameters: the theo ry of matrix equations for discrete parameters

and the theory of integral equations for continuous functions.

Being introductory in nature, this book deals mainly with “discrete inverse

theory,” that is, the part of the theory concerned with parameters that either are

truly discrete or can be adequately approximated as discrete. By adhering to

these limitations, inverse theory can be presented on a level that is accessible

to most first-ye ar graduate students and many college seniors in the applied

sciences. The only mathematics that is presumed is a working knowledge of

the calculus and linear algebra and some familiarity with general concepts from

probability theory and statistics.

Nevertheless, the treatment in this book is in no sense simplified. Realistic

examples, drawn from the scientific literature, are used to illustrate the various

techniques. Since in practice the solutions to most inverse problems require sub-

stantial computational effort, attention is given to how realistic problems can be

solved.

vii

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