Geophysical Data Analysis: Discrete Inverse Theory, Volume 45

3rd Edition

MATLAB Edition

Authors: William Menke
Hardcover ISBN: 9780123971609
eBook ISBN: 9780123977847
Imprint: Academic Press
Published Date: 21st June 2012
Page Count: 330
Tax/VAT will be calculated at check-out
Compatible Not compatible
VitalSource PC, Mac, iPhone & iPad Amazon Kindle eReader
ePub & PDF Apple & PC desktop. Mobile devices (Apple & Android) Amazon Kindle eReader
Mobi Amazon Kindle eReader Anything else

Institutional Access

Table of Contents




Chapter 1. Describing Inverse Problems

1.1 Formulating Inverse Problems

1.2 The Linear Inverse Problem

1.3 Examples of Formulating Inverse Problems

1.4 Solutions to Inverse Problems

1.5 Problems


Chapter 2. Some Comments on Probability Theory

2.1 Noise and Random Variables

2.2 Correlated Data

2.3 Functions of Random Variables

2.4 Gaussian Probability Density Functions

2.5 Testing the Assumption of Gaussian Statistics

2.6 Conditional Probability Density Functions

2.7 Confidence Intervals

2.8 Computing Realizations of Random Variables

2.9 Problems


Chapter 3. Solution of the Linear, Gaussian Inverse Problem, Viewpoint 1: The Length Method

3.1 The Lengths of Estimates

3.2 Measures of Length

3.3 Least Squares for a Straight Line

3.4 The Least Squares Solution of the Linear Inverse Problem

3.5 Some Examples

3.6 The Existence of the Least Squares Solution

3.7 The Purely Underdetermined Problem

3.8 Mixed-Determined Problems

3.9 Weighted Measures of Length as a Type of A Priori Information

3.10 Other Types of A Priori Information

3.11 The Variance of the Model Parameter Estimates

3.12 Variance and Prediction Error of the Least Squares Solution

3.13 Problems


Chapter 4. Solution of the Linear, Gaussian Inverse Problem, Viewpoint 2: Generalized Inverses

4.1 Solutions Versus Operators

4.2 The Data Resolution Matrix

4.3 The Model Resolution Matrix

4.4 The Unit Covariance Matrix

4.5 Resolution and Covariance of Some Generalized Inverses

4.6 Measures of Goodness of Resolution and Covariance

4.7 Generalized Inverses with Good Resolution and Covariance

4.8 Sidelobes and


Since 1984, Geophysical Data Analysis has filled the need for a short, concise reference on inverse theory for individuals who have an intermediate background in science and mathematics. The new edition maintains the accessible and succinct manner for which it is known, with the addition of:

  • MATLAB examples and problem sets
  • Advanced color graphics
  • Coverage of new topics, including Adjoint Methods; Inversion by Steepest Descent, Monte Carlo and Simulated Annealing methods; and Bootstrap algorithm for determining empirical confidence intervals

Key Features

  • Additional material on probability, including Bayesian influence, probability density function, and metropolis algorithm
  • Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies
  • Numerous examples and end-of-chapter homework problems help you explore and further understand the ideas presented
  • Use as classroom text facilitated by a complete set of exemplary lectures in Microsoft PowerPoint format and homework problem solutions for instructors


Graduate students and researchers in solid earth geophysics, seismology, atmospheric sciences and other areas of applied physics (e.g. image processing) and mathematics.


No. of pages:
© Academic Press 2012
Academic Press
Paperback ISBN:
eBook ISBN:
Hardcover ISBN:


"This is a practical book on data analysis based on numerical Matlab procedures for solving inverse problems with a special application in seismology. The book is useful both as a textbook for graduate students in geophysics and as a numerical data processing reference book for researchers not only in geophysics but also those involved in acoustic tomography and X-ray imaging data processing."--Zentrallblatt MATH 1250

Praise for the second edition:

"The author has produced a meaningful guide to the subject; one which a student (or professional unfamiliar with the field) can follow without great difficulty and one in which many motivational guideposts are provided....I think that the value of the book is outstanding....It deserves a prominent place on the shelf of every scientist or engineer who has data to interpret."--GEOPHYSICS

"As a meteorologist, I have used least squares, maximum likelihood, maximum entropy, and empirical orthogonal functions during the course of my work, but this book brought together these somewhat disparate techniques into a coherent, unified package....I recommend it to meteorologists involved with data analysis and parameterization."--Roland B. Stull, THE BULLETIN OF THE AMERICAN METEOROLOGICAL SOCIETY

"This book provides an excellent introductory account of inverse theory with geophysical applications....My experience in using this book, along with supplementary material in a course for the first year graduate students, has been very positive. I unhesitatingly recommend it to any student or researcher in the geophysical sciences."--PACEOPH

About the Authors

William Menke Author

William Menke is a Professor of Earth and Environmental Sciences at Columbia University, USA. His research focuses on the development of data analysis algorithms for time series analysis and imaging in the earth and environmental sciences and the application of these methods to volcanoes, earthquakes and other natural hazards.

Affiliations and Expertise

Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY, USA