Geophysical Data Analysis: Discrete Inverse Theory

MATLAB Edition


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

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
  • Online data sets and MATLAB scripts that can be used as an inverse theory tutorial.

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


Book information

  • Published: June 2012
  • ISBN: 978-0-12-397160-9


"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

Table of Contents

Chapter 1: Describing Inverse Problems
Chapter 2: Some Comments on Probability Theory
Chapter 3: Solution of the Linear, Gaussian Inverse Problem, Viewpoint 1: The Length Method
Chapter 4: Solution of the Linear, Gaussian Inverse Problem, Viewpoint 2: Generalized Inverses
Chapter 5: Solution of the Linear, Gaussian Inverse Problem, Viewpoint 3: Maximum Likelihood Methods
Chapter 6: Nonuniqueness and Localized Averages
Chapter 7: Applications of Vector Spaces
Chapter 8: Linear Inverse Problems and Non-Gaussian Statistics
Chapter 9: Nonlinear Inverse Problems
Chapter 10: Factor Analysis
Chapter 11: Continuous Inverse Theory and Tomography
Chapter 12: Sample Inverse Problems
Chapter 13: Applications of Inverse Theory to Solid Earth Geophysics