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Geophysical Data Analysis: Discrete Inverse Theory de William Menke

Geophysical Data Analysis: Discrete Inverse Theory: International Geophysics, cartea 45

Autor William Menke
en Limba Engleză Hardback – 4 oct 1989
Please use extracts from reviews of first edition

Key Features* Updated and thoroughly revised edition* additional material on geophysical/acoustic tomography* Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies
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Specificații

ISBN-13: 9780124909212
ISBN-10: 0124909213
Pagini: 302
Dimensiuni: 152 x 229 mm
Editura: ELSEVIER SCIENCE
Seria International Geophysics

Public țintă

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

Cuprins

Preface.Introduction.DESCRIBING INVERSE PROBLEMSFormulating Inverse Problems.The Linear Inverse Problem.Examples of Formulating Inverse Problems.Solutions to Inverse Problems.SOME COMMENTS ON PROBABILITY THEORYNoise and Random Variables.Correlated Data.Functions of Random Variables.Gaussian Distributions.Testing the Assumption of Gaussian StatisticsConfidence Intervals.SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 1:THE LENGTH METHODThe Lengths of Estimates.Measures of Length.Least Squares for a Straight Line.The Least Squares Solution of the Linear Inverse Problem.Some Examples.The Existence of the Least Squares Solution.The Purely Underdetermined Problem.Mixed*b1Determined Problems.Weighted Measures of Length as a Type of A Priori Information.Other Types of A Priori Information.The Variance of the Model Parameter Estimates.Variance and Prediction Error of the Least Squares Solution.SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 2: GENERALIZED INVERSESSolutions versus Operators.The Data Resolution Matrix.The Model Resolution Matrix.The Unit Covariance Matrix.Resolution and Covariance of Some Generalized Inverses.Measures of Goodness of Resolution and Covariance.Generalized Inverses with Good Resolution and Covariance.Sidelobes and the Backus-Gilbert Spread Function.The Backus-Gilbert Generalized Inverse for the Underdetermined Problem.Including the Covariance Size.The Trade-off of Resolution and Variance.SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 3: MAXIMUM LIKELIHOOD METHODSThe Mean of a Group of Measurements.Maximum Likelihood Solution of the Linear Inverse Problem.A Priori Distributions.Maximum Likelihood for an Exact Theory.Inexact Theories.The Simple Gaussian Case with a Linear Theory.The General Linear, Gaussian Case.Equivalence of the Three Viewpoints.The F Test of Error Improvement Significance.Derivation of the Formulas of Section 5.7.NONUNIQUENESS AND LOCALIZED AVERAGESNull Vectors and Nonuniqueness.Null Vectors of a Simple Inverse Problem.Localized Averages of Model Parameters.Relationship to the Resolution Matrix.Averages versus Estimates.Nonunique Averaging Vectors and A Priori Information.APPLICATIONS OF VECTOR SPACESModel and Data Spaces.Householder Transformations.Designing Householder Transformations.Transformations That Do Not Preserve Length.The Solution of the Mixed-Determined Problem.Singular-Value Decomposition and the Natural Generalized Inverse.Derivation of the Singular-Value Decomposition.Simplifying Linear Equality and Inequality Constraints.Inequality Constraints.LINEAR INVERSE PROBLEMS AND NON-GAUSSIAN DISTRIBUTIONSL1 Norms and Exponential Distributions.

Recenzii

"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

Descriere

Descriere de la o altă ediție sau format:

Geophysical Data Analysis: Diverse Inverse Theory, Fourth Edition is a revised and expanded introduction to inverse theory and tomography as it is practiced by geophysicists. It demonstrates the methods needed to analyze a broad spectrum of geophysical datasets, with special attention to those methods that generate images of the earth. Data analysis can be a mathematically complex activity, but the treatment in this volume is carefully designed to emphasize those mathematical techniques that readers will find the most familiar and to systematically introduce less-familiar ones.
Using problems and case studies, along with MATLAB computer code and summaries of methods, the book provides data scientists and engineers in geophysics with the tools necessary to understand and apply mathematical techniques and inverse theory.

 

 

 

  • Includes material on probability, including Bayesian influence, probability density function and metropolis algorithm
  • Offers detailed discussion of the application of inverse theory to tectonic, gravitational and geomagnetic studies
  • Contains numerous examples, color figures and end-of-chapter homework problems to help readers explore and further understand presented ideas
  • Includes MATLAB examples and problem sets
  • Updated and refined throughout to bring the text in line with current understanding and improved examples and case studies
  • Expanded sections to cover material, such as second-derivation smoothing and chi-squared tests not covered in the previous edition