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
Arvustused
"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
Muu info
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
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.
William Menke is a Professor of Earth and Environmental Sciences at Columbia University. 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. He has thirty years of experience teaching data analysis methods to both undergraduates and graduate students. Relevant courses that he has taught include, at the undergraduate level, Environmental Data Analysis and The Earth System, and at the graduate level, Geophysical Inverse Theory, Quantitative Methods of Data Analysis, Geophysical Theory and Practical Seismology.
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