Geophysical data analysis : discrete inverse theory /

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Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Menke, William
Formato: Electrónico eBook
Idioma:Inglés
Publicado: San Diego : Academic Press, ©1989.
Edición:Rev. ed.
Colección:International geophysics series ; v. 45.
Temas:
Geophysics > Measurement.
Oceanography > Measurement.
Inverse problems (Differential equations) > Numerical solutions.
Problèmes inverses (Équations différentielles) > Solutions numériques.
SCIENCE > Earth Sciences > Geography.
SCIENCE > Earth Sciences > Geology.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Preface.
  • Introduction.
  • DESCRIBING INVERSE PROBLEMS
  • Formulating Inverse Problems.
  • The Linear Inverse Problem.
  • Examples of Formulating Inverse Problems.
  • Solutions to Inverse Problems.
  • SOME COMMENTS ON PROBABILITY THEORY
  • Noise and Random Variables.
  • Correlated Data.
  • Functions of Random Variables.
  • Gaussian Distributions.
  • Testing the Assumption of Gaussian Statistics
  • Confidence Intervals.
  • SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 1:THE LENGTH METHOD
  • The 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 INVERSES
  • Solutions 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 METHODS
  • The 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 AVERAGES
  • Null 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 SPACES
  • Model 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 DISTRIBUTIONS
  • L1 Norms and Exponential Distributions.

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