模型参数估计的反问题理论与方法

Preface

1TheGeneralDiscreteInverseProblem

1.1ModelSpaceandDataSpace

1.2StatesofInformation

1.3ForwardProblem

1.4MeasurementsandAPrioriInformation

1.5DefiningtheSolutionoftheInverseProblem

1.6UsingtheSolutionoftheInverseProblem

2MonteCarloMethods

2.1Introduction

2.2TheMovieStrategyforInverseProblems

2.3SamplingMethods

2.4MonteCarloSolutiontoInverseProblems

2.5SimulatedAnnealing

3TheLeast-SquaresCriterion

3.1Preamble:TheMathematicsofLinearSpaces

3.2TheLeast-SquaresProblem

3.3EstimatingPosteriorUncertainties

3.4Least-SquaresGradientandHessian

4Least-Absolute-ValuesCriterionandMinimaxCriterion

4.1Introduction

4.2Preamble:ln-Norms

4.3Theln-NormProblem

4.4Thel1-NormCriterionforInverseProblems

4.5Theln-NormCriterionforInverseProblems

5FunctionalInverseProblems

5.1RandomFunctions

5.2SolutionofGeneralInverseProblems

5.3IntroductiontoFunctionalLeastSquares

5.4DerivativeandTransposeOperatorsinFunctionalSpaces

5.5GeneralLeast-SquaresInversion

5.6Example:X-RayTomographyasanInverseProblem

5.7Example:Travel-TimeTomography

5.8Example:NonlinearInversionofElasticWaveforms

6Appendices

6.1VolumetricProbabilityandProbabilityDensity

6.2HomogeneousProbabilityDistributions

6.3HomogeneousDistributionforElasticParameters

6.4HomogeneousDistributionforSecond-RankTensors

6.5CentralEstimatorsandEstimatorsofDispersion

6.6GeneralizedGaussian

6.7Log-NormalProbabilityDensity

6.8Chi-SquaredProbabilityDensity

6.9MonteCarloMethodofNumericalIntegration

6.10SequentialRandomRealization

6.11CascadedMetropolisAlgorithm

6.12DistanceandNorm

6.13TheDifferentMeaningsoftheWordKernel

6.14TransposeandAdjointofaDifferentialOperator

6.15TheBayesianViewpointofBackus(1970)

6.16TheMethodofBackusandGilbert

6.17DisjunctionandConjunctionofProbabilities

6.18PartitionofDataintoSubsets

6.19MarginalizinginLinearLeastSquares

6.20RelativeInformationofTwoGaussians

6.21ConvolutionofTwoGaussians

6.22Gradient-BasedOptimizationAlgorithms

6.23ElementsofLinearProgramming

6.24SpacesandOperators

6.25UsualFunctionalSpaces

6.26MaximumEntropyProbabilityDensity

6.27TwoPropertiesofln-Norms

6.28DiscreteDerivativeOperator

6.29LagrangeParameters

6.30MatrixIdentities

6.31InverseofaPartitionedMatrix

6.32NormoftheGeneralizedGaussian

7Problems

7.1EstimationoftheEpicentralCoordinatesofaSeismicEvent

7.2MeasuringtheAccelerationofGravity

7.3ElementaryApproachtoTomography

7.4LinearRegressionwithRoundingErrors

7.5UsualLeast-SquaresRegression

7.6Least-SquaresRegressionwithUncertaintiesinBothAxes

7.7LinearRegressionwithanOutlier

7.8ConditionNumberandAPosterioriUncertainties

7.9ConjunctionofTwoProbabilityDistributions

7.10AdjointofaCovarianceOperator

7.11Problem7.1Revisited

7.12Problem7.3Revisited

7.13AnExampleofPartialDerivatives

7.14Shapesoftheln-NormMisfitFunctions

7.15UsingtheSimplexMethod

7.16Problem7.7Revisited

7.17GeodeticAdjustmentwithOutliers

7.18InversionofAcousticWaveforms

7.19UsingtheBackusandGilbertMethod

7.20TheCoefficientsintheBackusandGilbertMethod

7.21TheNormAssociatedwiththe1DExponentialCovariance

7.22TheNormAssociatedwiththe1DRandomWalk

7.23TheNormAssociatedwiththe3DExponentialCovariance

ReferencesandReferencesforGeneralReading

Index

　　Promptedbyrecentdevelopmentsininversetheory,InverseProblemTheoryandMethodsforModelParameterEstimationisacompletelyrewrittenversionofa1987bookbythesameauthor.InthisversiontherearemanyalgorithmicdetailsforMonteCarlomethods,leastsquaresdiscreteproblems,andleast-squaresproblemsinvolvingfunctions.Inaddition,somenotionsareclarified,theroleofoptimizationtechniquesisunderplayed,andMonteCarlomethodsaretakenmuchmoreseriously.Thefirstpartofthebookdealsexclusivelywithdiscreteinverseproblemswithafinitenumberofparameters,whilethesecondpartofthebookdealswithgeneralinverseproblems....