Tarantola A. — Inverse problem theory and methods for model parameter estimation :: Электронная библиотека попечительского совета мехмата МГУ

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Tarantola A. — Inverse problem theory and methods for model parameter estimation

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Название: Inverse problem theory and methods for model parameter estimation

Автор: Tarantola A.

Аннотация:

The use of actual observations to infer the properties of a model is an inverse problem, which are often difficult as they may not have a unique solution. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, including many heuristic arguments. Prompted by recent developments in inverse theory, this text is a completely rewritten version of a 1987 book by the same author, and includes many algorithmic details for Monte Carlo methods, least-squares discrete problems, and least-squares problems involving functions. In addition, some notions are clarified, the role of optimization techniques is underplayed, and Monte Carlo methods are taken much more seriously.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1

Год издания: 2004

Количество страниц: 352

Добавлена в каталог: 02.11.2010

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Предметный указатель

$\sigma$ -field      6
${l}_{1}$ -norm      81 82
${l}_{1}$ -norm, criterion      89
${l}_{1}$ -norm, criterion (and the method of steepest descent)      93
${l}_{1}$ -norm, linear programming      228
${l}_{1}$ -norm, misfit function      89
${l}_{2}$ -norm      236
${l}_{p}$ -norm      82
${l}_{p}$ -norm, criterion      88
${l}_{p}$ -norm, misfit function      290
${l}_{p}$ -norm, properties      246
${l}_{\infty}$ -norm      82
${l}_{\infty}$ -norm, criterion      96
${l}_{\infty}$ -norm, criterion (and linear programming)      99
${l}_{\infty}$ -norm, criterion (and the method of steepest descent)      98
${l}_{\infty}$ -norm, minimization (using linear programming)      229
A posteriori, covariance operator      69
A posteriori, probabilities      37
A posteriori, probability density      34
A posteriori, state of information      32
a priori information      27
Absolutely continuous      11
Acoustic waveforms inversion      144 297
action      189
Additive noise      26
Adjoint      187
Adjoint, formal      187
Adjoint, of a differential operator      184
Adjoint, operator      62 242
Adjoint, relation with transpose      62
Afifi      177
Aki      72 145 146
Alterman      300
Analysis of uncertainties      38
Anders sen      42
Application      230
Armstrong      229
Aster      80
Atlas      232
Azen      177
Back-projection      142
Backus      72 108 133 135 190 191
Backus and Gilbert method      191
Backus and Gilbert method, coefficients      308
Backus and Gilbert method, example      304
Bakhvalov      180
Balakrishnan      104
Banach space      236
Barnes      156
Barrodale      229 230
Bartels      225
Basis of a linear space      237
Bayer      229
Bayes      9
Bayes theorem      18 20
Bayesian      9
Bijective      230
Bilinear form      240
Bit      12
Bjork      77
Boothby      2
Bordley      14
Borel      xi
Born approximation      128
Boscovich      82
Boucher      45 46
box      11 37
Bradley      95
Brownian motion      44 52
Broyden      220
Buffon      41
bulk modulus      11
C6a      203 217 219
Canonical problem (of linear programming)      225
Cartesian parameter      163
Cascaded Metropolis algorithm      51 182
Cauchy sequence      233
Cauchy — Schwarz inequality      183
Censor      225
Center      171
Central estimator      170
Change of coordinates      8
Characterization of a random function      102
Charara      156
Chart      232
Chebyshev norm      98
Chi-squared, function      64 178
Chi-squared, probability density      177
Christofferson      72
Ciarlet      80 203 217 219 225
Cimino      225
Circle in the ${l}_{p}$ -norm sense      83
Circular covariance      113
Claerbout      81 82 96
Clayton      113 117
Closed, interval      231
Closed, subset      231
Combination of states of information      13 32
complete      233
Compliance      2 165
Components of a model      4
Computing probabilities      47
Condition number      215 279
Conditional, probability      16
Conditional, probability density      19
Conjugate directions      216
Conjunction of probabilities, airplane navigator      14
Conjunction of probabilities, impact on a screen      15
Conjunction, of probability densities      195 285
Conjunction, of states of information      13 14
Conn      229
Continuous, function      232
Continuous, linear operator      237 241
Continuous, operator      234
Contravariant metric      61
Convergence of quasi-Newton      69
Convolution of two Gaussians      202
coordinates      4
Coordinates, Cartesian      3
Coordinates, over the model manifold      3
Correlation      71
Correlation, coefficient      173
Correlation, length      118
Cost function      64
Cottle      225
Courant      190
Covariance      172
Covariance function      106
Covariance function, circular      113
Covariance function, exponential      111
Covariance function, Gaussian      113
Covariance function, random walk      114
Covariance function, white noise      114
Covariance operator      60 110
Covariance operator, adjoint      288
Covariance, neglected      31
Covariance, posterior      66 70
Covariant metric      61
Cuer      225 229
Curvature      210
Cylinder measure      191
Dahlquist      77
Dantzig      95 225 226
Data, components      5
Data, manifold      5
Data, space      5
Data, space (linear)      5
Data, vector      5
Dautray      190
Davidon      220

De Ghellinck      225
Delta function      9
Deltaness criterion      192
Densities of rocks      29
density      8
Density of volume      10
Derivative operator      119
Derivative operator, discrete      247
Deutsch      30
Differential operator      184
digit      12
Dimension of a linear space      237
Discretization of a function      29
Disjunction of states of information      13 14
dispersion      171
Distance      183 232
Djikpesse      93 95
Domain of definition      230
Draper      74
Dual, bases      59
Dual, boundary conditions      186
Dual, of a linear space      109
Dual, of an ${l}_{p}$ -normed space      83
Dual, problems      225
Dual, space      58 239
Duality, product      58
Duality, theorem      226
Dubes      173
Dumped least-squares      80
Ecker      225
Efficiency of Metropolis algorithm      53
Eigenvector analysis      73
Elastic waveforms, inversion      144
Elasticity      2—4
Elfving      225
Emptiness of large-dimensional spaces      42
Energy function      54
Epicentral estimation      253 289
Equivalent parameterizations      2
Estimation of uncertainties      70
Estimator of dispersion      170
Event      6
Existence of the solution of an inverse problem      34
Exponential, 3D covariance (norm)      313
Exponential, covariance (norm)      308 311
Exponential, covariance function      111
Exponential, covariance function and associated norm      118
Exponential, norm      308
Exponential, norm (3D)      313
Fenton      112 117
Feshbach      145 190
Fields smooth      3
FIFO method      96
Finite-dimensional linear space      237
Fisher probability density      39
Fletcher      203 216 217 219 220
FORM      239
Forward, modeling      2
Forward, operator      20
Forward, problem      20
Frankel      113 117
Franklin      108 133
Frechet derivative      120 299
Frechet derivative, acoustic waveforms      148
Frechet derivative, elastic waveforms      148
Frechet derivative, inversion of waveforms      125
Frechet derivative, travel-time tomography      123
Frechet derivative, X-ray tomography      121
Function      230
Functional least squares      108
Functional linear problem      134
Functions smooth      3
Fuzzy sets      14
Fuzzy sets, intersection      14
Fuzzy sets, union      14
Gacs      225
Gass      95 226
Gauss      xii 64 81
Gauss — Markoff theorem      68
Gaussian model for inverse problems      36
Gaussian, covariance function      113
Gaussian, generalized      174
Gaussian, linear model for inverse problems      36
Gaussian, model for inverse problems      36
Gaussian, random field      45
Gaussian, random function      106
Gaussian, sequential simulation      135
Gaussian, uncertainties      26 35
Geman      49 54
Generalized, Gaussian      174
Genest      14
Genetic algorithms      51
Geodetic adjustment (with outlier)      296
Geostatistics      30
Gibbs sampler      49
Gilbert      72 135 191
Gill      203
Global optimization (software)      80
Global optimum      69
Goldberg      51
Goldfarb      220
Golfrey      229
Goodness of fit      179
Goovaerts      30
Gradient      204
Gradient, least squares      75
Gradient, norm      209
Gradient, versus steepest vector      205
Gradient-based optimization algorithms      203
Gravity's acceleration (measure of)      256
Green, function      145
Green, theorem      184 187 189
Guyaguler      38
Hacijan      225
Half-life of a nucleus      28
Half-range      171
Hammersley      180
Handscomb      180
Hastings      50
Hax      95
Herman      121 142
hessian      204
Hessian, least squares      75
Hessian, matrix      76
Hessian, of the least-squares misfit function      205
Hestenes      217
hilbert      190
Hilbert space      117 190 241
Histograms the making of      14
Hofstadter      8
Homogeneous, probability (for seismic velocities)      168
Homogeneous, probability density      7 10
Homogeneous, probability density (for second rank tensors)      170
Homogeneous, probability density (invariance)      11
Homogeneous, probability distributions      160
Hooke'slaw      164
Huijbregts      30
Husebye      72
Hypocentral estimation      253 289
Image      230
Implicit sum convention      59
Incompressibility modulus      11 165
Independent, events      18
Independent, samples      7 52
Independent, variables      19
Infinite-dimensional linear space      237
Information content      12
Information perfect      9
Injective      230
Instrument, perfect      26

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