Inverse problem theory and methods for model parameter estimation:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia, PA
Society for Industrial and Applied Mathematics
2005
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XII, 342 S. Ill., graph. Darst. |
| ISBN: | 0898715725 9780898715729 |
Staff View
MARC
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| 100 | 1 | |a Tarantola, Albert |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Inverse problem theory and methods for model parameter estimation |c Albert Tarantola |
| 264 | 1 | |a Philadelphia, PA |b Society for Industrial and Applied Mathematics |c 2005 | |
| 300 | |a XII, 342 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a aInverse problems (Differential equations) | |
| 650 | 0 | 7 | |a Inverses Problem |0 (DE-588)4125161-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Inverses Problem |0 (DE-588)4125161-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012906200&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-012906200 | ||
Record in the Search Index
| _version_ | 1804132921184878592 |
|---|---|
| adam_text | Contents
Preface
xi
1
The General Discrete Inverse Problem
1
1.1
Model Space and Data Space
...................... 1
1.2
States of Information
.......................... 6
1.3
Forward Problem
............................ 20
1.4
Measurements and A Priori Information
................ 24
1.5
Defining the Solution of the Inverse Problem
.............. 32
1.6
Using the Solution of the Inverse Problem
............... 37
2
Monte Carlo Methods
41
2.1
Introduction
............................... 41
2.2
The Movie Strategy for Inverse Problems
................ 44
2.3
Sampling Methods
............................ 48
2.4
Monte Carlo Solution to Inverse Problems
............... 51
2.5
Simulated Annealing
.......................... 54
3
The Least-Squares Criterion
57
3.1
Preamble: The Mathematics of Linear Spaces
............. 57
3.2
The Least-Squares Problem
....................... 62
3.3
Estimating Posterior Uncertainties
................... 70
3.4
Least-Squares Gradient and Hessian
.................. 75
4
Least-Absolute-Values Criterion and Minimax Criterion
81
4.1
Introduction
............................... 81
4.2
Preamble: ¿p-Norms
........................... 82
4.3
The ip-Norm Problem
......:................... 86
4.4
The ¿i-Norm Criterion for Inverse Problems
.............. 89
4.5
The ¿oo-Norm Criterion for Inverse Problems
.............. 96
5
Functional Inverse Problems
101
5.1
Random Functions
............................101
5.2
Solution of General Inverse Problems
..................108
5.3
Introduction to Functional Least Squares
................108
5.4
Derivative and Transpose Operators in Functional Spaces
.......119
vii
v¡¡¡
Contents
5.5
General
Least-Squares
Inversion ....................133
5.6
Example:
Х
-Ray Tomography as an Inverse
Problem .........140
5.7
Example: Travel-Time Tomography
..................143
5.8
Example: Nonlinear Inversion of Elastic Waveforms
..........144
6
Appendices
159
6.1
Volumetric Probability and Probability Density
.............159
6.2
Homogeneous Probability Distributions
.................160
6.3
Homogeneous Distribution for Elastic Parameters
...........164
6.4
Homogeneous Distribution for Second-Rank Tensors
.........170
6.5
Central Estimators and Estimators of Dispersion
............170
6.6
Generalized Gaussian
..........................174
6.7
Log-Normal Probability Density
....................175
6.8
Chi-Squared Probability Density
....................177
6.9
Monte Carlo Method of Numerical Integration
.............179
6.10
Sequential Random Realization
.....................181
6.11
Cascaded Metropolis Algorithm
.....................182
6.12
Distance and Norm
...........................183
6.13
The Different Meanings of the Word Kernel
..............183
6.14
Transpose and Adjoint of a Differential Operator
............184
6.15
The Bayesian Viewpoint of Backus
(1970)...............190
6.16
The Method of Backus and Gilbert
...................191
6.17
Disjunction and Conjunction of Probabilities
..............195
6.18
Partition of Data into Subsets
......................197
6.19
Marginalizing in Linear Least Squares
.................200
6.20
Relative Information of Two
Gaussiane
.................201
6.21
Convolution of Two Gaussians
.....................202
6.22
Gradient-Based Optimization Algorithms
................203
6.23
Elements of Linear Programming
....................223
6.24
Spaces and Operators
..........................230
6.25
Usual Functional Spaces
.........................242
6.26
Maximum Entropy Probability Density
.................245
6.27
Two Properties of ¿p-Norms
.......................246
6.28
Discrete Derivative Operator
......................247
6.29 Lagrange
Parameters
..........................249
6.30
Matrix Identities
.............................249
6.31
Inverse of a Partitioned Matrix
.....................250
6.32
Norm of the Generalized Gaussian
...................250
7
Problems
253
7.1
Estimation oftheEpicentral Coordinates of a Seismic Event
......253
7.2
Measuring the Acceleration of Gravity
.................256
7.3
Elementary Approach to Tomography
..................259
7.4
Linear Regression with Rounding Errors
................266
7.5
Usual Least-Squares Regression
.....................269
7.6
Least-Squares Regression with Uncertainties in Both Axes
......273
Contents ix
7.7 Linear Regression
with an Outlier
....................275
7.8
Condition Number and A Posteriori Uncertainties
...........279
7.9
Conjunction of Two Probability Distributions
..............285
7.10
Adjoint of a Covariance Operator
....................288
7.11
Problem
7.1
Revisited
..........................289
7.12
Problem
7.3
Revisited
..........................289
7.13
An Example of Partial Derivatives
...................290
7.14
Shapes of the ¿p-Norm Misfit Functions
................290
7.15
Using the Simplex Method
.......................293
7.16
Problem
7.7
Revisited
..........................295
7.17
Geodetic Adjustment with Outliers
...................296
7.18
Inversion of Acoustic Waveforms
....................297
7.19
Using the Backus and Gilbert Method
..................304
7.20
The Coefficients in the Backus and Gilbert Method
...........308
7.21
The Norm Associated with the ID Exponential Covariance
......308
7.22
The Norm Associated with the ID Random Walk
...........311
7.23
The Norm Associated with the
3D
Exponential Covariance
......313
References and References for General Reading
317
Index
333
|
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| id | DE-604.BV019532894 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:00:30Z |
| institution | BVB |
| isbn | 0898715725 9780898715729 |
| language | English |
| lccn | 2004059038 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012906200 |
| oclc_num | 56672375 |
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| owner | DE-20 DE-703 DE-355 DE-BY-UBR DE-634 DE-188 |
| owner_facet | DE-20 DE-703 DE-355 DE-BY-UBR DE-634 DE-188 |
| physical | XII, 342 S. Ill., graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | marc |
| spelling | Tarantola, Albert Verfasser aut Inverse problem theory and methods for model parameter estimation Albert Tarantola Philadelphia, PA Society for Industrial and Applied Mathematics 2005 XII, 342 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index aInverse problems (Differential equations) Inverses Problem (DE-588)4125161-1 gnd rswk-swf Inverses Problem (DE-588)4125161-1 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012906200&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tarantola, Albert Inverse problem theory and methods for model parameter estimation aInverse problems (Differential equations) Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4125161-1 |
| title | Inverse problem theory and methods for model parameter estimation |
| title_auth | Inverse problem theory and methods for model parameter estimation |
| title_exact_search | Inverse problem theory and methods for model parameter estimation |
| title_full | Inverse problem theory and methods for model parameter estimation Albert Tarantola |
| title_fullStr | Inverse problem theory and methods for model parameter estimation Albert Tarantola |
| title_full_unstemmed | Inverse problem theory and methods for model parameter estimation Albert Tarantola |
| title_short | Inverse problem theory and methods for model parameter estimation |
| title_sort | inverse problem theory and methods for model parameter estimation |
| topic | aInverse problems (Differential equations) Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | aInverse problems (Differential equations) Inverses Problem |
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