Pragmatic inversion of geophysical data:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Ho
Springer
1992
|
| Series: | Lecture notes in earth sciences
39 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | IX, 262 S. Ill., graph. Darst. |
| ISBN: | 3540556222 0387556222 |
Staff View
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| 245 | 1 | 0 | |a Pragmatic inversion of geophysical data |c Sven-Erik Hjelt |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Ho |b Springer |c 1992 | |
| 300 | |a IX, 262 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
Chapter 1 INTRODUCTION
1.1 Definition of Inversion 3
1.2 Geophysical Models 10
1.3 Model Parameters 16
1.4 Fitting Model Fields to Data 17
1.5 Factors Affecting Inversion 18
1.6 Computational Aspects 25
1.7 Psychological Aspects of Inversion 29
1.8 What then is Pragmatic Inversion? 31
References 32
Chapter 2 INTERPRETATION USING NOMOGRAMS
2.1 Characteristic Points 35
2.2 Nomograms and Their Use 38
2.2.1 Gravity Nomograms 38
2.2.2 Nomogram for Interpretation of VLF Resistivity Data 41
2.2.3 Nomograms for Magnetic Dipole (Slingram) Profiling 42
2.3 Computerized Nomograms 44
2.4 On the Accuracy of Characteristic Point Inversion 46
References 46
Chapter 3 LINEAR PARAMETERS
3.1 Defining the Linear Problem 51
3.1.1 Genuine Linear Problems 51
3.1.2 Discretization of the Linear Model 52
3.1.3 Linearization 53
3.1.4 Iterative Approaches 55
3.2 Fitting Linear Models to Data 57
3.2.1 Systems of Linear Equations 57
3.2.2 Exact Fit 60
3.2.3 Least Squares (LSQ) 60
3.3 Iterative Solutions: The Method of Gauss-Seidel 61
3.4 Generalized Inversion 63
3.4.1 Singular Value Decomposition (SVD) 64
3.4.1.1 Zero Eigenvalues 66
3.4.1.2 Zero Eigenvalues, a Least-Squares Approach 67
3.4.1.3 Why are Small Eigenvalues Dangerous? 69
3.4.2 SVD of a Rectangular Matrix 72
3.4.3 Geophysical Examples of the Use of SVD 73
3.4.3.1 Gravity 73
3.4.3.2 Earth Density Model 78
3.4.3.3 Magnetometry 81
3.4.3.4 Magnetometry, Theoretical Plate Models 82
3.4.3.5 Electromagnetism 90
3.4.3.6 Seismology 94
VIII
3.4.3.7 Oceanography 96
3.4.3.8 Joint Inversion 97
3.4.4 Ridge Regression 100
3.5 The Backus-Gilbert Approach 101
3.5.1 Definitions 101
3.5.2 Parameter Trade-Off 103
3.6 Geophysical Tomography 104
3.6.1 Seismic Tomography 105
3.6.2 Tomography and the Radon Transform 107
3.6.3 Example on Seismic Regional Tomography 110
References 112
Chapter 4 Non-Linear Parameters
4.1 Definitions 117
4.1.1 Objective Functions and Norms 118
4.1.1.1 Exact Fit 118
4.1.1.2 Least Squares 118
4.1.1.3 Robust Methods. The Minimax Solution 119
4.1.1.4 Weighted Objective Functions 119
4.1.2 Properties of Objective Functions 121
4.1.3 Constrained Optimization 127
4.1.3.1 Penalty Functions 127
4.1.3.2 Lagrangian Multipliers 128
4.1.4 Stopping Criteria in Iterative Optimization 129
4.2 One-Dimensional Optimization 131
4.2.1 Golden Cut 132
4.2.2 Fibonacci Search 133
4.2.3 Speedup by Parabolic Fit 134
4.2.4 The Secant Method 136
4.2.5 The Gradient Method 136
4.2.5.1 On the Instability of the Newton Iteration 137
4.3 Multidimensional Search 138
4.3.1 Direct Search 142
4.3.1.1 Sequential Search (Search by Parameters) 142
4.3.1.2 Hyperparabolic Fit 142
4.3.1.3 Pattern Search 144
4.3.2 Multivariate Search 147
4.3.2.1 The Simplex Method 147
4.3.2.2 Steepest Descent Methods: the Gradient Method 149
4.3.2.3 Steepest Descent Methods: the Method of Conjugate
Directions 150
4.3.2.4 The Levenberg-Morrison-Marquardt Algorithm 152
4.3.3 Random Search Methods 153
4.4 Examples 155
4.4.1 Magnetic 2D Profiling 156
4.4.2 Gravity Inversion 165
4.4.3 Seismic Refraction 166
4.4.4 Magnetotellurics 167
References 171
IX
Chapter 5 MAXIMUM LIKELIHOOD AND MAXIMUM ENTROPY
5.1 Introduction and Definitions 177
5.1.1 Probability Density 177
5.1.2 Measure of Information 179
5.2 Probabilistic Formulations of the Inversion Problem 181
5.2.1 The Principle of Maximum Likelihood 181
5.2.2 The Maximum Entropy Method 184
5.2.3 Bayesian Estimation 186
5.2.4 Some Useful Expressions for the Probabilistic Approach
of Inversion 187
5.2.4.1 Normal Distribution 187
5.2.4.2 Smoothness 188
5.2.4.3 Weighted Least Squares 189
5.2.4.4 Parameter Boundaries 189
5.2.4.5 More on a Priori Information 190
References 192
Chapter 6 ANALYTIC INVERSION
6.1 General Principles 197
6.1.1 Combination of Components 197
6.2 Examples of Analytic Inversion 200
6.2.1 Magnetometry 200
6.2.2 EM Magnetic Dipole and an Infinitely Well Conducting
Half-Plane 207
References 211
Chapter 7 ADVANCED INVERSION METHODS
7.1 Functional Analytical Methods 215
7.1.1 Methods of Singular Points 216
7.1.2 Method of Tightening Contours 216
7.1.3 Method fo Finite Functions 219
7.2 Continuation of Fields 222
7.3 Migration 226
References 226
Chapter 8 ERROR ANALYSIS
8.1 Introduction 231
8.2 On Linearized Errors 232
8.3 Minimal Error in Least-Squares Inversion 233
8.4 Correlation Between Parameters 234
8.5 Advanced Concepts of Error Analysis 240
References 243
Chapter 9 PARALLEL COMPUTATION IN MODELLING AND INVERSION
9.1 Parallelism in Geophysical Problems 248
9.2 Forward Problems 249
9.3 Inversion by Optimization 250
9.4 Large Systems of Equations 253
References 254
SUBJECT INDEX
257
|
| any_adam_object | 1 |
| author | Hjelt, Sven-Erik |
| author_facet | Hjelt, Sven-Erik |
| author_role | aut |
| author_sort | Hjelt, Sven-Erik |
| author_variant | s e h seh |
| building | Verbundindex |
| bvnumber | BV005772028 |
| callnumber-first | Q - Science |
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| ctrlnum | (OCoLC)26543495 (DE-599)BVBBV005772028 |
| dewey-full | 550 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 550 - Earth sciences |
| dewey-raw | 550 |
| dewey-search | 550 |
| dewey-sort | 3550 |
| dewey-tens | 550 - Earth sciences |
| discipline | Geologie / Paläontologie Physik Geographie |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:34:26Z |
| institution | BVB |
| isbn | 3540556222 0387556222 |
| language | English |
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| physical | IX, 262 S. Ill., graph. Darst. |
| publishDate | 1992 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in earth sciences |
| series2 | Lecture notes in earth sciences |
| spelling | Hjelt, Sven-Erik Verfasser aut Pragmatic inversion of geophysical data Sven-Erik Hjelt Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Ho Springer 1992 IX, 262 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in earth sciences 39 Literaturangaben Geofisica Géophysique - Observations Inversion (Géophysique) Geophysics Observations Inversion (Geophysics) Inversionstheorie (DE-588)4162240-6 gnd rswk-swf Datenauswertung (DE-588)4131193-0 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Geophysik (DE-588)4020252-5 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Geophysik (DE-588)4020252-5 s Datenanalyse (DE-588)4123037-1 s Inverses Problem (DE-588)4125161-1 s DE-604 Inversionstheorie (DE-588)4162240-6 s Datenauswertung (DE-588)4131193-0 s Lecture notes in earth sciences 39 (DE-604)BV023550940 39 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003606282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hjelt, Sven-Erik Pragmatic inversion of geophysical data Lecture notes in earth sciences Geofisica Géophysique - Observations Inversion (Géophysique) Geophysics Observations Inversion (Geophysics) Inversionstheorie (DE-588)4162240-6 gnd Datenauswertung (DE-588)4131193-0 gnd Inverses Problem (DE-588)4125161-1 gnd Geophysik (DE-588)4020252-5 gnd Datenanalyse (DE-588)4123037-1 gnd |
| subject_GND | (DE-588)4162240-6 (DE-588)4131193-0 (DE-588)4125161-1 (DE-588)4020252-5 (DE-588)4123037-1 |
| title | Pragmatic inversion of geophysical data |
| title_auth | Pragmatic inversion of geophysical data |
| title_exact_search | Pragmatic inversion of geophysical data |
| title_full | Pragmatic inversion of geophysical data Sven-Erik Hjelt |
| title_fullStr | Pragmatic inversion of geophysical data Sven-Erik Hjelt |
| title_full_unstemmed | Pragmatic inversion of geophysical data Sven-Erik Hjelt |
| title_short | Pragmatic inversion of geophysical data |
| title_sort | pragmatic inversion of geophysical data |
| topic | Geofisica Géophysique - Observations Inversion (Géophysique) Geophysics Observations Inversion (Geophysics) Inversionstheorie (DE-588)4162240-6 gnd Datenauswertung (DE-588)4131193-0 gnd Inverses Problem (DE-588)4125161-1 gnd Geophysik (DE-588)4020252-5 gnd Datenanalyse (DE-588)4123037-1 gnd |
| topic_facet | Geofisica Géophysique - Observations Inversion (Géophysique) Geophysics Observations Inversion (Geophysics) Inversionstheorie Datenauswertung Inverses Problem Geophysik Datenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003606282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023550940 |
| work_keys_str_mv | AT hjeltsvenerik pragmaticinversionofgeophysicaldata |