Full seismic waveform modelling and inversion:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer
2011
|
| Series: | Advances in geophysical and environmental mechanics and mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 343 S. Ill., graph. Darst. |
| ISBN: | 9783642158063 |
Staff View
MARC
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| 245 | 1 | 0 | |a Full seismic waveform modelling and inversion |c Andreas Fichtner |
| 264 | 1 | |a Heidelberg [u.a.] |b Springer |c 2011 | |
| 300 | |a XX, 343 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
1 PRELIMINARIES 1
1.1 A BRIEF HISTORICAL OVERVIEW 1
1.2 THE FULL WAVEFORM TOMOGRAPHIE INVERSE PROBLEM - PROBABILISTIC VS.
DETERMINISTIC 3
1.3 TERMINOLOGY: FULL LANGUAGE CONFUSION 4
PART I NUMERICAL SOLUTION OF THE ELASTIC WAVE EQUATION
2 INTRODUCTION 9
2.1 NOTATIONAL CONVENTIONS 9
2.2 THE ELASTIC WAVE EQUATION 11
2.2.1 GOVERNING EQUATIONS 11
2.2.2 FORMULATIONS OF THE ELASTIC WAVE EQUATION 13
2.3 THE ACOUSTIC WAVE EQUATION 14
2.4 DISCRETISATION IN SPACE 15
2.5 DISCRETISATION IN TIME OR FREQUENCY 16
2.5.1 TIME-DOMAIN MODELLING 16
2.5.2 FREQUENCY-DOMAIN MODELLING 18
2.6 SUMMARY OF NUMERICAL METHODS 19
3 FINITE-DIFFERENCE METHODS 23
3.1 BASIC CONCEPTS IN ONE DIMENSION 24
3.1.1 FINITE-DIFFERENCE APPROXIMATIONS 24
3.1.2 DISCRETISATION OF THE ID WAVE EQUATION 30
3.1.3 VON NEUMANN ANALYSIS: STABILITY AND NUMERICAL DISPERSION 34
3.2 EXTENSION TO THE 3D CARTESIAN CASE 38
3.2.1 THE STAGGERED GRID 39
3.2.2 ANISOTROPY AND INTERPOLATION 43
3.2.3 IMPLEMENTATION OF THE FREE SURFACE 45
3.3 THE 3D SPHERICAL CASE 50
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1005646627
DIGITALISIERT DURCH
IMAGE 2
XVI CONTENTS
3.4 POINT SOURCE IMPLEMENTATION 53
3.5 ACCURACY AND EFFICIENCY 55
4 SPECTRAL-ELEMENT METHODS 59
4.1 BASIC CONCEPTS IN ONE DIMENSION 59
4.1.1 WEAK SOLUTION OF THE WAVE EQUATION 60
4.1.2 SPATIAL DISCRETISATION AND THE GALERKIN METHOD 60 4.2 EXTENSION TO
THE 3D CASE 66
4.2.1 MESH GENERATION 66
4.2.2 WEAK SOLUTION OF THE ELASTIC WAVE EQUATION 70
4.2.3 DISCRETISATION OF THE EQUATIONS OF MOTION 71
4.2.4 POINT SOURCE IMPLEMENTATION 76
4.3 VARIANTS OF THE SPECTRAL-ELEMENT METHOD 79
4.4 ACCURACY AND EFFICIENCY 81
5 VISCO-ELASTIC DISSIPATION 83
5.1 MEMORY VARIABLES 83
5.2 Q MODELS 85
6 ABSORBING BOUNDARIES 89
6.1 ABSORBING BOUNDARY CONDITIONS 89
6.1.1 PARAXIAL APPROXIMATIONS OF THE ACOUSTIC WAVE EQUATION . 90 6.1.2
PARAXIAL APPROXIMATIONS AS BOUNDARY CONDITIONS FOR ACOUSTIC WAVES 92
6.1.3 HIGH-ORDER ABSORBING BOUNDARY CONDITIONS FOR ACOUSTIC WAVES 94
6.1.4 GENERALISATION TO THE ELASTIC CASE 96
6.1.5 DISCUSSION 97
6.2 GAUSSIAN TAPER METHOD 98
6.3 PERFECTLY MATCHED LAYERS (PML) 99
6.3.1 GENERAL DEVELOPMENT 99
6.3.2 STANDARDPML 103
6.3.3 CONVOLUTIONAL PML 104
6.3.4 OTHER VARIANTS OF THE PML METHOD 108
PART II ITERATIVE SOLUTION OF THE FULL WAVEFORM INVERSION PROBLEM
7 INTRODUCTION TO ITERATIVE NON-LINEAR MINIMISATION 113
7.1 BASIC CONCEPTS: MINIMA, CONVEXITY AND NON-UNIQUENESS 114 7.1.1 LOCAL
AND GLOBAL MINIMA 114
7.1.2 CONVEXITY: GLOBAL MINIMA AND (NON)UNIQUENESS 116 7.2 OPTIMALITY
CONDITIONS 121
7.3 ITERATIVE METHODS FOR NON-LINEAR MINIMISATION 122
IMAGE 3
CONTENTS XVII
7.3.1 GENERAL DESCENT METHODS 122
7.3.2 THE METHOD OF STEEPEST DESCENT 125
7.3.3 NEWTON S METHOD AND ITS VARIANTS 126
7.3.4 THE CONJUGATE-GRADIENT METHOD 128
7.4 CONVERGENCE 134
7.4.1 THE MULTI-SCALE APPROACH 134
7.4.2 REGULARISATION 137
8 THE TIME-DOMAIN CONTINUOUS ADJOINT METHOD 141
8.1 INTRODUCTION 141
8.2 GENERAL FORMULATION 143
8.2.1 FRECHET KERNELS 145
8.2.2 TRANSLATION TO THE DISCRETISED MODEL SPACE 145 8.2.3 SUMMARY OF
THE ADJOINT METHOD 146
8.3 DERIVATIVES WITH RESPECT TO THE SOURCE 147
8.4 SECOND DERIVATIVES 148
8.4.1 MOTIVATION: THE ROLE OF SECOND DERIVATIVES IN OPTIMISATION AND
RESOLUTION ANALYSIS 149
8.4.2 EXTENSION OF THE ADJOINT METHOD TO SECOND DERIVATIVES .. 152 8.5
APPLICATION TO THE ELASTIC WAVE EQUATION 157
8.5.1 DERIVATION OF THE ADJOINT EQUATIONS 157
8.5.2 PRACTICAL IMPLEMENTATION 161
9 FIRST AND SECOND DERIVATIVES WITH RESPECT TO STRUCTURAL AND SOURCE
PARAMETERS 163
9.1 FIRST DERIVATIVES WITH RESPECT TO SELECTED STRUCTURAL PARAMETERS ..
163 9.1.1 PERFECTLY ELASTIC AND ISOTROPIE MEDIUM 165
9.1.2 PERFECTLY ELASTIC MEDIUM WITH RADIAL ANISOTROPY 167 9.1.3
ISOTROPIE VISCO-ELASTIC MEDIUM: Q^ AND Q K 170
9.2 FIRST DERIVATIVES WITH RESPECT TO SELECTED SOURCE PARAMETERS 172
9.2.1 DISTRIBUTED SOURCES AND THE RELATION TO TIME-REVERSAL IMAGING 172
9.2.2 MOMENT TENSOR POINT SOURCE 172
9.3 SECOND DERIVATIVES WITH RESPECT TO SELECTED STRUCTURAL PARAMETERS
173 9.3.1 PHYSICAL INTERPRETATION AND STRUCTURE OF THE HESSIAN 173 9.3.2
PRACTICAL RESOLUTION OF THE SECONDARY ADJOINT EQUATION .. 178 9.3.3
HESSIAN RECIPE 179
9.3.4 PERFECTLY ELASTIC AND ISOTROPIE MEDIUM 181
9.3.5 PERFECTLY ELASTIC MEDIUM WITH RADIAL ANISOTROPY 183 9.3.6
ISOTROPIE VISCO-ELASTIC MEDIUM 185
10 THE FREQUENCY-DOMAIN DISCRETE ADJOINT METHOD 1 89 10.1 GENERAL
FORMULATION 189
10.2 SECOND DERIVATIVES 191
IMAGE 4
XVIII CONTENTS
11 MISFIT FUNCTIONALS AND ADJOINT SOURCES 193
11.1 DERIVATIVE OF THE PURE WAVE FIELD AND THE ADJOINT GREENS FUNCTION
194 11.2 L 2 WAVEFORM DIFFERENCE 195
11.3 CROSS-CORRELATION TIME SHIFTS 197
11.4 2 AMPLITUDES 200
11.5 TIME-FREQUENCY MISFITS 201
11.5.1 DEFINITION OF PHASE AND ENVELOPE MISFITS 202
11.5.2 PRACTICAL IMPLEMENTATION OF PHASE DIFFERENCE MEASUREMENTS 203
11.5.3 AN EXAMPLE 205
11.5.4 ADJOINT SOURCES 207
12 FRECHET AND HESSIAN KERNEL GALLERY 211
12.1 BODY WAVES 212
12.1.1 CROSS-CORRELATION TIME SHIFTS 213
12.1.2 L 2 AMPLITUDES 219
12.2 SURFACE WAVES 221
12.2.1 ISOTROPIE EARTH MODELS 221
12.2.2 RADIAL ANISOTROPY 224
12.3 HESSIAN KERNELS: TOWARDS QUANTITATIVE TRADE-OFF AND RESOLUTION
ANALYSIS 225
12.4 ACCURACY-ADAPTIVE TIME INTEGRATION 229
PART III APPLICATIONS
13 FULL WAVEFORM TOMOGRAPHY ON CONTINENTAL SCALES 233 13.1 MOTIVATION
233
13.2 SOLUTION OF THE FORWARD PROBLEM 235
13.2.1 SPECTRAL ELEMENTS IN NATURAL SPHERICAL COORDINATES 235 13.2.2
IMPLEMENTATION OF LONG-WAVELENGTH EQUIVALENT CRUSTAL MODELS 238
13.3 QUANTIFICATION OF WAVEFORM DIFFERENCES 246
13.4 APPLICATION TO THE AUSTRALASIAN UPPER MANTLE 249
13.4.1 DATA SELECTION AND PROCESSING 251
13.4.2 INITIAL MODEL 253
13.4.3 MODEL PARAMETERISATION 255
13.4.4 TOMOGRAPHIE IMAGES AND WAVEFORM FITS 256 13.4.5 RESOLUTION
ANALYSIS 260
13.5 DISCUSSION 261
13.5.1 FORWARD PROBLEM SOLUTION 262
13.5.2 THE CRUST 262
13.5.3 TIME-FREQUENCY MISFITS 262
13.5.4 DEPENDENCE ON THE INITIAL MODEL 263
IMAGE 5
CONTENTS
13.5.5 ANISOTROPY 263
13.5.6 RESOLUTION 264
14 APPLICATION OF FULL WAVEFORM TOMOGRAPHY TO ACTIVE-SOURCE
SURFACE-SEISMIC DATA 267
14.1 INTRODUCTION 267
14.2 DATA 268
14.3 DATA PRE-CONDITIONING AND WEIGHTING 271
14.4 MISFIT FUNCTIONAL 272
14.5 INITIAL MODEL 272
14.6 INVERSION AND RESULTS 274
14.7 DATA FIT 276
14.8 DISCUSSION 278
15 SOURCE STACKING DATA REDUCTION FOR FULL WAVEFORM TOMOGRAPHY AT THE
GLOBAL SCALE 281
15.1 INTRODUCTION 281
15.2 DATA REDUCTION 282
15.3 THE SOURCE STACKED INVERSE PROBLEM 283
15.4 VALIDATION TESTS 284
15.4.1 PARAMETERISATION 285
15.4.2 EXPERIMENT SETUP AND INPUT MODELS 285
15.4.3 TEST IN A SIMPLE TWO-PARAMETER MODEL 287
15.4.4 TESTS IN A REALISTIC DEGREE-6 GLOBAL MODEL 289 15.5 TOWARDS REAL
CASES: DEALING WITH MISSING DATA 294 15.6 DISCUSSION AND CONCLUSIONS 298
APPENDIX A MATHEMATICAL BACKGROUND FOR THE SPECTRAL-ELEMENT METHOD 301
A. 1 ORTHOGONAL POLYNOMIALS 301
A.2 FUNCTION INTERPOLATION 302
A.2.1 INTERPOLATING POLYNOMIAL 302
A.2.2 LAGRANGE INTERPOLATION 303
A.2.3 LOBATTO INTERPOLATION 305
A.2.4 FEKETE POINTS 309
A.2.5 INTERPOLATION ERROR 310
A.3 NUMERICAL INTEGRATION 312
A.3.1 EXACT NUMERICAL INTEGRATION AND THE GAUSS QUADRATURE ..312 A.3.2
GAUSS-LEGENDRE-LOBATTO QUADRATURE 314
APPENDIX B TIME-FREQUENCY TRANSFORMATIONS 317
IMAGE 6
XX CONTENTS
REFERENCES 321
INDEX 339
|
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| institution | BVB |
| isbn | 9783642158063 |
| language | English |
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| physical | XX, 343 S. Ill., graph. Darst. |
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| series2 | Advances in geophysical and environmental mechanics and mathematics |
| spelling | Fichtner, Andreas 1979- Verfasser (DE-588)141464984 aut Full seismic waveform modelling and inversion Andreas Fichtner Heidelberg [u.a.] Springer 2011 XX, 343 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advances in geophysical and environmental mechanics and mathematics Zugl.: München, Univ., Diss., 2010 Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Seismische Tomografie (DE-588)4604149-7 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Seismische Tomografie (DE-588)4604149-7 s Inverses Problem (DE-588)4125161-1 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-15807-0 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021206309&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fichtner, Andreas 1979- Full seismic waveform modelling and inversion Numerisches Verfahren (DE-588)4128130-5 gnd Seismische Tomografie (DE-588)4604149-7 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4604149-7 (DE-588)4125161-1 (DE-588)4113937-9 |
| title | Full seismic waveform modelling and inversion |
| title_auth | Full seismic waveform modelling and inversion |
| title_exact_search | Full seismic waveform modelling and inversion |
| title_full | Full seismic waveform modelling and inversion Andreas Fichtner |
| title_fullStr | Full seismic waveform modelling and inversion Andreas Fichtner |
| title_full_unstemmed | Full seismic waveform modelling and inversion Andreas Fichtner |
| title_short | Full seismic waveform modelling and inversion |
| title_sort | full seismic waveform modelling and inversion |
| topic | Numerisches Verfahren (DE-588)4128130-5 gnd Seismische Tomografie (DE-588)4604149-7 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Numerisches Verfahren Seismische Tomografie Inverses Problem Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021206309&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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