Mathematics of multidimensional seismic imaging, migration, and inversion:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2001
|
| Series: | Interdisciplinary applied mathematics
13 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 488 - 497 |
| Physical Description: | XXIX, 510 S. graph. Darst. : 24 cm |
| ISBN: | 0387950613 |
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| 245 | 1 | 0 | |a Mathematics of multidimensional seismic imaging, migration, and inversion |c N. Bleistein ; J. K. Cohen ; J. W. Stockwell |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
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| 490 | 1 | |a Interdisciplinary applied mathematics |v 13 | |
| 500 | |a Literaturverz. S. 488 - 497 | ||
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Record in the Search Index
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| adam_text | N. BLEISTEIN J.K. COHEN J.W. STOCKWELL, JR. MATHEMATICS OF
MULTIDIMENSIONAL SEISMIC IMAGING, MIGRATION, AND INVERSION WITH 71
ILLUSTRATIONS SPRINGER CONTENTS PREFACE VII LIST OF FIGURES XXIII 1
MULTIDIMENSIONAL SEISMIC INVERSION 1 1.1 INVERSE PROBLEMS AND IMAGING 2
1.2 THE NONLINEARITY OF THE SEISMIC INVERSE PROBLEM 4 1.3 HIGH FREQUENCY
5 1.4 MIGRATION VERSUS INVERSION 7 1.5 SOURCE-RECEIVER CONFIGURATIONS 12
1.6 BAND AND APERTURE LIMITING OF DATA 18 1.7 DIMENSIONS: 2D VERSUS 2.5D
VERSUS 3D 20 1.8 ACOUSTIC VERSUS ELASTIC INVERSION 20 1.9 A MATHEMATICAL
PERSPECTIVE ON THE GEOMETRY OF MIGRATION 22 2 THE ONE-DIMENSIONAL
INVERSE PROBLEM 24 2.1 PROBLEM FORMULATION IN ONE SPATIAL DIMENSION 25
2.1.1 THE 1D MODEL IN A GEOPHYSICAL CONTEXT 25 2.1.2 THE 1D MODEL AS A
MATHEMATICAL TESTGROUND . . 27 2.2 MATHEMATICAL TOOLS FOR FORWARD
MODELING 28 2.2.1 THE GOVERNING EQUATION AND RADIATION CONDITION 28
2.2.2 FOURIER TRANSFORM CONVENTIONS 29 2.2.3 GREEN S FUNCTIONS 32 XVI
CONTENTS 2.2.4 GREEN S THEOREM 33 2.3 THE FORWARD SCATTERING PROBLEM 35
2.3.1 THE FORWARD SCATTERING PROBLEM IN 1D 36 2.3.2 THE BORN
APPROXIMATION AND ITS CONSEQUENCES . 40 2.3.3 THE INVERSE SCATTERING
INTEGRAL EQUATION 41 2.4 CONSTANT-BACKGROUND, ZERO-OFFSET INVERSION 42
2.4.1 CONSTANT-BACKGROUND, SINGLE-LAYER 43 2.4.2 MORE LAYERS,
ACCUMULATED ERROR 56 2.4.3 A NUMERICAL EXAMPLE 58 2.4.4 SUMMARY 59 2.5
INVERSION IN A VARIABLE-BACKGROUND MEDIUM 60 2.5.1 MODERN MATHEMATICAL
ISSUES 64 2.5.2 SUMMARY 66 2.5.3 IMPLEMENTATION OF THE
VARIABLE-WAVESPEED THEORY 70 2.5.4 SUMMARY 76 2.6 REEVALUATION OF THE
SMALL-PERTURBATION ASSUMPTION ... 77 2.7 COMPUTER IMPLEMENTATION 78
2.7.1 SAMPLING 79 2.8 VARIABLE DENSITY 81 3 INVERSION IN HIGHER
DIMENSIONS 88 3.1 THE SCATTERING PROBLEM IN UNBOUNDED MEDIA 90 3.2 THE
BORN APPROXIMATION 94 3.2.1 THE BORN APPROXIMATION AND HIGH FREQUENCY .
. 99 3.2.2 THE CONSTANT-BACKGROUND ZERO-OFFSET EQUATION . 103 3.2.3 ONE
EXPERIMENT, ONE DEGREE OF FREEDOM IN A . . 103 3.3 ZERO-OFFSET
CONSTANT-BACKGROUND INVERSION IN 3D .... 106 3.3.1 RESTRICTIONS ON THE
CHOICE OF K^ 111 3.4 HIGH FREQUENCY, AGAIN 113 3.4.1 REFLECTION FROM A
SINGLE TILTED PLANE 117 3.4.2 THE REFLECTIVITY FUNCTION 119 3.4.3
ALTERNATIVE REPRESENTATIONS OF THE REFLECTIVITY FUNCTION 121 3.5
TWO-AND-ONE-HALF DIMENSIONS 123 3.5.1 ZERO-OFFSET, TWO-AND-ONE-HALF
DIMENSIONAL INVERSION 125 3.6 KIRCHHOFF INVERSION 127 3.6.1 STATIONARY
PHASE COMPUTATIONS 127 3.6.2 TWO-AND-ONE-HALF-DIMENSIONAL KIRCHHOFF
INVERSION 136 3.6.3 2D MODELING AND INVERSION 138 3.7 TESTING THE
INVERSION FORMULA WITH KIRCHHOFF DATA . . . 144 3.7.1 THE KIRCHHOFF
APPROXIMATION 144 3.7.2 ASYMPTOTIC INVERSION OF KIRCHHOFF DATA 146
CONTENTS XVII 3.7.3 SUMMARY 152 3.8 REVERSE-TIME WAVE-EQUATION MIGRATION
DEDUCED FROM THE KIRCHHOFF APPROXIMATION 156 4 LARGE-WAVENUMBER FOURIER
IMAGING 161 4.1 THE CONCEPT OF APERTURE 163 4.2 THE RELATIONSHIP BETWEEN
APERTURE AND SURVEY PARAMETERS 164 4.2.1 RAYS, FOURIER TRANSFORMS, AND
APERTURES 165 4.2.2 APERTURE AND MIGRATION DIP 166 4.2.3 MIGRATION DIP
AND APERTURES 168 4.2.4 SUMMARY 176 4.3 EXAMPLES OF APERTURE-LIMITED
FOURIER INVERSION 176 4.3.1 APERTURE-LIMITED INVERSION OF A DIRAC DELTA
FUNCTION (A POINT SCATTERER) 177 4.3.2 APERTURE-LIMITED INVERSION OF A
SINGULAR FUNCTION (A REFLECTING PLANE) 179 4.3.3 GENERALIZATION TO
SINGULAR FUNCTIONS OF OTHER TYPES OF SURFACES*ASYMPTOTIC EVALUATION ....
184 4.3.4 RELEVANCE TO INVERSE SCATTERING 189 4.3.5 APERTURE-LIMITED
FOURIER INVERSION OF SMOOTHER FUNCTIONS 189 4.3.6 APERTURE-LIMITED
FOURIER INVERSION OF STEPLIKE FUNCTIONS 189 4.3.7 APERTURE-LIMITED
FOURIER INVERSION OF A RAMPLIKE FUNCTION 192 4.3.8 APERTURE-LIMITED
INVERSION OF AN INFINITELY DIFFERENTIABLE FUNCTION 194 4.3.9 SUMMARY 196
4.4 APERTURE-LIMITED FOURIER IDENTITY OPERATORS 196 4.4.1 THE
SIGNIFICANCE OF THE BOUNDARY VALUES IN D Y . 198 4.4.2 STATIONARY
PHASE ANALYSIS FOR JO 201 4.4.3 THE NEAR-SURFACE CONDITION 208 4.4.4
EXTRACTING INFORMATION ABOUT / ON S Y 208 4.4.5 PROCESSING FOR A
SCALED SINGULAR FUNCTION OF THE BOUNDARY SURFACE S Y 209 4.4.6 THE
NORMAL DIRECTION 211 4.4.7 INTEGRANDS WITH OTHER TYPES OF SINGULARITIES
. . . 212 4.4.8 SUMMARY 214 4.4.9 MODERN MATHEMATICAL ISSUES 215 5
INVERSION IN HETEROGENEOUS MEDIA 216 5.1 ASYMPTOTIC INVERSION OF THE
BORN-APPROXIMATE INTEGRAL EQUATION*GENERAL RESULTS 217 5.1.1 RECORDING
GEOMETRIES 217 XVIII CONTENTS 5.1.2 FORMULATION OF THE 3D,
VARIABLE-BACKGROUND, INVERSE-SCATTERING PROBLEM 220 5.1.3 INVERSION FOR
A REFLECTIVITY FUNCTION 225 5.1.4 SUMMARY OF ASYMPTOTIC VERIFICATION 227
5.1.5 INVERSION IN TWO DIMENSIONS 227 5.1.6 GENERAL INVERSION RESULTS,
STATIONARY TRIPLES, AND COS 9 S 232 5.1.7 AN ALTERNATIVE DERIVATION:
REMOVING THE SMALL-PERTURBATION RESTRICTION AT THE REFLECTOR . 238 5.1.8
DISCUSSION 241 5.2 THE BEYLKIN DETERMINANT H, AND SPECIAL CASES OF 3D
INVERSION 242 5.2.1 GENERAL PROPERTIES OF THE BEYLKIN DETERMINANT . 243
5.2.2 COMMON-SHOT INVERSION 245 5.2.3 COMMON-OFFSET INVERSION 247 5.2.4
ZERO-OFFSET INVERSION 249 5.3 BEYLKIN DETERMINANTS AND RAY JACOBIANS IN
THE COMMON-SHOT AND COMMON-RECEIVER CONFIGURATIONS . . 250 5.4
ASYMPTOTIC INVERSION OF KIRCHHOFF DATA FOR A SINGLE REFLECTOR 257 5.4.1
STATIONARY PHASE ANALYSIS OF THE INVERSION OF KIRCHHOFF DATA 258 5.4.2
DETERMINATION OF COS 0 S AND C + 263 5.4.3 FINDING STATIONARY POINTS 265
5.4.4 DETERMINATION OF THE MATRIX SIGNATURE 268 5.4.5 THE QUOTIENT/I/L
DET^H 1 / 2 269 5.5 VERIFICATION BASED ON THE FOURIER IMAGING PRINCIPLE
. . . 271 5.6 VARIABLE DENSITY 276 5.6.1 VARIABLE-DENSITY REFLECTIVITY
INVERSION FORMULAS . 277 5.6.2 THE MEANING OF THE VARIABLE-DENSITY
REFLECTIVITY FORMULAS 278 5.7 DISCUSSION OF RESULTS AND LIMITATIONS 279
5.7.1 SUMMARY 281 6 TWO-AND-ONE-HALF-DIMENSIONAL INVERSION 282 6.1 2.5D
RAY THEORY AND MODELING 283 6.1.1 TWO-AND-ONE-HALF-DIMENSIONAL RAY
THEORY . . . 283 6.2 2.5D INVERSION AND RAY THEORY 290 6.2.1 THE 2.5D
BEYLKIN DETERMINANT 292 6.2.2 THE GENERAL 2.5D INVERSION FORMULAS FOR
REFLECTIVITY 293 6.3 THE BEYLKIN DETERMINANT H AND SPECIAL CASES OF 2.5D
INVERSION 297 6.3.1 GENERAL PROPERTIES OF THE BEYLKIN DETERMINANT . .
297 6.3.2 COMMON-SHOT INVERSION 299 CONTENTS XIX 6.3.3 A NUMERICAL
EXAMPLE*EXTRACTION OF REFLECTIVITY FROM A COMMON-SHOT INVERSION 299
6.3.4 CONSTANT-BACKGROUND PROPAGATION SPEED 301 6.3.5 VERTICAL SEISMIC
PROFILING 302 6.3.6 WELL-TO-WELL INVERSION 304 6.3.7 INVERT FOR WHAT?
304 6.3.8 COMMON-OFFSET INVERSION 305 6.3.9 A NUMERICAL
EXAMPLE*EXTRACTION OF THE REFLECTION COEFFICIENT AND COSOE S FROM A
COMMON-OFFSET INVERSION 307 6.3.10 A NUMERICAL EXAMPLE*IMAGING A
SYNCLINE WITH COMMON-OFFSET INVERSION 307 6.3.11 CONSTANT BACKGROUND
INVERSION 309 6.3.12 ZERO-OFFSET INVERSION 309 7 THE GENERAL THEORY OF
DATA MAPPING 311 7.1 INTRODUCTION TO DATA MAPPING 312 7.1.1 KIRCHHOFF
DATA MAPPING (KDM) 314 7.1.2 AMPLITUDE PRESERVATION 315 7.1.3 A ROUGH
SKETCH OF THE FORMULATION OF THE KDM PLATFORM 315 7.1.4 POSSIBLE
KIRCHHOFF DATA MAPPINGS 317 7.2 DERIVATION OF A 3D KIRCHHOFF DATA
MAPPING FORMULA . . 319 7.2.1 SPATIAL STRUCTURE OF THE KDM OPERATOR 322
7.2.2 FREQUENCY STRUCTURE OF THE OPERATOR AND ASYMPTOTIC PRELIMINARIES
323 7.2.3 DETERMINATION OF INCIDENCE ANGLE 327 7.3 2.5D KIRCHHOFF DATA
MAPPING 328 7.3.1 DETERMINATION OF INCIDENCE ANGLE 330 7.4 APPLICATION
OF KDM TO KIRCHHOFF DATA IN 2.5D 331 7.4.1 ASYMPTOTIC ANALYSIS OF 2.5D
KDM 339 7.4.2 STATIONARY PHASE ANALYSIS IN 7 341 7.4.3 VALIDITY OF THE
STATIONARY PHASE ANALYSIS .... 344 7.5 COMMON-SHOT DOWNWARD CONTINUATION
OF RECEIVERS (OR SOURCES) 347 7.5.1 TIME-DOMAIN DATA MAPPING FOR OTHER
IMPLEMENTATIONS 349 7.5.2 STATIONARY PHASE IN TJ 351 7.6 2.5D
TRANSFORMATION TO ZERO-OFFSET (TZO) 354 7.6.1 TZO IN THE FREQUENCY
DOMAIN 355 7.6.2 A HAIE-TYPE TZO 361 7.6.3 GARDNER/FOREL-TYPE TZO 363
7.6.4 ON THE SIMPLIFICATION OF THE SECOND DERIVATIVES OF THE PHASE 365
7.7 3D DATA MAPPING 374 XX CONTENTS 7.7.1 STATIONARY PHASE IN 7 375
7.7.2 DISCUSSION OF THE SECOND DERIVATIVES OF THE PHASE . 377 7.7.3 3D
CONSTANT-BACKGROUND TZO 380 7.7.4 THE 72 INTEGRAL AS A BANDLIMITED DELTA
FUNCTION . 381 7.7.5 SPACE/FREQUENCY TZO IN CONSTANT BACKGROUND . 384
7.7.6 A HAIE-TYPE 3D TZO 386 7.8 SUMMARY AND CONCLUSIONS 387 A
DISTRIBUTION THEORY 389 A.L INTRODUCTION 389 A.2 LOCALIZATION VIA DIRAC
DELTA FUNCTIONS 390 A.3 FOURIER TRANSFORMS OF DISTRIBUTIONS 397 A.4
RAPIDLY DECREASING FUNCTIONS 399 A.5 TEMPERATE DISTRIBUTIONS 400 A.6 THE
SUPPORT OF DISTRIBUTIONS 401 A.7 STEP FUNCTIONS 402 A.7.1 HUBERT
TRANSFORMS 404 A.8 BANDLIMITED DISTRIBUTIONS 405 B THE FOURIER TRANSFORM
OF CAUSAL FUNCTIONS 409 B.L INTRODUCTION 409 B.2 EXAMPLE: THE 1D
FREE-SPACE GREEN S FUNCTION 415 C DIMENSIONAL VERSUS DIMENSIONLESS
VARIABLES 418 OL THE WAVE EQUATION 419 C.L.L MATHEMATICAL DIMENSIONAL
ANALYSIS 419 C.1.2 PHYSICAL DIMENSIONAL ANALYSIS 421 C.2 THE HELMHOLTZ
EQUATION 422 C.3 INVERSION FORMULAS 425 D AN EXAMPLE OF ILL-POSEDNESS
430 D.L ILL-POSEDNESS IN INVERSION 431 E AN ELEMENTARY INTRODUCTION TO
RAY THEORY AND THE KIRCHHOFF APPROXIMATION 435 E.L THE EIKONAL AND
TRANSPORT EQUATIONS 436 E.2 SOLVING THE EIKONAL EQUATION BY THE METHOD
OF CHARACTERISTICS 438 E.2.1 CHARACTERISTIC EQUATIONS FOR THE EIKONAL
EQUATION 442 E.2.2 CHOOSING A = |: A AS THE RUNNING PARAMETER . . 443
E.2.3 CHOOSING A = C 2 /2: R, TRAVELTIME, AS THE RUNNING PARAMETER 444
E.2.4 CHOOSING A = C( X)/2: S, ARCLENGTH, AS THE RUNNING PARAMETER 444
CONTENTS XXI E.3 RAY AMPLITUDE THEORY 446 E.3.1 THE ODE FORM OF THE
TRANSPORT EQUATION .... 448 E.3.2 DIFFERENTIATION OF A DETERMINANT 449
E.3.3 VERIFICATION OF ( E.3.12) 452 E.3.4 HIGHER-ORDER TRANSPORT
EQUATIONS 453 E.4 DETERMINING INITIAL DATA FOR THE RAY EQUATIONS 453
E.4.1 INITIAL DATA FOR THE 3D GREEN S FUNCTION 454 E.4.2 INITIAL DATA
FOR THE 2D GREEN S FUNCTION 457 E.4.3 INITIAL DATA FOR REFIECTED AND
TRANSMITTED RAYS . 459 E.5 2.5 D RAY THEORY 463 E.5.1 2.5D RAY EQUATIONS
464 E.5.2 2.5D AMPLITUDES 465 E.5.3 THE 2.5D TRANSPORT EQUATION 465 E.6
RAYTRACING IN VARIABLE-DENSITY MEDIA 467 E.6.1 RAY AMPLITUDE THEORY IN
VARIABLE-DENSITY MEDIA 468 E.6.2 REFIECTED AND TRANSMITTED RAYS IN
VARIABLE-DENSITY MEDIA 469 E.7 DYNAMIC RAYTRACING 470 E.7.1 A SIMPLE
EXAMPLE, RAYTRACING IN CONSTANT-WAVESPEED MEDIA 473 E.7.2 DYNAMIC
RAYTRACING IN ER 474 E.7.3 DYNAMIC RAYTRACING IN R 475 E.7.4 TWO
DIMENSIONS 475 E.7.5 CONCLUSIONS 475 E.8 THE KIRCHHOFF APPROXIMATION 476
E.8.1 PROBLEM FORMULATION 478 E.8.2 GREEN S THEOREM AND THE WAVEFIELD
REPRESENTATION 479 E.8.3 THE KIRCHHOFF APPROXIMATION 483 E.8.4 2.5D 486
E.8.5 SUMMARY 487 REFERENCES 489 AUTHOR INDEX 499 SUBJECT INDEX 503
|
| any_adam_object | 1 |
| author | Bleistein, Norman Cohen, Jack K. Stockwell, John W. |
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| callnumber-subject | TN - Mining Engineering and Metallurgy |
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| ctrlnum | (OCoLC)44313348 (DE-599)BVBBV013646287 |
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| dewey-ones | 550 - Earth sciences |
| dewey-raw | 550/.28 |
| dewey-search | 550/.28 |
| dewey-sort | 3550 228 |
| dewey-tens | 550 - Earth sciences |
| discipline | Geowissenschaften Geologie / Paläontologie Physik Geographie |
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| id | DE-604.BV013646287 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:49:31Z |
| institution | BVB |
| isbn | 0387950613 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009323548 |
| oclc_num | 44313348 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-83 |
| physical | XXIX, 510 S. graph. Darst. : 24 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Interdisciplinary applied mathematics |
| series2 | Interdisciplinary applied mathematics |
| spelling | Bleistein, Norman Verfasser aut Mathematics of multidimensional seismic imaging, migration, and inversion N. Bleistein ; J. K. Cohen ; J. W. Stockwell New York [u.a.] Springer 2001 XXIX, 510 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Interdisciplinary applied mathematics 13 Literaturverz. S. 488 - 497 Inverse scattering transform Seismic reflection method Reflexionsseismik (DE-588)4177335-4 gnd rswk-swf Inverses Streuproblem (DE-588)4027547-4 gnd rswk-swf Reflexionsseismik (DE-588)4177335-4 s Inverses Streuproblem (DE-588)4027547-4 s DE-604 Cohen, Jack K. Verfasser aut Stockwell, John W. Verfasser aut Interdisciplinary applied mathematics 13 (DE-604)BV004216726 13 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009323548&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bleistein, Norman Cohen, Jack K. Stockwell, John W. Mathematics of multidimensional seismic imaging, migration, and inversion Interdisciplinary applied mathematics Inverse scattering transform Seismic reflection method Reflexionsseismik (DE-588)4177335-4 gnd Inverses Streuproblem (DE-588)4027547-4 gnd |
| subject_GND | (DE-588)4177335-4 (DE-588)4027547-4 |
| title | Mathematics of multidimensional seismic imaging, migration, and inversion |
| title_auth | Mathematics of multidimensional seismic imaging, migration, and inversion |
| title_exact_search | Mathematics of multidimensional seismic imaging, migration, and inversion |
| title_full | Mathematics of multidimensional seismic imaging, migration, and inversion N. Bleistein ; J. K. Cohen ; J. W. Stockwell |
| title_fullStr | Mathematics of multidimensional seismic imaging, migration, and inversion N. Bleistein ; J. K. Cohen ; J. W. Stockwell |
| title_full_unstemmed | Mathematics of multidimensional seismic imaging, migration, and inversion N. Bleistein ; J. K. Cohen ; J. W. Stockwell |
| title_short | Mathematics of multidimensional seismic imaging, migration, and inversion |
| title_sort | mathematics of multidimensional seismic imaging migration and inversion |
| topic | Inverse scattering transform Seismic reflection method Reflexionsseismik (DE-588)4177335-4 gnd Inverses Streuproblem (DE-588)4027547-4 gnd |
| topic_facet | Inverse scattering transform Seismic reflection method Reflexionsseismik Inverses Streuproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009323548&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004216726 |
| work_keys_str_mv | AT bleisteinnorman mathematicsofmultidimensionalseismicimagingmigrationandinversion AT cohenjackk mathematicsofmultidimensionalseismicimagingmigrationandinversion AT stockwelljohnw mathematicsofmultidimensionalseismicimagingmigrationandinversion |