Surface waves and discontinuities:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin
Akad.-Verl.
1987
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019121330&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 213 - 222 |
| Umfang: | 229 S. Ill. |
| ISBN: | 3055002776 |
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| 100 | 1 | |a Malischewsky, Peter |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Surface waves and discontinuities |c Peter Malischewsky |
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1987 | |
| 300 | |a 229 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1819261807133458432 |
|---|---|
| adam_text | CONTENTS
PREFACE 5
1. INTRODUCTION 11
LI. GENERAL BACKGROUND 11
1.2. GENERAL REMARKS ABOUT WAVE-GUIDES WITH DISCONTINUITIES 14
2. MATHEMATICAL ASPECTS 17
2.1. THE BOUNDARY CONDITIONS AND THEIR SEISMOLOGICAL INTERPRETATION ....
17
2.1.1. GENERAL REMARKS 17
2.1.2.
APPROXIMATIONS OF AN ELASTIC LAYER OVER AN ELASTIC HALF-SPACE AFTER
TIERSTEN
(1969)
AND
ALSOP
ET AL.
(1971) 18
2.2. THE DIFFERENTIAL OPERATORS IN CLOSED DOMAINS 22
2.3. THE DIFFERENTIAL OPERATORS IN OPEN DOMAINS 25
3. THE UNDISTURBED WAVE-GUIDE 30
3.1. THE MODE CONCEPTION .- . . . 30
3.2. THE CLOSED WAVE-GUIDE 30
3.2.1. GENERAL REMARKS 30
3.2.2. THE EIGENSPECTRUM 31
3.2.2.1. WAVE-GUIDE TYPE I YY 31
3.2.2.2. WAVE-GUIDE TYPE II 33
3.2.3. THE EIGENFUNCTIONS 35
3.2.3.1. WAVE-GUIDE TYPE I 35
3.2.3.2. WAVE-GUIDE TYPE II 36
3.2.4. ORTHOGONALITY AND NORMALIZATION . . . . ; 37
3.3. THE OPEN WAVE-GUIDE 39
3.3.1. GENERAL REMARKS 39
3.3.2. THE EIGENSPECTRUM . 40
3.3.3. LEAKING MODES 41
3.3.4. THE EIGENFUNCTIONS 48
3.3.5. ORTHOGONALITY AND NORMALIZATION 50
3.3.6. THE RADIATION CONDITIONS 52
HTTP://D-NB.INFO/871489244
8
CONTENTS
4. THE DISTURBED WAVE-GUIDE 54
4.1. GENERAL REMARKS 54
4.2. THE BRA-KET FORMALISM (INTERRELATIONS WITH QUANTUM THEORY) 55
4.2.1. THE IDEAL WAVE-GUIDE 55
4.2.2. THE WAVE-GUIDE WITH WEAK DISTURBANCES . . . 59
4.2.2.1. DIRAC S PERTURBATION THEORY 59
4.2.2.2. APPLICATIONS OF THE PERTURBATION THEORY 63
4.2.2.2.1. GENERAL REMARKS 63
4.2.2.2.2. SEPARATION OF THE PERTURBATION OPERATOR
S
FOR DISTURBANCES OF MATERIAL
PARAMETERS 63
4.2.2.2.3. THE TRANSIENT FUNCTION 64
4.2.2.2.4. APPLICATION OF THE PERTURBATION THEORY TO A DISCONTINUITY OF
SURFACE IM
PEDANCE 68
4.3. THE CLOSED WAVE-GUIDE WITH A VERTICAL DISCONTINUITY OR AN IMPEDANCE
JUMP, RESPECTIVELY 69
4.3.1. GENERAL REMARKS 69
4.3.2. EXPANSION IN TERMS OF EIGENFUNCTIONS IN THE REGIONS RIGHT AND
LEFT OF THE
DISCONTINUITY 69
4.3.3. SETTING UP AN INFINITE SYSTEM OF EQUATIONS FOR THE REFLECTION AND
TRANS
MISSION COEFFICIENTS OF THE SLOW MODE FOR WAVE-GUIDE TYPE I 70
4.3.4. SOLUTION OF THE SYSTEM OF EQUATIONS BY PERTURBATION THEORY 74
4.3.4.1. DETERMINATION OF THE REFLECTION COEFFICIENTS
A
Y
74
4.3.4.2. DISCUSSION OF THE RESONANT CASE A^
V
= 0 76
4.3.5. DETERMINATION OF THE REFLECTION AND TRANSMISSION COEFFICIENTS FOR
THE SLOW
MODE WITH THE LQBR-METHOD 77
4.3.5.1. WAVE-GUIDE TYPE I 77
4.3.5.2. WAVE^GUIDE TYPE II 78
4.3.6. SOLUTION OF THE SYSTEM OF EQUATIONS USING A COMPUTER PROGRAM AND
COMPARISON OF THE VARIOUS SOLUTIONS 78
4.3.7. COMPARISON OF THE EXACT SOLUTION AFTER WIENER-HOPF WITH THE LQBR
APPROXIMATION CONCERNING THE REFLECTION COEFFICIENT OF THE SLOW MODE
FOR A WAVE-GUIDE TYPE II WITH AN IMPEDANCE JUMP 86
4.4. THE OPEN WAVE-GUIDE WITH VERTICAL DISCONTINUITY AND AN IMPEDANCE
JUMP 88
4.4.1. GENERAL REMARKS 88
4.4.2. APPLICATION OF THE MODE-MATCHING METHOD 89
4.4.3. SETTING UP OF A SINGULAR INTEGRAL EQUATION FOR THE DETERMINATION
OF THE
REFLECTION AND TRANSMISSION COEFFICIENTS 92
4.4.4. DISCUSSION OF THE SINGULAR INTEGRAL EQUATION FOR
A(Y)
97
4.4.5. DETERMINATION OF AN APPROXIMATE SOLUTION USING A PERTURBATION
METHOD . 101
4.4.6. DISCUSSION OF THE APPROXIMATE SOLUTION 104
4.4.6.1. CONSIDERATION OF THE PROPERTIES OF A
7
(Y) 104
4.4.6.2. DETERMINATION OF AN APPROXIMATION OF SECOND ORDER FOR THE
REFLECTION
COEFFICIENT A USING A
/
(Y) 105
CONTENTS
9
4.4.6.3. THE USE OF
A(Y)
FOR THE DETERMINATION OF THE RADIATION PATTERN 107
4.4.7. THE EXACT SOLUTION AFTER WIENER-HOPF FOR THE IMPEDANCE JUMP
DISCONTI
NUITY 113
4.4.8. CLASSIFICATION OF THE DISCONTINUITIES UNDER CONSIDERATION 114
4.4.8.1. CONDITION FOR THE EXISTENCE OF AN ELEMENTARY SOLUTION OF THE
DISCONTI
NUITY PROBLEM 114
4.4.8.2. CONDITION FOR THE TRANSITION IMPEDANCE JUMP - VERTICAL
DISCONTINUITY. 116
4.4.9. APPLICATION OF THE LQBR-METHOD TO SEVERAL TEST CASES AND
COMPARISON
WITH THE APPROXIMATIVE SOLUTION AND THE EXACT ONE 117
4.4.9.1. GENERAL REMARKS 117
4.4.9.2. DERIVATION OF THE LQBR-METHOD FOR THE DISCONTINUITY MODELS
UNDER
CONSIDERATION 118
4.4.9.3. COMPARISON OF VARIOUS LEAST-SQUARES METHODS 123
4.4.9.4. MODEL CALCULATIONS AND COMPARISON OF THE LQBR-APPROXIMATION
WITH
THE EXACT SOLUTION 125
4.4.9.4.1. GENERAL REMARKS 125
4.4.9.4.2. COMPARISON OF APPROXIMATIVE AND EXACT SOLUTIONS FOR VARIOUS
PARAMETER
VALUES 126
4.4.9.4.3. SIMULATION OF THE PERIOD DEPENDENCE 132
4.4.9.4.4. SIMULATION OF A VERTICAL DISCONTINUITY (CONTRAST IN /I AND Q)
136
4.4.10. DISCUSSION OF FURTHER ATTEMPTS AT SOLUTION IN LITERATURE 138
4.5. LATERAL INHOMOGENEITIES AND SEISMIC SURFACE WAVES 143
4.5.1. GENERAL REMARKS 143
4.5.2. THE INTERPRETATION OF SURFACE WAVES IN MEDIA WITH LATERAL INHOMO
GENEITIES 144
4.5.3. FURTHER INVESTIGATION OF DISCONTINUITIES WITH SURFACE WAVES 147
4.5.3.1. GENERAL REMARKS 147
4.5.3.2. METHODS USED IN SEISMOLOGICAL LITERATURE FOR THE DETERMINATION
OF RE
FLECTION AND TRANSMISSION COEFFICIENTS OF SURFACE WAVES 148
4.5.3.2.1. LEAST-SQUARE BOUNDARY RESIDUAL (LQBR) METHODS 148
4.5.3.2.2. NUMERICAL RESULTS ON THE BASIS OF THE LQBR-METHOD 150
4.5.3.2.3. RAY-THEORETICAL METHODS 156
4.5.3.2.4. KAZI S METHOD 158
4.5.3.2.5. BUKCHIN S METHOD 161
4.5.3.2.6. THE METHOD OF COUPLED MODES AFTER KENNETT 164
4.5.3.2.7. FURTHER APPROXIMATION TECHNIQUES 167
4.5.3.3. THE PENETRATION IN DEPTH OF DISCONTINUITIES 169
4.5.4. SEISMOLOGICAL APPLICATIONS OF THE THEORETICAL CONCEPTIONS
CONCERNING THE
REFLECTION AND TRANSMISSION OF SURFACE WAVES 174
5. THE WIENER-H OPF TECHNIQUE 178
5.1. GENERAL REMARKS 178
5.2. APPLICATION OF THE WIENER-HOPF TECHNIQUE TO AN IMPEDANCE JUMP IN AN
OPEN WAVE-GUIDE 179
5.2.1. PRELIMINARY REMARKS AND DERIVATION OF TWO FUNCTIONAL EQUATIONS .
. . 179
10
CONTENTS
5.2.2. SOLUTION OF THE FUNCTIONAL EQUATIONS I AND II 183
5.2.3. FACTORIZATION OF THE FUNCTION W(K) 184
5.2.4. DETERMINATION OF THE REFLECTION AND TRANSMISSION COEFFICIENTS FOR
AN
INCIDENT SURFACE WAVE 191
5.3. APPLICATION OF THE WIENER-HOPF TECHNIQUE TO AN IMPEDANCE JUMP IN A
YY
CLOSED WAVE-GUIDE 195
5.3.1. PRELIMINARY REMARKS AND DERIVATION OF THE FUNCTIONAL EQUATIONS I
AND II. 195
5.3.2. SOLUTION OF THE FUNCTIONAL EQUATIONS I AND II AND FACTORIZATION
OF [ (K). 197
5.3.3. DETERMINATION OF THE REFLECTION COEFFICIENT FOR AN INCIDENT SLOW
MODE . . 199
6. THE THREE-DIMENSIONAL PROBLEM : 202
6.1. GENERAL REMARKS 202
6.2. SOME SPECIAL CASES 203
6.3. SOME REMARKS CONCERNING RAYLEIGH WAVES 205
7. APPENDIX 207
7.1. CALCULATION OF THE INTEGRALS I
X
, /
2
, I
3
207
7.2. PERTURBATION METHOD FOR COMPLEX ROOTS 210
7.3. THE BOUNDARY CONDITIONS OF THE TYPE LOOSELY BONDED INTERFACE . . .
. 211
8. REFERENCES 213
SUBJECT INDEX 223
AUTHOR INDEX 227
|
| any_adam_object | 1 |
| author | Malischewsky, Peter |
| author_facet | Malischewsky, Peter |
| author_role | aut |
| author_sort | Malischewsky, Peter |
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| building | Verbundindex |
| bvnumber | BV025874122 |
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| discipline | Physik Geographie |
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| id | DE-604.BV025874122 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:09:12Z |
| institution | BVB |
| isbn | 3055002776 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019121330 |
| oclc_num | 632838947 |
| open_access_boolean | |
| owner | DE-11 |
| owner_facet | DE-11 |
| physical | 229 S. Ill. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Akad.-Verl. |
| record_format | marc |
| spellingShingle | Malischewsky, Peter Surface waves and discontinuities Diskontinuität (DE-588)4150167-6 gnd Erdkruste (DE-588)4015169-4 gnd Seismische Welle (DE-588)4180762-5 gnd Erdbebenwelle (DE-588)4152644-2 gnd Oberflächenwelle (DE-588)4193158-0 gnd |
| subject_GND | (DE-588)4150167-6 (DE-588)4015169-4 (DE-588)4180762-5 (DE-588)4152644-2 (DE-588)4193158-0 |
| title | Surface waves and discontinuities |
| title_auth | Surface waves and discontinuities |
| title_exact_search | Surface waves and discontinuities |
| title_full | Surface waves and discontinuities Peter Malischewsky |
| title_fullStr | Surface waves and discontinuities Peter Malischewsky |
| title_full_unstemmed | Surface waves and discontinuities Peter Malischewsky |
| title_short | Surface waves and discontinuities |
| title_sort | surface waves and discontinuities |
| topic | Diskontinuität (DE-588)4150167-6 gnd Erdkruste (DE-588)4015169-4 gnd Seismische Welle (DE-588)4180762-5 gnd Erdbebenwelle (DE-588)4152644-2 gnd Oberflächenwelle (DE-588)4193158-0 gnd |
| topic_facet | Diskontinuität Erdkruste Seismische Welle Erdbebenwelle Oberflächenwelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019121330&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT malischewskypeter surfacewavesanddiscontinuities |