Theory of elastic waves:
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| Main Author: | |
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| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
Potsdam
Geoforschungszentrum
2007
|
| Series: | Scientific technical report / Geoforschungszentrum Potsdam
2007,03 |
| Subjects: | |
| Online Access: | Volltext Volltext Inhaltsverzeichnis |
| Physical Description: | 228 S. zahlr. graph. Darst. |
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Record in the Search Index
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|---|---|
| adam_text |
THEORY OF ELASTIC WAVES GERHARD MIILLER SUB GOTTINGEN 7 220 309 116 2007
B 25678 EDITORS MICHAEL WEBER - GFZ & UNIVERSITAT POTSDAM GEORG RIIMPKER
- UNIVERSITAT FRANKFURT DIRK GAJEWSKI - UNIVERSITAT HAMBURG GERMANY
CONTENTS 1 LITERATURE 9 2 FOUNDATIONS OF ELASTICITY THEORY 11 2.1
ANALYSIS OF STRAIN 12 2.2 ANALYSIS OF STRESS 21 2.3 EQUILIBRIUM
CONDITIONS 23 2.4 STRESS-STRAIN RELATIONS 26 2.5 EQUATION OF MOTION,
BOUNDARY AND INITIAL 31 2.6 DISPLACEMENT, POTENTIALS AND WAVE TYPES . .
\ 34 3 BODY WAVES 39 3.1 PLANE BODY WAVES 39 3.2 THE INITIAL VALUE
PROBLEM FOR PLANE WAVES 40 3.3 SIMPLE BOUNDARY VALUE PROBLEMS FOR PLANE
WAVES 43 3.4 SPHERICAL WAVES FROM EXPLOSION POINT SOURCES 45 3.5
SPHERICAL WAVES FROM SINGLE FORCE AND DIPOLE 49 3.5.1 SINGLE FORCE POINT
SOURCE 49 3.5.2 DIPOLE POINT SOURCES 56 3.6 REFLECTION AND REFRACTION OF
PLANE WAVES 62 3.6.1 PLANE WAVES WITH ARBITRARY PROPAGATION DIRECTION 62
3.6.2 BASIC EQUATIONS 63 3.6.3 REFLECTION AND REFRACTION OF SH-WAVES 66
3.6.4 REFLECTION OF P-WAVES AT A FREE SURFACE 76 5 6 CONTENTS 3.6.5
REFLECTION AND REFRACTION COEFFICIENTS FOR LAYERED MEDIA . . 84 3.7
REFLECTIVITY METHOD: REFLECTION OF 92 3.7.1 THEORY 92 3.7.2 REFLECTION
AND HEAD WAVES 95 3.7.3 COMPLETE SEISMOGRAMS 97 3.8 EXACT, OR
GENERALISED RAY THEORY - GRT 98 3.8.1 INCIDENT CYLINDRICAL WAVE 99 3.8.2
WAVEFRONT APPROXIMATION FOR UR 102 3.8.3 REFLECTION AND REFRACTION OF
THE CYLINDRICAL WAVE 103 3.8.4 DISCUSSION OF REFLECTED WAVE TYPES 110
3.9 RAY SEISMICS IN CONTINUOUS INHOMOGENEOUS MEDIA 113 3.9.1 FERMAT'S
PRINCIPLE AND THE RAY EQUATION 114 3.9.2 HIGH FREQUENCY APPROXIMATION OF
THE EQUATION OF MOTION . 119 3.9.3 EIKONAL EQUATION AND SEISMIC RAYS 121
3.9.4 AMPLITUDES IN RAY SEISMIC APPROXIMATION 123 3.10 WKBJ METHOD 126
3.10.1 HARMONIC EXCITATION AND REFLECTION COEFFICIENT, 126 3.10.2
IMPULSIVE EXCITATION AND WKBJ-SEISMOGRAMS 131 4 SURFACE WAVES 135 4.1
FREE SURFACE WAVES IN LAYERED MEDIA 135 4.1.1 BASIC EQUATIONS 135 4.1.2
RAYLEIGH WAVES AT THE SURFACE OF AN HOMOGENEOUS HALF-SPACEL38 4.1.3 LOVE
WAVES AT THE SURFACE OF A LAYERED HALF-SPACE 142 4.1.4 DETERMINATION OF
THE PHASE VELOCITY OF SURFACE WAVES FROM OBSERVATIONS 150 4.1.5 THE
GROUP VELOCITY 153 4.1.6 DESCRIPTION OF SURFACE WAVES BY CONSTRUCTIVE
INTERFERENCE OF BODY WAVES 157 4.2 SURFACE WAVES FROM POINT SOURCES 160
4.2.1 IDEAL WAVE GUIDE FOR HARMONIC EXCITATION 160 4.2.2 THE MODAL
SEISMOGRAM OF THE IDEAL WAVE GUIDE 167 4.2.3 COMPUTATION OF MODAL
SEISMOGRAMS WITH THE METHOD OF STATIONARY PHASE 170 4.2.4 RAY
REPRESENTATION OF THE FIELD IN AN IDEAL WAVE GUIDE . . 173 CONTENTS 7 A
LAPLACE TRANSFORM AND DELTA FUNCTION 179 A.I INTRODUCTION TO THE LAPLACE
TRANSFORM 179 A.1.1 LITERATURE 179 A.1.2 DEFINITION OF THE LAPLACE
TRANSFORM 179 A.1.3 ASSUMPTIONS ON F(T) 180 A.1.4 EXAMPLES 180 A.1.5
PROPERTIES OF THE LAPLACE TRANSFORM 181 A.1.6 BACK-TRANSFORM 183 A.1.7
RELATION WITH THE FOURIER TRANSFORM 184 A.2 APPLICATION OF THE LAPLACE
TRANSFORM 184 A.2.1 LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT
COEF- FICIENTS 184 A.2.2 PARTIAL DIFFERENTIAL EQUATIONS 192 A.3 THE
DELTA FUNCTION 5(1) 194 A.3.1 INTRODUCTION OF 5(1.) 194 A.3.2 PROPERTIES
OF 5{T) 197 A.3.3 APPLICATION OF 5(1) 200 A.3.4 DUHAMERS LAW AND LINEAR
SYSTEMS .\ 202 A.3.5 PRACTICAL APPROACH FOR THE CONSIDERATION OF
NON-ZERO INITIAL VALUES OF THE PERTURBATION FUNCTION F(T) OF A LINEAR
PROBLEM205 B HILBERT TRANSFORM 209 B.I THE HILBERT TRANSFORM PAIR : 209
B.2 THE HILBERT TRANSFORM AS A FILTER 210 C BESSEL FUNCTIONS 215 D THE
SOMMERFELD INTEGRAL 219 E THE COMPUTATION OF MODAL SEISMOGRAMS 221 E.I
NUMERICAL CALCULATIONS 221 E.2 METHOD OF STATIONARY PHASE 222 E.3 AIRY
PHASES 224 INDEX 226 |
| adam_txt |
THEORY OF ELASTIC WAVES GERHARD MIILLER SUB GOTTINGEN 7 220 309 116 2007
B 25678 EDITORS MICHAEL WEBER - GFZ & UNIVERSITAT POTSDAM GEORG RIIMPKER
- UNIVERSITAT FRANKFURT DIRK GAJEWSKI - UNIVERSITAT HAMBURG GERMANY
CONTENTS 1 LITERATURE 9 2 FOUNDATIONS OF ELASTICITY THEORY 11 2.1
ANALYSIS OF STRAIN 12 2.2 ANALYSIS OF STRESS 21 2.3 EQUILIBRIUM
CONDITIONS 23 2.4 STRESS-STRAIN RELATIONS 26 2.5 EQUATION OF MOTION,
BOUNDARY AND INITIAL 31 2.6 DISPLACEMENT, POTENTIALS AND WAVE TYPES . .
\ 34 3 BODY WAVES 39 3.1 PLANE BODY WAVES 39 3.2 THE INITIAL VALUE
PROBLEM FOR PLANE WAVES 40 3.3 SIMPLE BOUNDARY VALUE PROBLEMS FOR PLANE
WAVES 43 3.4 SPHERICAL WAVES FROM EXPLOSION POINT SOURCES 45 3.5
SPHERICAL WAVES FROM SINGLE FORCE AND DIPOLE 49 3.5.1 SINGLE FORCE POINT
SOURCE 49 3.5.2 DIPOLE POINT SOURCES 56 3.6 REFLECTION AND REFRACTION OF
PLANE WAVES 62 3.6.1 PLANE WAVES WITH ARBITRARY PROPAGATION DIRECTION 62
3.6.2 BASIC EQUATIONS 63 3.6.3 REFLECTION AND REFRACTION OF SH-WAVES 66
3.6.4 REFLECTION OF P-WAVES AT A FREE SURFACE 76 5 6 CONTENTS 3.6.5
REFLECTION AND REFRACTION COEFFICIENTS FOR LAYERED MEDIA . . 84 3.7
REFLECTIVITY METHOD: REFLECTION OF 92 3.7.1 THEORY 92 3.7.2 REFLECTION
AND HEAD WAVES 95 3.7.3 COMPLETE SEISMOGRAMS 97 3.8 EXACT, OR
GENERALISED RAY THEORY - GRT 98 3.8.1 INCIDENT CYLINDRICAL WAVE 99 3.8.2
WAVEFRONT APPROXIMATION FOR UR 102 3.8.3 REFLECTION AND REFRACTION OF
THE CYLINDRICAL WAVE 103 3.8.4 DISCUSSION OF REFLECTED WAVE TYPES 110
3.9 RAY SEISMICS IN CONTINUOUS INHOMOGENEOUS MEDIA 113 3.9.1 FERMAT'S
PRINCIPLE AND THE RAY EQUATION 114 3.9.2 HIGH FREQUENCY APPROXIMATION OF
THE EQUATION OF MOTION . 119 3.9.3 EIKONAL EQUATION AND SEISMIC RAYS 121
3.9.4 AMPLITUDES IN RAY SEISMIC APPROXIMATION 123 3.10 WKBJ METHOD 126
3.10.1 HARMONIC EXCITATION AND REFLECTION COEFFICIENT, 126 3.10.2
IMPULSIVE EXCITATION AND WKBJ-SEISMOGRAMS 131 4 SURFACE WAVES 135 4.1
FREE SURFACE WAVES IN LAYERED MEDIA 135 4.1.1 BASIC EQUATIONS 135 4.1.2
RAYLEIGH WAVES AT THE SURFACE OF AN HOMOGENEOUS HALF-SPACEL38 4.1.3 LOVE
WAVES AT THE SURFACE OF A LAYERED HALF-SPACE 142 4.1.4 DETERMINATION OF
THE PHASE VELOCITY OF SURFACE WAVES FROM OBSERVATIONS 150 4.1.5 THE
GROUP VELOCITY 153 4.1.6 DESCRIPTION OF SURFACE WAVES BY CONSTRUCTIVE
INTERFERENCE OF BODY WAVES 157 4.2 SURFACE WAVES FROM POINT SOURCES 160
4.2.1 IDEAL WAVE GUIDE FOR HARMONIC EXCITATION 160 4.2.2 THE MODAL
SEISMOGRAM OF THE IDEAL WAVE GUIDE 167 4.2.3 COMPUTATION OF MODAL
SEISMOGRAMS WITH THE METHOD OF STATIONARY PHASE 170 4.2.4 RAY
REPRESENTATION OF THE FIELD IN AN IDEAL WAVE GUIDE . . 173 CONTENTS 7 A
LAPLACE TRANSFORM AND DELTA FUNCTION 179 A.I INTRODUCTION TO THE LAPLACE
TRANSFORM 179 A.1.1 LITERATURE 179 A.1.2 DEFINITION OF THE LAPLACE
TRANSFORM 179 A.1.3 ASSUMPTIONS ON F(T) 180 A.1.4 EXAMPLES 180 A.1.5
PROPERTIES OF THE LAPLACE TRANSFORM 181 A.1.6 BACK-TRANSFORM 183 A.1.7
RELATION WITH THE FOURIER TRANSFORM 184 A.2 APPLICATION OF THE LAPLACE
TRANSFORM 184 A.2.1 LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT
COEF- FICIENTS 184 A.2.2 PARTIAL DIFFERENTIAL EQUATIONS 192 A.3 THE
DELTA FUNCTION 5(1) 194 A.3.1 INTRODUCTION OF 5(1.) 194 A.3.2 PROPERTIES
OF 5{T) 197 A.3.3 APPLICATION OF 5(1) 200 A.3.4 DUHAMERS LAW AND LINEAR
SYSTEMS .\ 202 A.3.5 PRACTICAL APPROACH FOR THE CONSIDERATION OF
NON-ZERO INITIAL VALUES OF THE PERTURBATION FUNCTION F(T) OF A LINEAR
PROBLEM205 B HILBERT TRANSFORM 209 B.I THE HILBERT TRANSFORM PAIR : 209
B.2 THE HILBERT TRANSFORM AS A FILTER 210 C BESSEL FUNCTIONS 215 D THE
SOMMERFELD INTEGRAL 219 E THE COMPUTATION OF MODAL SEISMOGRAMS 221 E.I
NUMERICAL CALCULATIONS 221 E.2 METHOD OF STATIONARY PHASE 222 E.3 AIRY
PHASES 224 INDEX 226 |
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| spelling | Müller, Gerhard Verfasser aut Theory of elastic waves Gerhard Müller. Eds. Michael Weber ... Potsdam Geoforschungszentrum 2007 228 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Scientific technical report / Geoforschungszentrum Potsdam 2007,03 Elastische Welle (DE-588)4151684-9 gnd rswk-swf Elastische Welle (DE-588)4151684-9 s DE-604 Weber, Michael edt Erscheint auch als Online-Ausgabe urn:nbn:de:kobv:b103-07037 Geoforschungszentrum Potsdam Scientific technical report 2007,03 (DE-604)BV040700734 2007,3 http://www.gfz-potsdam.de/bib/pub/str0703/0703.pdf kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:kobv:b103-07037 kostenfrei Volltext GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015693449&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Müller, Gerhard Theory of elastic waves Elastische Welle (DE-588)4151684-9 gnd |
| subject_GND | (DE-588)4151684-9 |
| title | Theory of elastic waves |
| title_auth | Theory of elastic waves |
| title_exact_search | Theory of elastic waves |
| title_exact_search_txtP | Theory of elastic waves |
| title_full | Theory of elastic waves Gerhard Müller. Eds. Michael Weber ... |
| title_fullStr | Theory of elastic waves Gerhard Müller. Eds. Michael Weber ... |
| title_full_unstemmed | Theory of elastic waves Gerhard Müller. Eds. Michael Weber ... |
| title_short | Theory of elastic waves |
| title_sort | theory of elastic waves |
| topic | Elastische Welle (DE-588)4151684-9 gnd |
| topic_facet | Elastische Welle |
| url | http://www.gfz-potsdam.de/bib/pub/str0703/0703.pdf https://nbn-resolving.org/urn:nbn:de:kobv:b103-07037 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015693449&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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