Elastic wave propagation and generation in seismology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XVIII, 444 S. graph. Darst. |
| ISBN: | 0521817307 0521520460 |
Internformat
MARC
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| 100 | 1 | |a Pujol, Jose |d 1945- |e Verfasser |0 (DE-588)114642972X |4 aut | |
| 245 | 1 | 0 | |a Elastic wave propagation and generation in seismology |c Jose Pujol |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2003 | |
| 300 | |a XVIII, 444 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Elastic waves | |
| 650 | 4 | |a Seismology | |
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| 650 | 0 | 7 | |a Seismische Welle |0 (DE-588)4180762-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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| adam_text | Contents
Preface
page
xiii
Acknowledgements
xviii
Introduction to tensors and dyadics
1
1.1
Introduction
1
1.2
Summary of vector analysis
2
1.3
Rotation of Cartesian coordinates. Definition of a vector
7
1.4
Cartesian tensors
11
1.4.1
Tensor operations
14
1.4.2
Symmetric and anti-symmetric tensors
16
1.4.3
Differentiation of tensors
17
1.4.4
The permutation symbol
18
1.4.5
Applications and examples
19
1.4.6
Diagonalization of a symmetric second-order tensor
23
1.4.7 Isotropie
tensors
28
1.4.8
Vector associated with a second-order anti-symmetric
tensor
28
1.4.9
Divergence or Gauss theorem
29
1.5
Infinitesimal rotations
30
1.6
Dyads and dyadics
32
1.6.1
Dyads
33
1.6.2
Dyadics
34
Deformation. Strain and rotation tensors
40
2.1
Introduction
40
2.2
Description of motion. Lagrangian and Eulerian points of view
41
2.3
Finite strain tensors
43
2.4
The infinitesimal strain tensor
45
vn
viii Contents
2.4.1
Geometric
meaning of
e¡¡
46
2.4.2
Proof that
єи
is a tensor
49
2.5
The rotation tensor
50
2.6
Dyadic form of the strain and rotation tensors
51
2.7
Examples of simple strain fields
52
3
The stress tensor
59
3.1
Introduction
59
3.2
Additional continuum mechanics concepts
59
3.2.1
Example
63
3.3
The stress vector
64
3.4
The stress tensor
67
3.5
The equation of motion. Symmetry of the stress tensor
70
3.6
Principal directions of stress
72
3.7 Isotropie
and deviatoric components of the stress tensor
72
3.8
Normal and shearing stress vectors
73
3.9
Stationary values and directions of the normal and shearing
stress vectors
75
3.10
Mohr s circles for stress
79
4
Linear elasticity
-
the elastic wave equation
84
4.1
Introduction
84
4.2
The equation of motion under the small-deformation
approximation
85
4.3
Thermodynamical considerations
86
4.4
Strain energy
88
4.5
Linear elastic and hyperelastic deformations
90
4.6 Isotropie
elastic solids
92
4.7
Strain energy density for the
isotropie
elastic solid
96
4.8
The elastic wave equation for a homogeneous
isotropie
medium
97
5
Scalar and elastic waves in unbounded media
100
5.1
Introduction
100
5.2
The 1-D scalar wave equation
100
5.2.1
Example
103
5.3
The
3-D
scalar wave equation
103
5.4
Plane harmonic waves. Superposition principle
107
5.5
Spherical waves 111
5.6
Vector wave equation. Vector solutions
112
5.6.1
Properties of the
Hansen
vectors
115
Contents ix
5.6.2 Harmonie
potentials
116
5.7
Vector Helmholtz equation
116
5.8
Elastic wave equation without body forces
117
5.8.1
Vector P- and S-wave motion
118
5.8.2 Hansen
vectors for the elastic wave equation in the
frequency domain
119
5.8.3
Harmonic elastic plane waves
121
5.8.4
P-, SV-, and
S H
-wave displacements
123
5.9
Flux of energy in harmonic waves
125
Plane waves in simple models with plane boundaries
129
6.1
Introduction
129
6.2
Displacements
131
6.3
Boundary conditions
134
6.4
Stress vector
135
6.5
Waves incident at a free surface
136
6.5.1
Incident
S H
waves
136
6.5.2
Incident
Ρ
waves
137
6.5.3
Incident SV waves
144
6.6
Waves incident on a solid-solid boundary
152
6.6.1
Incident
S H
waves
152
6.6.2
Incident
Ρ
waves
157
6.6.3
Incident
S V
waves
164
6.7
Waves incident on a solid-liquid boundary
168
6.7.1
Incident
Ρ
waves
168
6.7.2
Incident
S V
waves
169
6.8
Ρ
waves incident on a liquid-solid boundary
169
6.9
Solid layer over a solid half-space
170
6.9.1
Incident SH waves
172
6.9.2
Incident
Ρ
and
S V
waves
179
Surface waves in simple models
-
dispersive waves
188
7.1
Introduction
188
7.2
Displacements
189
7.3
Love waves
191
7.3.1
Homogeneous half-space
191
7.3.2
Layer over a half-space
191
7.3.3
Love waves as the result of constructive interference
198
7.3.4
Vertically heterogeneous medium
199
7.4
Rayleigh waves
202
Contents
7.4.1
Homogeneous half-space
202
7.4.2
Layer over a half-space. Dispersive Rayleigh waves
206
7.4.3
Vertically heterogeneous medium
209
7.5
Stoneley waves
212
7.6
Propagation of dispersive waves
213
7.6.1
Introductory example. The dispersive string
214
7.6.2
Narrow-band waves. Phase and group velocity
215
7.6.3
Broad-band waves. The method of stationary phase
220
7.6.4
The Airy phase
227
Ray theory
234
8.1
Introduction
234
8.2
Ray theory for the
3-D
scalar wave equation
235
8.3
Ray theory for the elastic wave equation
237
8.3.1
Ρ
and
S
waves in
isotropie
media
240
8.4
Wave fronts and rays
242
8.4.1
Medium with constant velocity
244
8.4.2
Medium with a depth-dependent velocity
246
8.4.3
Medium with spherical symmetry
247
8.5
Differential geometry of rays
248
8.6
Calculus of variations. Fermat s principle
254
8.7
Ray amplitudes
258
8.7.1
Scalar wave equation
258
8.7.2
Elastic wave equation
261
8.7.3
Effect of discontinuities in the elastic parameters
268
8.8
Examples
269
8.8.1
S H
waves in a layer over a half-space at normal
incidence
270
8.8.2
Ray theory synthetic seismograms
274
Seismic point sources in unbounded homogeneous media
278
9.1
Introduction
278
9.2
The scalar wave equation with a source term
279
9.3
Helmholtz decomposition of a vector field
281
9.4
Lamé s
solution of the elastic wave equation
282
9.5
The elastic wave equation with a concentrated force in the
x¡
direction
285
9.5.1
Type of motion
288
9.5.2
Near and far fields
289
Contents xi
9.5.3
Example. The far field of a point force at the origin in
the xj direction
291
9.6
Green s function for the elastic wave equation
295
9.7
The elastic wave equation with a concentrated force in an
arbitrary direction
296
9.8
Concentrated couples and dipoles
297
9.9
Moment tensor sources. The far field
300
9.9.1
Radiation patterns. SV and
S H
waves
303
9.10
Equivalence of a double couple and a pair of compressional
and
tensional
dipoles
305
9.11
The tension and compression axes
306
9.12
Radiation patterns for the single couple M31 and the double
couple
Mn
+
M31
308
9.13
Moment tensor sources. The total field
311
9.13.1
Radiation patterns
313
10
The earthquake source in unbounded media
316
10.1
Introduction
316
10.2
A representation theorem
318
10.3
Gauss theorem in the presence of a surface of discontinuity
321
10.4
The body force equivalent to slip on a fault
322
10.5
Slip on a horizontal plane. Point-source approximation. The
double couple
325
10.6
The seismic moment tensor
329
10.7
Moment tensor for slip on a fault of arbitrary orientation
331
10.8
Relations between the parameters of the conjugate planes
338
10.9
Radiation patterns and focal mechanisms
339
10.10
The total field. Static displacement
347
10.11
Ray theory for the far field
352
11
Anelastic attenuation
357
11.1
Introduction
357
11.2
Harmonic motion. Free and damped oscillations
360
11.2.1
Temporal
Q
362
11.3
The string in a viscous medium
364
11.4
The scalar wave equation with complex velocity
365
11.4.1
Spatial
Q
366
11.5
Attenuation of seismic waves in the Earth
367
11.6
Mathematical aspects of causality and applications
370
11.6.1
The Hubert transform. Dispersion relations
371
xii Contents
11.6.2
Minimum-phase-shift functions
372
11.6.3
The Paley-Wiener theorem. Applications
375
11.7
Futterman s relations
377
11.8
Kalinin and Azimi s relation. The complex wave velocity
381
11.9
t*
384
11.10
The spectral ratio method. Window bias
384
11.11
Finely layered media and scattering attenuation
386
Hints
391
Appendices
407
A Introduction to the theory of distributions
407
В
The Hubert transform
419
С
Green s function for the
3-D
scalar wave equation
422
D
Proof of
(9.5.12)
425
E
Proof of
(9.13.1)
428
Bibliography
431
Index
439
Elastic Wave Propagation and Generation in Seismology
Seismology has complementary observational and theoretical components, and
a thorough understanding of the observations requires a sound theoretical back¬
ground. Seismological theory, however, can be a difficult mathematical subject
and introductory books do not generally give students the tools they need to solve
seismological problems by themselves. This book addresses these shortcomings
by bridging the gap between introductory textbooks and advanced monographs. It
provides the necessary mathematical machinery and demonstrates how to apply it.
The author s approach is to consider seismological phenomena as problems in
applied mathematics. To this end, each problem is carefully formulated and its
solution is derived in a step-by-step approach. Although some exposure to vector
calculus and partial differential equations is expected, most of the mathematics
needed is derived within the book. This includes Cartesian tensors, solution of
3-D
scalar and vector wave equations, Green s functions, and continuum mechanics
concepts. The book covers strain, stress, propagation of body and surface waves in
simple models (half-spaces and the layer over a half-space), ray theory for
Ρ
and
S
waves (including amplitude equations), near and far fields generated by moment
tensor sources in infinite media, and attenuation and the mathematics of causality.
Numerous programs for the computation of reflection and transmission coeffi¬
cients, for the generation of P- and 5-wave radiation patterns, and for near- and
far-field synthetic seismograms in infinite media are provided by the author on a
dedicated website. The book also includes problems for students to work through,
with solutions available on the associated website. This book will therefore find
a receptive audience among advanced undergraduate and graduate students inter¬
ested in developing a solid mathematical background to tackle more advanced
topics in seismology. It will also form a useful reference volume for researchers
wishing to brush up on the fundamentals.
JOSE PUJOL received a B.S. in Chemistry, from the
Universidad Nacional
del
Sur,
Bahia
Blanca, Argentina,
in
1968
and then went on to graduate studies in
quantum chemistry at Uppsala University, Sweden, and Karlsruhe University, Ger¬
many. Following further graduate studies in petroleum exploration at the University
of Buenos Aires, Argentina, he studied for an M.S. in geophysics, at the University
of Alaska
(1982)
and a Ph.D. at the University of Wyoming
(1985).
He has been
a faculty member at the University of Memphis since
1985
where he is currently
an Associate Professor in the Center for Earthquake Research and Information.
Professor Pujol s research interests include earthquake and exploration seismol¬
ogy, vertical seismic profiling, inverse problems, earthquake location and velocity
inversion, and attenuation studies using borehole data. He is also an associate editor
for the Seismological Society of America.
|
| any_adam_object | 1 |
| author | Pujol, Jose 1945- |
| author_GND | (DE-588)114642972X |
| author_facet | Pujol, Jose 1945- |
| author_role | aut |
| author_sort | Pujol, Jose 1945- |
| author_variant | j p jp |
| building | Verbundindex |
| bvnumber | BV040611885 |
| classification_rvk | RB 10115 UT 2500 |
| classification_tum | GEO 550f |
| ctrlnum | (OCoLC)635786864 (DE-599)BVBBV040611885 |
| dewey-full | 551.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 551 - Geology, hydrology, meteorology |
| dewey-raw | 551.22 |
| dewey-search | 551.22 |
| dewey-sort | 3551.22 |
| dewey-tens | 550 - Earth sciences |
| discipline | Geowissenschaften Geologie / Paläontologie Physik Geographie |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV040611885 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:27:17Z |
| institution | BVB |
| isbn | 0521817307 0521520460 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025439434 |
| oclc_num | 635786864 |
| open_access_boolean | |
| owner | DE-703 DE-83 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-83 DE-91G DE-BY-TUM |
| physical | XVIII, 444 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Pujol, Jose 1945- Verfasser (DE-588)114642972X aut Elastic wave propagation and generation in seismology Jose Pujol 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2003 XVIII, 444 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Elastic waves Seismology Erdbeben (DE-588)4015134-7 gnd rswk-swf Seismologie (DE-588)4379341-1 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Elastische Welle (DE-588)4151684-9 gnd rswk-swf Erdbebenwelle (DE-588)4152644-2 gnd rswk-swf Seismische Welle (DE-588)4180762-5 gnd rswk-swf Seismologie (DE-588)4379341-1 s Elastische Welle (DE-588)4151684-9 s DE-604 Seismische Welle (DE-588)4180762-5 s Wellenausbreitung (DE-588)4121912-0 s Erdbeben (DE-588)4015134-7 s Erdbebenwelle (DE-588)4152644-2 s Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025439434&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025439434&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Pujol, Jose 1945- Elastic wave propagation and generation in seismology Elastic waves Seismology Erdbeben (DE-588)4015134-7 gnd Seismologie (DE-588)4379341-1 gnd Wellenausbreitung (DE-588)4121912-0 gnd Elastische Welle (DE-588)4151684-9 gnd Erdbebenwelle (DE-588)4152644-2 gnd Seismische Welle (DE-588)4180762-5 gnd |
| subject_GND | (DE-588)4015134-7 (DE-588)4379341-1 (DE-588)4121912-0 (DE-588)4151684-9 (DE-588)4152644-2 (DE-588)4180762-5 |
| title | Elastic wave propagation and generation in seismology |
| title_auth | Elastic wave propagation and generation in seismology |
| title_exact_search | Elastic wave propagation and generation in seismology |
| title_full | Elastic wave propagation and generation in seismology Jose Pujol |
| title_fullStr | Elastic wave propagation and generation in seismology Jose Pujol |
| title_full_unstemmed | Elastic wave propagation and generation in seismology Jose Pujol |
| title_short | Elastic wave propagation and generation in seismology |
| title_sort | elastic wave propagation and generation in seismology |
| topic | Elastic waves Seismology Erdbeben (DE-588)4015134-7 gnd Seismologie (DE-588)4379341-1 gnd Wellenausbreitung (DE-588)4121912-0 gnd Elastische Welle (DE-588)4151684-9 gnd Erdbebenwelle (DE-588)4152644-2 gnd Seismische Welle (DE-588)4180762-5 gnd |
| topic_facet | Elastic waves Seismology Erdbeben Seismologie Wellenausbreitung Elastische Welle Erdbebenwelle Seismische Welle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025439434&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025439434&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pujoljose elasticwavepropagationandgenerationinseismology |