A student's guide to geophysical equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Subjects: | |
| Online Access: | Cover image Klappentext Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIII, 281 S. graph. Darst. |
| ISBN: | 9781107005846 9780521183772 |
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MARC
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| 100 | 1 | |a Lowrie, William |d 1939- |e Verfasser |0 (DE-588)173151795 |4 aut | |
| 245 | 1 | 0 | |a A student's guide to geophysical equations |c William Lowrie |
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Record in the Search Index
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|---|---|
| adam_text | A Student s
Guide
to
Geophysical Equations
The advent of accessible student computing packages has
mea
n t
that
geophysics students can now easily manipulate
datasets
and gain first-hand
modeling experience
-
essential in developing an intuitive understanding
of the physics of the Earth. Yet to gain a more in-depth understanding of the
physical theory, and to be able to develop new models and
soluti
ons,
it is
necessary to be able to derive the relevant equations from first principles.
This compact, handy book fills a gap left by most modern geophysics
textbooks, which generally do not have space to
deri
ve
all of the
importa
n t
formulae, showing the intermediate steps. This guide presents full
derivations for the classical equations of gravitation, gravity, tides,
Earth rotation, heat, geomagnetism, andfoundationalseismology,
illustrated with simple schematic diagrams. It supports
studen
t s
through
the successive steps and explains the logical sequence of a derivation-
facilitating self-study and helping students to tackle homework exercises
and prepareforexams.
Cover illustration: visualization of a global gravity model, sho.
v
ng
va
nation
in the
gra
vity
field acrossAsiaand Australia. Created with data
Vom
NASA s
Gravity Recovery and Climate Experiment (GRACE). Image
©
NASA/] PL/
U niversity
of Texas Center for Space Research.
Contents
Preface
page
xi
Acknowledgments
xiii
Mathematical background
1
. 1
Cartesian and spherical coordinates
1
.2
Complex numbers
1
.3
Vector relationships
4
.4
Matrices and tensors
8
.5
Conservative force, field, and potential
17
.6
The divergence theorem (Gauss s theorem)
18
.7
The curl theorem (Stokes theorem)
20
.8
Poisson s
equation
23
.9
Laplace s equation
26
.10
Power series
28
.11
Leibniz s rule
32
.12
Legendre polynomials
32
. 13
The Legendre differential equation
34
.14
Rodrigues
formula
41
.15
Associated Legendre polynomials
43
.16
Spherical harmonic functions
49
1.17
Fourier series, Fourier integrals, and Fourier transforms
52
Further reading
58
Gravitation
59
2.1
Gravitational acceleration and potential
59
2.2
Kepler s laws of planetary motion
60
2.3
Gravitational acceleration and the potential of a solid
sphere
66
2.4
Laplace s equation in spherical polar coordinates
69
2.5
MacCullagh s formula for the gravitational potential
74
Further reading
85
vu
viii Contents
Gravity
86
3.1
The ellipticity of the Earth s figure
86
3.2
The geopotential
88
3.3
The equipotential surface of gravity
91
3.4
Gravity on the reference spheroid
96
3.5
Geocentric and geographic latitude
102
3.6
The
geoid
106
Further reading
115
The tides
116
4.1
Origin of the lunar tide-raising forces
116
4.2
Tidal potential of the Moon
119
4.3
Love s numbers and the tidal deformation
124
4.4
Tidal friction and deceleration of terrestrial and lunar
rotations
130
Further reading
136
Earth s rotation
137
5.1
Motion in a rotating coordinate system
138
5.2
The Coriolis and
Eötvös
effects
140
5.3
Precession and forced nutation of Earth s rotation axis
142
5.4
The free, Eulerian nutation of a rigid Earth
155
5.5
The Chandler wobble
157
Further reading
169
Earth s heat
170
6.1
Energy and entropy
171
6.2
Thermodynamic potentials and Maxwell s relations
172
6.3
The melting-temperature gradient in the core
176
6.4
The adiabatic temperature gradient in the core
178
6.5
The
Grüneisen
parameter
179
6.6
Heat flow
182
Further reading
197
Geomagnetism
198
7.1
The
dipole
magnetic field and potential
198
7.2
Potential of the geomagnetic field
200
7.3
The Earth s
dipole
magnetic field
205
7.4
Secular variation
213
7.5
Power spectrum of the internal field
214
7.6
The origin of the internal field
217
Further reading
225
Foundations of seismology
227
8.1
Elastic deformation
227
Contents ix
8.2
Stress
228
8.3
Strain
233
8.4
Perfectly elastic stress-strain relationships
239
8.5
The seismic wave equation
244
8.6
Solutions of the wave equation
252
8.7
Three-dimensional propagation of plane P-and S-waves
254
Further reading
258
Appendix A Magnetic poles, the
dipole
field, and current loops
259
Appendix
В
Maxwell
s
equations of
electromagnetism
265
References
276
Index
278
|
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| isbn | 9781107005846 9780521183772 |
| language | English |
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| spelling | Lowrie, William 1939- Verfasser (DE-588)173151795 aut A student's guide to geophysical equations William Lowrie Cambridge [u.a.] Cambridge Univ. Press 2011 XIII, 281 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Mathematik Geophysics Mathematics Handbooks, manuals, etc Physics Formulae Handbooks, manuals, etc Geophysik (DE-588)4020252-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Earth Handbooks, manuals, etc Geophysik (DE-588)4020252-5 s Mathematisches Modell (DE-588)4114528-8 s DE-604 http://assets.cambridge.org/97811070/05846/cover/9781107005846.jpg Cover image Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022571543&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022571543&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lowrie, William 1939- A student's guide to geophysical equations Mathematik Geophysics Mathematics Handbooks, manuals, etc Physics Formulae Handbooks, manuals, etc Geophysik (DE-588)4020252-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4020252-5 (DE-588)4114528-8 |
| title | A student's guide to geophysical equations |
| title_auth | A student's guide to geophysical equations |
| title_exact_search | A student's guide to geophysical equations |
| title_full | A student's guide to geophysical equations William Lowrie |
| title_fullStr | A student's guide to geophysical equations William Lowrie |
| title_full_unstemmed | A student's guide to geophysical equations William Lowrie |
| title_short | A student's guide to geophysical equations |
| title_sort | a student s guide to geophysical equations |
| topic | Mathematik Geophysics Mathematics Handbooks, manuals, etc Physics Formulae Handbooks, manuals, etc Geophysik (DE-588)4020252-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Mathematik Geophysics Mathematics Handbooks, manuals, etc Physics Formulae Handbooks, manuals, etc Geophysik Mathematisches Modell Earth Handbooks, manuals, etc |
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