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El. knyga: Advanced Geodynamics: The Fourier Transform Method

(University of California, San Diego)
  • Formatas: EPUB+DRM
  • Išleidimo metai: 27-Jan-2022
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781009021494
Kitos knygos pagal šią temą:
Advanced Geodynamics: The Fourier Transform MethodDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Išleidimo metai: 27-Jan-2022
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781009021494
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David Sandwell developed this advanced textbook over a period of nearly 30 years for his graduate course at Scripps Institution of Oceanography. The book augments the classic textbook Geodynamics by Don Turcotte and Jerry Schubert, presenting more complex and foundational mathematical methods and approaches to geodynamics. The main new tool developed in the book is the multi-dimensional Fourier transform for solving linear partial differential equations. The book comprises nineteen chapters, including: the latest global data sets; quantitative plate tectonics; plate driving forces associated with lithospheric heat transfer and subduction; the physics of the earthquake cycle; postglacial rebound; and six chapters on gravity field development and interpretation. Each chapter has a set of student exercises that make use of the higher-level mathematical and numerical methods developed in the book. Solutions to the exercises are available online for course instructors, on request.

Recenzijos

'Advanced Geodynamics brings the unique perspective of a leading geophysicist to the solution of a wide array of problems in geodynamics. The approach emphasizes the use of advanced mathematics, in particular the Fourier transform, to obtain a quantitative understanding of the processes involved in shaping the Earth's surface. The advanced mathematical approach not only enhances the elegance of the solutions, but it enables the consideration of many problems not accessible with less sophisticated mathematical methods. The choice of problems benefits from the deep physical insights of the author to their solutions. The book discusses the physical processes involved in plate tectonics and the earthquake cycle and provides the latest relevant observational data sets. An emphasis is also placed on the use of gravity data to learn about these processes. The book is the product of decades of teaching by the author and is a must read for students of the physics of the Earth with the appropriate mathematical background.' Gerald Schubert, University of California, Los Angeles; co-author of Geodynamics 'Most authors would find writing a sequel to Turcotte and Schubert's classic book on Geodynamics a daunting task. Not so for David Sandwell, whose first book is a wonderful mix of observations and theory, elegant mathematics and a focus on the oceans and the Fourier method which together help illuminate some of the fundamental physical processes that underlie plate tectonics.' Tony Watts, University of Oxford; author of Isostasy and Flexure of the Lithosphere 'Advanced Geodynamics: The Fourier Transform Method by David Sandwell is a godsend for advanced undergraduate students, graduate students, and researchers actively engaged in the broad area of geodynamics. It complements the classic Geodynamics book by Turcotte & Schubert in a way nothing else could: by elevating the treatment to real, cutting-edge research problems via Fourier transforms that deliver simple and elegant solutions to complicated science problems.' Paul Wessel, University of Hawaii

Daugiau informacijos

Augments and extends the classic textbook Geodynamics by Turcotte and Schubert, presenting more complex and foundational math approaches.
Introduction 1(8)
1 Observations Related to Plate Tectonics
9(13)
1.1 Global Maps
9(11)
1.2 Exercises
20(2)
2 Fourier Transform Methods in Geophysics
22(16)
2.1 Introduction
22(1)
2.2 Definitions of Fourier Transforms
23(1)
2.3 Fourier Sine and Cosine Transforms
24(1)
2.4 Examples of Fourier Transforms
25(3)
2.5 Properties of Fourier Transforms
28(3)
2.6 Solving a Linear PDE Using Fourier Methods and the Cauchy Residue Theorem
31(3)
2.7 Fourier Series
34(1)
2.8 Exercises
35(3)
3 Plate Kinematics
38(11)
3.1 Plate Motions on a Flat Earth
38(1)
3.2 Triple Junction
38(4)
3.3 Plate Motions on a Sphere
42(3)
3.4 Velocity Azimuth
45(1)
3.5 Recipe for Computing Velocity Magnitude
46(1)
3.6 Triple Junctions on a Sphere
46(1)
3.7 Hot Spots and Absolute Plate Motions
47(1)
3.8 Exercises
47(2)
4 Marine Magnetic Anomalies
49(13)
4.1 Introduction
49(1)
4.2 Crustal Magnetization at a Spreading Ridge
49(3)
4.3 Uniformly Magnetized Block
52(1)
4.4 Anomalies in the Earth's Magnetic Field
53(1)
4.5 Magnetic Anomalies Due to Seafloor Spreading
54(6)
4.6 Discussion
60(1)
4.7 Exercises
61(1)
5 Cooling of the Oceanic Lithosphere
62(23)
5.1 Introduction
62(5)
5.2 Temperature versus Depth and Age
67(1)
5.3 Heat Flow versus Age
68(1)
5.4 Thermal Subsidence
69(4)
5.5 The Plate Cooling Model
73(5)
5.6 Buoyancy of the Cooling Lithosphere
78(2)
5.7 Exercises
80(5)
6 A Brief Review of Elasticity
85(6)
6.1 Stress
85(1)
6.2 Strain
86(1)
6.3 Stress versus Strain
86(1)
6.4 Principal Stress and Invariants
87(2)
6.5 Principal Stress and Strain
89(1)
6.6 Exercises
90(1)
7 Crustal Structure, Isostasy, Swell Push Force, and Rheology
91(22)
7.1 Introduction
91(1)
7.2 Oceanic Crustal Structure
92(1)
7.3 Continental Crustal Structure
93(1)
7.4 Vertical Force Balance: Isostasy
94(3)
7.5 Horizontal Force Balance: Swell Push Force
97(4)
7.6 Rheology of the Lithosphere
101(10)
7.7 Exercises
111(2)
8 Flexure of the Lithosphere
113(11)
8.1 Constant Flexural Rigidity, Line Load, No End Load
114(4)
8.2 Variable Flexural Rigidity, Arbitrary Line Load, No End Load
118(3)
8.3 Stability of Thin Elastic Plate under End Load
121(1)
8.4 Exercises
122(2)
9 Flexure Examples
124(21)
9.1 Seamounts
124(5)
9.2 Trenches
129(8)
9.3 Fracture Zone
137(4)
9.4 Exercises
141(4)
10 Elastic Solutions for Strike-Slip Faulting
145(24)
10.1 Interseismic Strain Buildup
145(10)
10.2 Geodetic Moment Accumulation Rate
155(3)
10.3 Inclined Fault Plane
158(3)
10.4 Matlab Examples
161(2)
10.5 Exercises: Response of an Elastic Half Space to a 3-D Vector Body Force
163(6)
11 Heat Flow Paradox
169(8)
11.1 Heat Flow Paradox
169(4)
11.2 Seismic Moment Paradox
173(3)
11.3 Exercises
176(1)
12 The Gravity Field of the Earth, Part 1
177(12)
12.1 Introduction
177(3)
12.2 Global Gravity
180(7)
12.3 Exercises
187(2)
13 Reference Earth Model: WGS84
189(6)
13.1 Some Definitions
189(2)
13.2 Disturbing Potential and Geoid Height
191(1)
13.3 Reference Gravity and Gravity Anomaly
192(1)
13.4 Free-Air Gravity Anomaly
193(1)
13.5 Summary of Anomalies
193(2)
14 Laplace's Equation in Spherical Coordinates
195(8)
14.1 Introduction
195(1)
14.2 Spherical Harmonics
195(3)
14.3 Laplace's Equation
198(1)
14.4 Earth's Gravity Field
199(3)
14.5 Exercises
202(1)
15 Laplace's Equation in Cartesian Coordinates and Satellite Altimetry
203(18)
15.1 Solution to Laplace's Equation
203(3)
15.2 Derivatives of the Gravitational Potential
206(3)
15.3 Geoid Height, Gravity Anomaly, and Vertical Gravity Gradient from Satellite Altimeter Profiles
209(6)
15.4 Vertical Deflections from Along-Track Slopes
215(5)
15.5 Exercises
220(1)
16 Poisson's Equation in Cartesian Coordinates
221(10)
16.1 Solution to Poisson's Equation
221(3)
16.2 Gravity Due to Seafloor Topography: Approximate Formula
224(1)
16.3 Gravity Anomaly from a 3-D Density Model
224(1)
16.4 Computation of Geoid Height and Gravity Anomaly
225(1)
16.5 Gravity Anomaly for a Slab: Bouguer Anomaly
226(1)
16.6 Gravity Anomaly from Topography: Parker's Exact Formula
227(3)
16.7 Exercises
230(1)
17 Gravity/Topography Transfer Function and Isostatic Geoid Anomalies
231(13)
17.1 Introduction
231(1)
17.2 Flexure Theory
231(3)
17.3 Gravity/Topography Transfer Function
234(1)
17.4 Geoid/Topography Transfer Function
235(1)
17.5 Isostatic Geoid Anomalies
236(2)
17.6 Geoid Height for Plate Cooling Model
238(2)
17.7 Isostatic Geoid and the Swell Push Force
240(2)
17.8 Exercises
242(2)
18 Postglacial Rebound
244(9)
18.1 Introduction and Dimensional Analysis
244(1)
18.2 Exact Solution
245(3)
18.3 Elastic Plate over a Viscous Half Space
248(4)
18.4 Exercises
252(1)
19 Driving Forces of Plate Tectonics
253(9)
19.1 Introduction
253(1)
19.2 Age of Subducting Lithosphere
254(2)
19.3 Forces due to Phase Changes
256(1)
19.4 Forces due to Thermal Buoyancy
256(2)
19.5 Asthenospheric Drag Force
258(1)
19.6 Discussion: Relative Magnitudes of Forces
259(1)
19.7 Exercises
260(2)
Bibliography 262(6)
Index 268
David T. Sandwell is a Professor of Geophysics at Scripps Institution of Oceanography, University of California San Diego. His research is focused on marine tectonics and geodynamics, and he develops global marine gravity and topography models from satellite altimetry and ship soundings. He is author of more than 190 research papers. He is a Fellow of Geological Society of America, the American Geophysical Union, the American Association for the Advancement of Science, and a member of the US National Academy of Sciences.
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