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Spectral Methods in Geodesy and Geophysics [Kõva köide]

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(Ohio State University, Columbus, USA)
  • Formaat: Hardback, 430 pages, kõrgus x laius: 234x156 mm, kaal: 720 g, 97 Illustrations, black and white
  • Ilmumisaeg: 28-Sep-2017
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1482245256
  • ISBN-13: 9781482245257
Teised raamatud teemal:
Spectral Methods in Geodesy and GeophysicsSuurem pilt
  • Formaat: Hardback, 430 pages, kõrgus x laius: 234x156 mm, kaal: 720 g, 97 Illustrations, black and white
  • Ilmumisaeg: 28-Sep-2017
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1482245256
  • ISBN-13: 9781482245257
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781482245257.html
Märksõnad:
The text develops the principal aspects of applied Fourier analysis and methodology with the main goal to inculcate a different way of perceiving global and regional geodetic and geophysical data, namely from the perspective of the frequency, or spectral, domain rather than the spatial domain. The word "methods" in the title is meant to convey that the transformation of a geophysical signal into the spectral domain can be applied for purposes of analysis as well as rapid computation. The text is written for graduate students; however, Chapters 1 through 4 and parts of 5 can also benefit undergraduates who have a solid and fluent knowledge of integral and differential calculus, have some statistical background, and are not uncomfortable with complex numbers. Concepts are developed by starting from the one-dimensional domain and working up to the spherical domain, which is part of every chapter. Many concepts are illustrated graphically with actual geophysical data primarily from signals of gravity, magnetism, and topography.
Dedication v
Preface vii
1 Introduction
1(12)
1.1 Definitions and Notations
1(4)
1.2 Geophysical Motivation
5(2)
1.3 Mathematical Preliminaries
7(5)
1.4 Summary
12(1)
2 Fourier Transforms of Functions on the Continuous Domain
13(69)
2.1 Introduction
13(1)
2.2 Fourier Series
13(9)
2.2.1 Properties of the Fourier Series Transform
18(4)
2.3 The Fourier Integral
22(18)
2.3.1 Properties of the Fourier Integral Transform
26(3)
2.3.2 Rectangle Function
29(4)
2.3.3 Gaussian Function
33(1)
2.3.4 Dirac Delta Function
34(4)
2.3.5 Fourier Transforms Using the Delta Function
38(2)
2.4 Two-Dimensional Transforms in Cartesian Space
40(7)
2.4.1 Two-Dimensional Fourier Series Transform
41(2)
2.4.2 Two-Dimensional Fourier Integral Transform
43(1)
2.4.3 Special Functions in Two Dimensions
44(3)
2.5 The Hankel Transform
47(3)
2.6 Legendre Transforms
50(25)
2.6.1 One-Dimensional Legendre Transform
53(2)
2.6.2 Two-Dimensional Fourier-Legendre Transform
55(5)
2.6.3 Properties of Fourier-Legendre Transforms
60(5)
2.6.4 Vector Spherical Harmonics
65(6)
2.6.5 Cap Function
71(1)
2.6.6 Gaussian Function on the Sphere
72(2)
2.6.7 Spherical Dirac Delta Function
74(1)
2.7 From Sphere to Plane
75(2)
2.8 Examples of Fourier Transform Pairs
77(5)
Exercises
78(4)
3 Convolutions and Windows on the Continuous Domain
82(57)
3.1 Introduction
82(1)
3.2 Convolutions of Non-Periodic Functions
83(6)
3.2.1 Properties of the Convolution
85(3)
3.2.2 Convolutions in Higher Dimensions
88(1)
3.3 Convolutions of Periodic Functions
89(3)
3.4 Convolutions on the Sphere
92(4)
3.5 Filters on the Line, Plane, and Sphere
96(18)
3.5.1 Filter Examples for Profiles and Spherical Signals
101(6)
3.5.2 Bandwidth and Resolution
107(7)
3.6 Window Functions
114(25)
3.6.1 Classical Tapers
115(8)
3.6.2 The Concentration Problem
123(7)
3.6.3 Truncated Convolutions on the Sphere
130(6)
Exercises
136(3)
4 Transforms, Convolutions, and Windows on the Discrete Domain
139(62)
4.1 Introduction
139(2)
4.2 Infinite Sequences
141(14)
4.2.1 Fourier Transforms of Infinite Sequences
141(6)
4.2.2 Discrete Convolutions
147(2)
4.2.3 Aliasing of the Fourier Spectrum
149(6)
4.3 Periodic Sequences
155(13)
4.3.1 Discrete Fourier Transform
156(3)
4.3.2 FFT
159(1)
4.3.3 Properties of the DFT and Higher Dimensions
160(3)
4.3.4 Discrete Cyclic Convolution
163(3)
4.3.5 Aliasing of the Discrete Fourier Spectrum
166(2)
4.4 Cyclic Versus Linear Discrete Convolution
168(8)
4.5 Discrete Functions on the Sphere
176(17)
4.5.1 Aliasing of the Fourier-Legendre Spectrum
181(2)
4.5.2 Spectral Analysis and Synthesis on the Sphere
183(8)
4.5.3 DFT of Convolutions on the Sphere
191(2)
4.6 Discrete Filters and Windows
193(8)
Exercises
198(3)
5 Correlation and Power Spectrum
201(93)
5.1 Introduction
201(2)
5.2 Correlation of Finite-Energy Functions
203(7)
5.3 Correlation of Finite-Power Functions
210(10)
5.4 Correlation of Periodic Functions
220(2)
5.5 Correlation of Functions on the Sphere
222(8)
5.6 Stochastic Processes
230(40)
5.6.1 Probability, Random Variables, and Processes
231(6)
5.6.2 The Statistics of Stochastic Processes
237(6)
5.6.3 The Variogram
243(2)
5.6.4 Non-Periodic Stationary Stochastic Processes
245(8)
5.6.5 Periodic Stochastic Processes
253(5)
5.6.6 Stochastic Processes on the Sphere
258(4)
5.6.7 Coherency
262(7)
5.6.8 Covariances for Discrete Processes
269(1)
5.7 Estimation of the Covariance and PSD
270(24)
5.7.1 Covariance Function Estimation
271(4)
5.7.2 PSD Estimation
275(12)
5.7.3 Spherical Power Spectrum Estimation
287(4)
Exercises
291(3)
6 Applications in Geodesy and Geophysics
294(105)
6.1 Introduction
294(1)
6.2 Spectrum of the Potential Function
295(30)
6.2.1 Potential Function
295(4)
6.2.2 Fourier Spectrum of the Potential
299(5)
6.2.3 Fourier-Legendre Spectrum of the Potential
304(4)
6.2.4 Green's Functions and Their Inverses from Spectral Relationships
308(17)
6.3 Global Spectral Analysis
325(21)
6.3.1 Gravitational Potential Models
326(6)
6.3.1.1 Low-Degree Harmonics as Density Moments
332(3)
6.3.2 Magnetic Field Models
335(4)
6.3.3 Topographic and Isostatic Models
339(7)
6.4 Local Spectral Analysis
346(16)
6.4.1 Power Laws and PSD/Covariance Models
347(6)
6.4.2 Gravity and Topography
353(5)
6.4.3 Poisson's Relationship in the Frequency Domain
358(4)
6.5 Convolutions by FFT
362(20)
6.5.1 Integrals in Physical Geodesy
364(1)
6.5.1.1 Weakly Singular Integral
365(4)
6.5.1.2 Strongly Singular Integral
369(4)
6.5.1.3 Hypersingular Integral
373(2)
6.5.2 Forward Models
375(7)
6.6 Least-Squares Collocation
382(17)
6.6.1 Theoretical Setup
383(3)
6.6.2 Frequency Domain Formulation
386(7)
6.6.3 Example
393(3)
Exercises
396(3)
References 399(8)
Index 407
Christopher Jekeli