1st Edition

Spectral Methods in Geodesy and Geophysics




ISBN 9781482245257
Published September 28, 2017 by CRC Press
430 Pages 97 B/W Illustrations

USD $220.00

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Book Description

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.

Table of Contents

Preface

Introduction
Definitions and Notations
Geophysical Motivation
Summary

Fourier Transforms of Functions on the Continuous Domain
Introduction
Fourier Series
The Fourier Integral
Two-Dimensional Transforms in Cartesian Space
The Hankel Transform
Legendre Transforms
From Sphere to Plane
Examples of Fourier Transform Pairs

Convolutions and Windows on the Continuous Domain
Introduction
Convolutions of Non-Periodic Functions
Convolutions of Periodic Functions
Convolutions on the Sphere
Filters on the Line, Plane, and Sphere
Window Functions

Transforms, Convolutions, and Windows on the Discrete Domain
Introduction
Infinite Sequences
Periodic Sequences
Cyclic Versus Linear Discrete Convolution
Discrete Functions on the Sphere
Discrete Filters and Windows

Correlation and Power Spectrum
Introduction
Correlation of Finite-Energy Functions
Correlation of Finite-Power Functions
Correlation of Periodic Functions
Correlation of Functions on the Sphere
Stochastic Processes
Estimation of the Covariance and PSD

Applications in Geodesy and Geophysics
Introduction
Spectrum of the Potential Function
Global Spectral Analysis
Local Spectral Analysis
Convolutions by FFT
Least-Squares Collocation

References
Exercises

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Author(s)

Biography

Christopher Jekeli