Jekeli Spectral Methods in Geodesy and Geophysics

1. Auflage 2017
ISBN: 978-1-4822-4526-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 430 Seiten

The purpose of the book is to provide a rigorous treatment of spectral analysis using Fourier-based techniques in the geosciences, specifically geodesy and geophysics that deal with global and regional spatial data. The basic motivation is to get students to think about spatial data in the corresponding spectral domain. As such, the book emphasizes spatial-frequency analysis for data on the plane and sphere. Most books in spectral analysis develop the topic for time signals and are oriented to electrical and communications engineering. There are very few books for the spatial domain, which develop methods in two dimensions on the plane or the sphere for geodetic and geophysical applications. In the modern era of satellite remote sensing, these techniques are particularly important, as space-borne sensors generate global data (gravity, magnetics, topography, sea level, etc.). The proposed book includes applications to stochastic processes on the plane and sphere, which are important for many estimation problems that are based on some kind of stochastic constraints in inverse theory. There is a final chapter that briefly outlines wavelet analysis. Although a bit outside the scope, it is included to illustrate the contrast to traditional spectral analysis, going more toward a time-frequency analysis. For example, some applications such as wavelet-denoising, as opposed to low-pass filtering, are considered important supplements to the usual spectral methods.

This book does not compete with the plethora of recent books on Spatial Data Analysis, which typically do not develop methods in the spectral domain. There are a few books on spectral methods in geophysics (none in geodesy) with which this book might compete. However, those books tend to emphasize specific applications, such as seismology or meteorology, rather than more general spatial signals on the plane and sphere. What this proposed book offers is more fundamental in this respect, and thus offers unique perspective for students in the geosciences.

Autoren/Hrsg.

Jekeli, Christopher

Fachgebiete

• Geowissenschaften Geologie Geophysik
• Mathematik | Informatik Mathematik Mathematik Allgemein Zahlensysteme
• Geowissenschaften Geologie Geologie

Inhaltsverzeichnis

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