Spectral Methods in Geodesy and Geophysics

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 correspon [...]
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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.