Spectral methods in geodesy and geophysics / Спектральные методы в геодезии и геофизике

The genesis of this book is a course first taught to students in Geodetic Science at the Ohio State University soon after the Fast Fourier Transform was introduced to spherical harmonic analysis of the Earth’s gravity field. That was in the 1980s and only a few text books existed that treated the subject from the geophysical viewpoint, specifically with the spatial coordinates as independent variables in two dimensions. The majority of books on Fourier analysis were written strictly with time as the independent variable because spectral analysis originated with and still primarily concerns communications theory and electrical engineering. In geodesy and geophysics the coordinate domain usually is approximated by a sphere, although much can be done by further approximating this domain locally by a plane. Both Cartesian and spherical domains are treated here with equal emphasis. Ellipsoidal spectral analysis, accounting for Earth’s equatorial eccentricity, is not covered since it quickly becomes difficult, if not intractable, for most of the common applicable analytical tools and because the methodology under the spherical approximation is still viable and quite adequate. On the other hand, a basic understanding of concepts for the sphere is most easily obtained by first considering the Cartesian one-dimensional case; and thus each chapter begins in this domain. <...>