ABSTRACT
This chapter offers a sampling of applications in geodesy and geophysics where spectral methods find utility, either in the interpretation of signals, including simply constructing useful physical models in the spectral domain, or in facilitating numerical computation associated with convolutions or correlations. Of the many physical attributes of the Earth that geophysicists use to study the Earth's interior, the gravitational and magnetostatic fields offer a global view of the internal structure at many different scales. Many problems in physical geodesy involve integrals of the gravitational potential or its derivatives. The most famous are the Stokes and Pizzetti formulas that combine gravity anomalies on the geoid with Stokes's function to yield the geoid undulation and disturbing potential, respectively. The external field, due to electric currents in the ionosphere and magnetosphere, is highly variable in time, depending on the influence of solar radiation that also changes daily with Earth's rotation.
