ABSTRACT
In geodesy, geophysics, and many other disciplines dealing with signals of any sort, one very often operates on the signal, not from point to point, but corporately, in terms of a convolution. Many linear systems that have an input and an output can be described as a convolution. Indeed, all linear filters are convolutions. The principal relevant result for spectral analysis is that convolutions of signals in the space or time domain translate into simple products of spectra in the corresponding spectral domain. This means that convolutions may be analyzed very easily if the spectra of the convolved functions are known. Most physical convolution models in geodesy and geophysics are based on a spherical formulation. While the Cartesian approximation may suffice for local applications, analyses that require a global interpretation, or make use of global data, or simply require higher accuracy by accounting for the Earth's curvature, are better expressed in the spherical domain equation.
