The role of two-point functions in geodesy and their classification

In geodesy, two-point functions appear as covariance functions, convolution kernels like the Green functions, transfer functions of the gravity field functionals and filter kernels. Knowledge of their structure both in the spatial and the spectral domains opens vistas not only for understanding their behaviour, but also enabling their design. Here, we develop the two-point functions in terms of spherical harmonic functions and discuss their structure. We identify homogeneity and isotropy as the two key structural properties of the two-point functions that provide a solid basis for their classification.