The spectral response of Stokes’s integral to modification and truncation

In this paper, we study the spectral response of Stokes’s integral, which is determined by its modification and truncation. Two spectrally modified Stokes’s kernel functions are selected and compared to the unmodified Stokes’s kernel in terms of the spectral transfer coefficient effectiveness. Stokes’s integral is truncated at four spherical cap sizes with spherical radii ψ0 = 1◦,3◦,6◦,9◦. The results suggest that the unmodified Stokes’s integral is spectrally unstable when being arbitrarily truncated, and a modification to Stokes‘s kernel is required for a smooth geoid model.