A surface spherical harmonic expansion of gravity anomalies with respect to a geodetic reference ellipsoid can be used to model the global gravity field and reveal its spectral properties. In this paper, a direct and rigorous transformation between solid spherical harmonic coefficients of the Earth’s disturbing potential and surface spherical harmonic coefficients of gravity anomalies in ellips...

The tube method or the volume-of-tube approximates tail probability of maximum a smooth Gaussian random field with zero mean and unit variance. This evaluates volume spherical about index set, then transforms it to probability. In this study, we generalize case in which variance is not constant. We provide formula for non-constant radius terms curvature tensors, inhomogeneous variance, as well ...