The ellipsoidal correction to the Stokes kernel for precise geoid determination

Solving the geodetic boundary-value problem (GBVP) for the precise determination of the geoid requires proper use of the fundamental equation of physical geodesy as the boundary condition given on the geoid. The Stokes formula and kernel are the result of spherical approximation of this fundamental equation, which is a violation of the proper relation between the observed quantity (gravity anomaly) and the sought function (geoid). The violation is interpreted here as the improper formulation of the boundary condition, which implies the spherical Stokes kernel to be in error compared with the proper kernel of integral transformation. To remedy this error, two correction kernels to the Stokes kernel were derived: the first in both closed and spectral forms and the second only in spectral form. Contributions from the first correction kernel to the geoid across the globe were [−0.867 m, +1.002 m] in the low-frequency domain implied by the GRIM4-S4 purely satellite-derived geopotential model. It is a few centimeters, on average, in the high-frequency domain with some exceptions of a few meters in places of high topographical relief and sizable geological features in accordance with the EGM96 combined geopotential model. The contributions from the second correction kernel to the geoid are [−0.259 m, +0.217 m] and [−0.024 m, +0.023 m] in the low- and high-frequency domains, respectively.     

Ellipsoidal Neumann geodetic boundary-value problem based on surface gravity disturbances: case study of Iran

An ellipsoidal Neumann type geodetic boundary-value problem (GBVP) for the computation of disturbing potential on the surface of the Earth based on the surface gravity disturbance as the boundary data is formulated. The solution methodology of the GBVP can be algorithmically summarized as follows: (i) using global navigation satellite systems (GNSS) coordinates of the gravity stations, the surface gravity disturbances are generated as the boundary data. (ii) Applying the deflection correction to the gravity disturbances to arrive at the derivative of the surface disturbing potential along the ellipsoidal normal. (iii) Removing the low frequencies part of the gravity field using harmonic expansion to degree and order 110. (iv) Using the short wavelength part of the corrected gravity disturbances derived in the previous section as the boundary data within the constructed GBVP to derive the short wavelength disturbing potential over the Earth surface. (v) The computed shortwave length signals of disturbing potentials are converted to disturbing potential values by restoring the removed effects.