Spectral Combination of Vertical and Horizontal Spheroidal Boundary-Value Problems: A Theoretical Study

Abstract The spectral combination method or technique encompasses all procedures to combine heterogeneous datasets by spectral weights, which depend on spherical harmonic degree n . It was initially developed to combine terrestrial gravity data and a global geopotential model optimally to calculate the geoid or quasigeoid. Later on, this technique was extended to combine solutions of spherical geodetic boundary-value problems. It is well-known that the Earth is considerably flattened at the poles, and its shape is closer to a rotational ellipsoid rather than a sphere. Spheroidal formulation provides higher accuracy despite being more complex. This contribution applies the spectral combination method to solutions of vertical and horizontal spheroidal boundary-value problems. For this purpose, we derive the corresponding spectral weights for each solution of vertical and horizontal spheroidal boundary-value problems, as well as for their combination.