The spheroidal fixed-free two-boundary-value problem for geoid determination (the spheroidal Bruns' transform)

The target of the spheroidal Gauss-Listing geoid determination is presented as a solution of the spheroidal fixed-free two-boundary value problem based on a spheroidal Bruns' transformation ("spheroidal Bruns' formula"). The nonlinear spheroidal Bruns' transform (nonlinear spheroidal Bruns' formula)? the spheroidal fixed part and the spheroidal free part of the two-boundary value problem are derived. Four different spheroidal gravity models are treated, in particular to determine whether they pass the test to fit to the postulate of a level ellipsoidal gravity field, namely of Somigliana-Pizzetti type.