Ellipsoidal geoidal undulations (ellipsoidal Bruns formula): case studies

  title={Ellipsoidal geoidal undulations (ellipsoidal Bruns formula): case studies},
  author={Alireza Azmoudeh Ardalan and Erik W. Grafarend},
  journal={Journal of Geodesy},
Abstract. The Bruns formula is presented in its nonlinear form for any type of reference fields and reference equipotential surfaces. The classical Bruns formula is derived from the reference field of the first term of spherical harmonic expansion (w=gm/r) based on the reference equipotential sphere Sr02 of radius r0=gm/W0. W0 is the potential value of the Gauss–Listing geoid. Four reference fields of ellipsoidal type, namely (1) the first term of ellipsoidal (spheroidal) harmonic expansion of… Expand
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