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.

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

  • Martin Pitoňák,
  • Jiří Belinger,
  • Pavel Novák,
  • Michal Šprlák

摘要

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.