This study investigates the spectral weighting and combination of solutions to vertical and horizontal spherical and spheroidal boundary-value problems (BVPs) for downward continuation of satellite gravitational field observations. We derive the integral kernels required for transforming vertical and horizontal components of the disturbing gravitational vector into the radial derivative of disturbing gravitational potential in the spheroidal approximation. The methods are tested in a closed-loop numerical experiment over Greenland using synthetic data generated from EGM2008 and contaminated with the Gaussian noise. The results show that the vertical component of the disturbing gravitational vector provides the most accurate input for downward continuation in both geometries. The spherical vertical-only estimator yields the best fit for the disturbing potential and its radial derivative. However, normalized standard deviation (NSTD) analysis reveals that the spheroidal approximation results in consistently smaller relative errors for the radial derivative, indicating a modest but systematic benefit when modelling quantities with strong dependence on Earth’s ellipticity.

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Comparison of Spectral Combination of Solutions to Vertical and Horizontal Spherical and Spheroidal Boundary-Value Problems: A Theoretical Study

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

摘要

This study investigates the spectral weighting and combination of solutions to vertical and horizontal spherical and spheroidal boundary-value problems (BVPs) for downward continuation of satellite gravitational field observations. We derive the integral kernels required for transforming vertical and horizontal components of the disturbing gravitational vector into the radial derivative of disturbing gravitational potential in the spheroidal approximation. The methods are tested in a closed-loop numerical experiment over Greenland using synthetic data generated from EGM2008 and contaminated with the Gaussian noise. The results show that the vertical component of the disturbing gravitational vector provides the most accurate input for downward continuation in both geometries. The spherical vertical-only estimator yields the best fit for the disturbing potential and its radial derivative. However, normalized standard deviation (NSTD) analysis reveals that the spheroidal approximation results in consistently smaller relative errors for the radial derivative, indicating a modest but systematic benefit when modelling quantities with strong dependence on Earth’s ellipticity.