## Abstract

According to definition of the Stokes-Helmert method of geoid determination by Vaníček and Martinec (1994), and Vaníček et al. (1999), the fundamental formula of physical geodesy is formulated at the physical surface of the Earth in the Helmert space. To minimize the primary indirect effect on the geoidal heights, the second Helmert’s technique of condensation is used, where the topographical and atmospheric masses are redistributed directly onto the geoid surface as a single spherical condensation layer (Helmert, 1884; Lambert, 1930; Heck, 1993; Martinec et al., 1993). Thereby, the inverse Dirichlet’s boundary value problem and Stokes’ (1849) boundary value problem are solved in the Helmert space. Problematic aspects of the inverse solution to Dirichlet’s problem in the Helmert space have been discussed from a different point of view recently by Heck (2003), and Jekeli and Serpas (2003). To avoid this problem, the Stokes-Helmert method is reformulated so that, the inverse Dirichlet’s problem is solved in the No Topography space (Vaníček et al., 2004). After obtaining the geoid-generated gravity anomalies on the geoid surface, the primary indirect effect is minimized solving Stokes’ problem in the Helmert space. This method has been used by Tenzer and Vaníček (2003) for a determination of the geoid at the territory of the Canadian Rocky Mountains. Principially the same approach was introduced before by Pellinen (1962) and later discussed by Moritz (1968). This paper focuses on theoretical aspects of the above method.

Translated title of the contribution | On numerical aspects of Stokes-Helmert method of geoid determination formulated for the no topography space |
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Original language | Italian |

Pages (from-to) | 213-226 |

Number of pages | 14 |

Journal | Bollettino di Geodesia e Scienze Affini |

Volume | 63 |

Issue number | 3 |

Publication status | Published - 2004 |

Externally published | Yes |

## Keywords

- Boundary value problem
- Downward continuation
- Geoid
- Gravity

## ASJC Scopus subject areas

- Engineering(all)