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Techniques for Geoid Determination
Published in Petr Vaníček, Nikolaos T. Christou, GEOID and Its GEOPHYSICAL INTERPRETATIONS, 2020
is still the most important formula of physical geodesy. It enables the computation of the geometric quantity N (geoidal undulation) from the gravity anomaly (Δg). R is the mean surface radius of the Earth, γ is the mean surface gravity, and the integration is carried out over the unit sphere (σ). Stokes’ kernel function S(ψ) can be written as a series of Legendre’s polynomials Pn (cosψ): () S(ψ)=∑n=2∞2n+1n−1Pn(cosψ)
Geodesy Fundamentals
Published in Julio Sanchez, Maria P. Canton, William Perrizo, Space Image Processing, 2018
Julio Sanchez, Maria P. Canton
Geodesy is an applied field of physical geography that relates to the size and shape of the earth and to measurements on its surface. It is usually divided into two parts: geometrical geodesy and physical geodesy. The second one, physical geodesy, relates to the gravity fields of the earth and how these fields affect its shape. In the following discussion we ignore physical geodesy and concentrate on the earth’s shape and measurement.
Geoid determination using band limited airborne horizontal gravimetric data
Published in Journal of Spatial Science, 2022
Kailiang Deng, Guobin Chang, Motao Huang, Huaien Zeng, Xin Chen
Improving the precision of geoid determination is one of the most important applications of airborne gravimetric data. In data processing of the gravimetric data at the specific flying height to the geoidal undulations at the geoid, certain kinds of downward continuation are involved; and hence, special attention should be paid to the numerical errors in solving this ill-posed problem. In this paper, the general band-limited horizontal boundary value problem is formulated and an approach, called the one-step approach, is proposed to solve this problem in the framework of the boundary value theory of physical geodesy. The numerical instability problem is effectively fixed by the proposed approach and the efficacy is validated by numerical examples using the EGM2008 model.