Far-zone contributions to the gravity field quantities by means of Molodensky’s truncation coefficients
Source: Studia Geophysica et Geodaetica, Volume 53, Number 2, April 2009 , pp. 157-167(11)
Abstract:To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric geoid/quasigeoid modelling, the surface domain of Green’s integrals is subdivided into the near-zone and far-zone integration sub-domains. The inversion is performed for the near zone using regional detailed gravity data. The farzone contributions to the gravity field quantities are estimated from an available global geopotential model using techniques for a spherical harmonic analysis of the gravity field. For computing the far-zone contributions by means of Green’s integrals, truncation coefficients are applied. Different forms of truncation coefficients have been derived depending on a type of integrals in solving various geodetic boundary-value problems. In this study, we utilise Molodensky’s truncation coefficients to Green’s integrals for computing the far-zone contributions to the disturbing potential, the gravity disturbance, and the gravity anomaly. We also demonstrate that Molodensky’s truncation coefficients can be uniformly applied to all types of Green’s integrals used in solving the boundaryvalue problems. The numerical example of the far-zone contributions to the gravity field quantities is given over the area of study which comprises the Canadian Rocky Mountains. The coefficients of a global geopotential model and a detailed digital terrain model are used as input data.
Document Type: Research Article
Affiliations: 1: Faculty of Aerospace Engineering, Physical and Space Geodesy (PSG), Delft University of Technology, Kluyverweg 1, 2629 HS, Delft, The Netherlands, Email: R.Tenzer@tudelft.nl 2: Department of Mathematics, University of Western Bohemia, 306 14, Plzeň, Czech Republic 3: Faculty of Aerospace Engineering, Physical and Space Geodesy (PSG), Delft University of Technology, Kluyverweg 1, 2629 HS, Delft, The Netherlands 4: Department of Civil Engineering, Tallinn University of Technology, Ehitajate tee 5, 19086, Tallinn, Estonia 5: Geophysical Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 28, Bratislava, Slovak Republic
Publication date: April 1, 2009