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  • 1.
    Eshagh, Mehdi
    University West, Department of Engineering Science, Division of Computer, Electrical and Surveying Engineering.
    Non-singular expressions for vector and gradient tensor of gravitation in a geocentric spherical frame2008In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 34, no 12, p. 1762-1768Article in journal (Refereed)
    Abstract [en]

    The traditional expressions of the gravitational vector (GV) and the gravitational gradient tensor (GGT) have complicated forms depending on the first- and the second-order derivatives of associated Legendre functions (ALF), and also singular terms when approaching the poles. This article presents alternative expressions for the GV and GGT, which are independent of the derivatives, and are also non-singular. By using such expressions, it suffices to compute the ALF to two additional degrees and orders, instead of computing the first and the second derivatives of all the ALF. Therefore, the formulas are suitable for computer programming. Matlab software as well as an output of a numerical computation around the North Pole is also presented based on the derived formulas.

  • 2.
    Novak, Pavel
    et al.
    University of West Bohemia, NTIS–New Technologies for Information Society, Faculty of Applied Sciences, Univerzitní 22, 30614 Plzeň, .
    Tenzer, Robert
    University of Otago, National School of Surveying, Division of Sciences, 310 Castle Street, Dunedin, New Zealand.
    Eshagh, Mehdi
    Royal Institute of Technology, Division of Geodesy and Geoinformatics,.
    Bagherbandi, Mohammad
    Royal Institute of Technology, Division of Geodesy and Geoinformatics,.
    Evaluation of gravitational gradients generated by Earth's crustal structures2013In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 51, p. 22-33Article in journal (Refereed)
    Abstract [en]

    Spectral formulas for the evaluation of gravitational gradients generated by upper Earth's mass components are presented in the manuscript. The spectral approach allows for numerical evaluation of global gravitational gradient fields that can be used to constrain gravitational gradients either synthesised from global gravitational models or directly measured by the spaceborne gradiometer on board of the GOCE satellite mission. Gravitational gradients generated by static atmospheric, topographic and continental ice masses are evaluated numerically based on available global models of Earth's topography, bathymetry and continental ice sheets. CRUST2.0 data are then applied for the numerical evaluation of gravitational gradients generated by mass density contrasts within soft and hard sediments, upper, middle and lower crust layers. Combined gravitational gradients are compared to disturbing gravitational gradients derived from a global gravitational model and an idealised Earth's model represented by the geocentric homogeneous biaxial ellipsoid GRS80. The methodology could be used for improved modelling of the Earth's inner structure.

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