NDLI: On the local multiscale determination of the Earth’s disturbing potential from discrete deflections of the vertical

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On the local multiscale determination of the Earth’s disturbing potential from discrete deflections of the vertical

Content Provider	Springer Nature Link
Author	Freeden, W. Schreiner, M. Mayer, C. Fehlinger, T.
Copyright Year	2008
Abstract	As a first approximation, the Earth is a sphere; as a second approximation, it may be considered an ellipsoid of revolution. The deviations of the actual Earth’s gravity field from the ellipsoidal “normal” field are so small that they can be understood to be linear. The splitting of the Earth’s gravity field into a “normal” and a remaining small “disturbing” field considerably simplifies the problem of its determination. Under the assumption of an ellipsoidal Earth model, high observational accuracy is achievable only if the deviation (deflection of the vertical) of the physical plumb line, to which measurements refer, from the ellipsoidal normal is not ignored. Hence, the determination of the disturbing potential from known deflections of the vertical is a central problem of physical geodesy. In this paper, we propose a new, well-promising method for modelling the disturbing potential locally from the deflections of the vertical. Essential tools are integral formulae on the sphere based on Green’s function with respect to the Beltrami operator. The determination of the disturbing potential from deflections of the vertical is formulated as a multiscale procedure involving scale-dependent regularized versions of the surface gradient of the Green function. The modelling process is based on a multiscale framework by use of locally supported surface curl-free vector wavelets.
Ending Page	490
Page Count	18
Starting Page	473
File Format	PDF
ISSN	14200597
e-ISSN	15731499
Journal	Computational Geosciences
Issue Number	4
Volume Number	12
Language	English
Publisher	Springer Netherlands
Publisher Date	2008-05-27
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geotechnical Engineering Hydrogeology Deflections of the vertical Geodesy, mapping problems Potentials, prospecting Local multiscale approximation Earth’s disturbing potential Locally supported (Green’s) vector wavelets Mathematical Modeling and Industrial Mathematics Wavelets and other special systems Soil Science & Conservation
Content Type	Text
Resource Type	Article
Subject	Computers in Earth Sciences Computational Theory and Mathematics Computer Science Applications Computational Mathematics

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