TY - INPR
A1 - Freeden, Willi
A1 - Fehlinger, Thomas
A1 - Mayer, Carsten
A1 - Schreiner, Michael
T1 - On the Local Multiscale Determination of the Earth`s Disturbing Potential From Discrete Deflections of the Vertical
N2 - 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 of 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.
T3 - Schriften zur Funktionalanalysis und Geomathematik - 32
KW - Earth's disturbing potential
KW - deflections of the vertical
KW - locally supported (Green's) vector wavelets
KW - local multiscale
Y1 - 2007
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1947
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-15228
ER -