NDLI: Estimation of the normal Eötvös matrix for low geometric heights

Content Provider	Springer Nature Link
Author	Manoussakis, Gerassimos
Copyright Year	2013
Abstract	The normal Eötvös matrix is a three dimensional symmetric matrix. Its elements are the second order partial derivatives of the normal potential, expressed in a local Cartesian coordinate system. With the help of the Eötvös matrix it is possible to determine the variation of the normal gravity vector locally around a point P. In addition, the Eötvös matrix contains information about equipotential surfaces and the curvature of the plumbline. In this work we present a method to estimate the elements of the Eötvös matrix at an arbitrary point P above the ellipsoid, whose geometrical height is low. Under this condition, it is shown that the second order partial derivatives of the normal potential vary linearly along the line vertical to the ellipsoid and passing through P. It is worth mentioning that the proposed method to estimate the elements of the Eötvös matrix is much simpler than by following the definition of the matrix. In addition, it will be shown that if Q is the projection of P along the plumbline to the ellipsoid, then the values of the Eötvös matrix elements at point P are strongly related with plumbline curvature and the principal curvatures at Q. Finally, simple relations about plumbline curvature and the gradient of the normal gravity vector at point P will be presented.
Starting Page	179
Ending Page	189
Page Count	11
File Format	PDF
ISSN	22135812
Journal	Acta Geodaetica et Geophysica Hungarica
Volume Number	48
Issue Number	2
e-ISSN	22135820
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-04-04
Publisher Institution	Quarterly of the Hungarian Academy of Sciences
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Plumbline curvature Normal potential Normal gravity Geophysics/Geodesy Eötvös matrix
Content Type	Text
Resource Type	Article
Subject	Building and Construction Geology Geophysics

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