Downward continuation and geoid determination based on band-limited airborne gravity data |
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Authors: | P Novák B Heck |
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Institution: | (1) Department of Geomatics Engineering, The University of Calgary, 2500 University Drive NW, Calgary, Canada T2N 1N4 e-mail: pnovak@ucalgary.ca; Tel.: +1 403 220 8794; Fax: +1 403 284 1980, CA;(2) Geodetic Institute, University of Karlsruhe, Englerstrasse 7, 76128 Karlsruhe, Germany e-mail: heck@gik.uni-karlsruhe.de; Tel.: +49 721 608 3674; Fax:+49 721 608 6808, DE |
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Abstract: | The downward continuation of the harmonic disturbing gravity potential, derived at flight level from discrete observations
of airborne gravity by the spherical Hotine integral, to the geoid is discussed. The initial-boundary-value approach, based
on both the direct and inverse solution to Dirichlet's problem of potential theory, is used. Evaluation of the discretized
Fredholm integral equation of the first kind and its inverse is numerically tested using synthetic airborne gravity data.
Characteristics of the synthetic gravity data correspond to typical airborne data used for geoid determination today and in
the foreseeable future: discrete gravity observations at a mean flight height of 2 to 6 km above mean sea level with minimum
spatial resolution of 2.5 arcmin and a noise level of 1.5 mGal. Numerical results for both approaches are presented and discussed.
The direct approach can successfully be used for the downward continuation of airborne potential without any numerical instabilities
associated with the inverse approach. In addition to these two-step approaches, a one-step procedure is also discussed. This
procedure is based on a direct relationship between gravity disturbances at flight level and the disturbing gravity potential
at sea level. This procedure provided the best results in terms of accuracy, stability and numerical efficiency. As a general
result, numerically stable downward continuation of airborne gravity data can be seen as another advantage of airborne gravimetry
in the field of geoid determination.
Received: 6 June 2001 / Accepted: 3 January 2002 |
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Keywords: | : Downward continuation – Airborne Gravimetry – Geoid – Band-limited Gravity |
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