Determination of the Boundary Values for the Stokes-Helmert Problem

The definition of the mean Helmert anomaly is reviewed and the theoretically correct procedure for computing this quantity on the Earth's surface and on the Helmert co-geoid is suggested. This includes a discussion of the role of the direct topographical and atmospherical effects, primary and s...

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Main Authors: Huang, J., Novak, P., Martinec, Z., Featherstone, Will, Vanicek, P., Pagiatakis, S., Veronneau, M.
Format: Journal Article
Published: Springer - Verlag 1999
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/29922
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author Huang, J.
Novak, P.
Martinec, Z.
Featherstone, Will
Vanicek, P.
Pagiatakis, S.
Veronneau, M.
author_facet Huang, J.
Novak, P.
Martinec, Z.
Featherstone, Will
Vanicek, P.
Pagiatakis, S.
Veronneau, M.
author_sort Huang, J.
building Curtin Institutional Repository
collection Online Access
description The definition of the mean Helmert anomaly is reviewed and the theoretically correct procedure for computing this quantity on the Earth's surface and on the Helmert co-geoid is suggested. This includes a discussion of the role of the direct topographical and atmospherical effects, primary and secondary indirect topographical and atmospherical effects, ellipsoidal corrections to the gravity anomaly, its downward continuation and other effects. For the rigorous derivations it was found necessary to treat the gravity anomaly systematically as a point function, defined by means of the fundamental gravimetric equation. It is this treatment that allows one to formulate the corrections necessary for computing the `one-centimetre geoid'. Compared to the standard treatment, it is shown thata `correction for the quasigeoid-to-geoid separation', amounting to about 3 cm for our area of interest, has to be considered. It is also shown that the `secondary indirect effect' has to be evaluated at the topography rather than at the geoid level. This results in another difference of the order of several centimetres in the area of interest. An approach is then proposed for determining the mean Helmert anomalies from gravity data observed on the Earth's surface. This approach is based on the widely-held belief that complete Bouguer anomalies are generally fairly smooth and thus particularly useful for interpolation, approximation and averaging. Numerical results from the Canadian Rocky Mountains for all the corrections as well as the downward continuation are shown.
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publishDate 1999
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spelling curtin-20.500.11937-299222018-03-29T09:08:37Z Determination of the Boundary Values for the Stokes-Helmert Problem Huang, J. Novak, P. Martinec, Z. Featherstone, Will Vanicek, P. Pagiatakis, S. Veronneau, M. Precise geoid determinations Gravity - anomaly Geodetic boundary value problem - Downward continuation of gravity The definition of the mean Helmert anomaly is reviewed and the theoretically correct procedure for computing this quantity on the Earth's surface and on the Helmert co-geoid is suggested. This includes a discussion of the role of the direct topographical and atmospherical effects, primary and secondary indirect topographical and atmospherical effects, ellipsoidal corrections to the gravity anomaly, its downward continuation and other effects. For the rigorous derivations it was found necessary to treat the gravity anomaly systematically as a point function, defined by means of the fundamental gravimetric equation. It is this treatment that allows one to formulate the corrections necessary for computing the `one-centimetre geoid'. Compared to the standard treatment, it is shown thata `correction for the quasigeoid-to-geoid separation', amounting to about 3 cm for our area of interest, has to be considered. It is also shown that the `secondary indirect effect' has to be evaluated at the topography rather than at the geoid level. This results in another difference of the order of several centimetres in the area of interest. An approach is then proposed for determining the mean Helmert anomalies from gravity data observed on the Earth's surface. This approach is based on the widely-held belief that complete Bouguer anomalies are generally fairly smooth and thus particularly useful for interpolation, approximation and averaging. Numerical results from the Canadian Rocky Mountains for all the corrections as well as the downward continuation are shown. 1999 Journal Article http://hdl.handle.net/20.500.11937/29922 10.1007/s001900050235 Springer - Verlag restricted
spellingShingle Precise geoid determinations Gravity - anomaly Geodetic boundary value problem - Downward continuation of gravity
Huang, J.
Novak, P.
Martinec, Z.
Featherstone, Will
Vanicek, P.
Pagiatakis, S.
Veronneau, M.
Determination of the Boundary Values for the Stokes-Helmert Problem
title Determination of the Boundary Values for the Stokes-Helmert Problem
title_full Determination of the Boundary Values for the Stokes-Helmert Problem
title_fullStr Determination of the Boundary Values for the Stokes-Helmert Problem
title_full_unstemmed Determination of the Boundary Values for the Stokes-Helmert Problem
title_short Determination of the Boundary Values for the Stokes-Helmert Problem
title_sort determination of the boundary values for the stokes-helmert problem
topic Precise geoid determinations Gravity - anomaly Geodetic boundary value problem - Downward continuation of gravity
url http://hdl.handle.net/20.500.11937/29922