The terrain correction in a moving tangent space
Conventionally the terrain/topographic reduction is based on the Bouguer Plate, which is flat and extends in the local tangent plane/horizontal plane to infinity. Here we aim at an error estimate of such a "planar approximation" of the Newton integral of the type of a disturbing potential...
Main Authors: | , |
---|---|
Format: | Article in Journal/Newspaper |
Language: | unknown |
Subjects: | |
Online Access: | https://kramerius.lib.cas.cz/view/uuid:6fcf33f8-88dc-411e-93d1-2e8e99eca93d https://doi.org/10.1023/A:1022088927779 |
id |
ftczechacademysc:oai:kramerius.lib.cas.cz:uuid:6fcf33f8-88dc-411e-93d1-2e8e99eca93d |
---|---|
record_format |
openpolar |
spelling |
ftczechacademysc:oai:kramerius.lib.cas.cz:uuid:6fcf33f8-88dc-411e-93d1-2e8e99eca93d 2024-03-17T08:59:22+00:00 The terrain correction in a moving tangent space Grafarend, Erik, 1939- Hanke, S print média svazek https://kramerius.lib.cas.cz/view/uuid:6fcf33f8-88dc-411e-93d1-2e8e99eca93d https://doi.org/10.1023/A:1022088927779 unknown https://kramerius.lib.cas.cz/view/uuid:6fcf33f8-88dc-411e-93d1-2e8e99eca93d issn:0039-3169 doi:https://doi.org/10.1023/A:1022088927779 policy:private terénní korekce terrain correction topographic reduction Newton gravitation in a moving tangent space 7 550 model:article ftczechacademysc https://doi.org/10.1023/A:1022088927779 2024-02-19T22:56:34Z Conventionally the terrain/topographic reduction is based on the Bouguer Plate, which is flat and extends in the local tangent plane/horizontal plane to infinity. Here we aim at an error estimate of such a "planar approximation" of the Newton integral of the type of a disturbing potential and gravitational disturbance as linearized forms of the gravitational potential and the modulus of gravitational field intensity. To effect this quality control of the conventional terrain reduction, we first transform the spherical Newton functional from an equatorial frame of reference to an oblique meta-equatorial frame of reference with the evaluation point as a meta-North pole, and then by means of an oblique equiareal map projection of the azimuthal type to a tangent plane which moves at the evaluation point. The first term of these transformed Newton functionals is the "planar approximation". The difference between the exact Newton kernels and their "planar approximation" are plotted and tabulated in Tables 1-3. Three configurations are studied in detail: for points at radius r = 10 km around the evaluation point the systematic error varies from 0.26% for a spherical height difference of the order of H − H* = 5 km, more than 0.80% for a spherical height difference of the order of H − H* = 1 km, and more than 1.60% for a spherical height difference of H − H* = 500 m. In contrast, the systematic error for spherical height difference H − H* = 1 km at a distance of r = 1000 km from the evaluation point increases to 44%. Indeed, the newly derived exact Newton kernels which are of the convolution type and are represented in the tangent space moving with the evaluation point can be preferably used with little extra computational effort. E. W. Grafarend, S. Hanke. Obsahuje bibliografii Article in Journal/Newspaper North Pole Czech Academy of Sciences: dKNAV North Pole |
institution |
Open Polar |
collection |
Czech Academy of Sciences: dKNAV |
op_collection_id |
ftczechacademysc |
language |
unknown |
topic |
terénní korekce terrain correction topographic reduction Newton gravitation in a moving tangent space 7 550 |
spellingShingle |
terénní korekce terrain correction topographic reduction Newton gravitation in a moving tangent space 7 550 Grafarend, Erik, 1939- Hanke, S The terrain correction in a moving tangent space |
topic_facet |
terénní korekce terrain correction topographic reduction Newton gravitation in a moving tangent space 7 550 |
description |
Conventionally the terrain/topographic reduction is based on the Bouguer Plate, which is flat and extends in the local tangent plane/horizontal plane to infinity. Here we aim at an error estimate of such a "planar approximation" of the Newton integral of the type of a disturbing potential and gravitational disturbance as linearized forms of the gravitational potential and the modulus of gravitational field intensity. To effect this quality control of the conventional terrain reduction, we first transform the spherical Newton functional from an equatorial frame of reference to an oblique meta-equatorial frame of reference with the evaluation point as a meta-North pole, and then by means of an oblique equiareal map projection of the azimuthal type to a tangent plane which moves at the evaluation point. The first term of these transformed Newton functionals is the "planar approximation". The difference between the exact Newton kernels and their "planar approximation" are plotted and tabulated in Tables 1-3. Three configurations are studied in detail: for points at radius r = 10 km around the evaluation point the systematic error varies from 0.26% for a spherical height difference of the order of H − H* = 5 km, more than 0.80% for a spherical height difference of the order of H − H* = 1 km, and more than 1.60% for a spherical height difference of H − H* = 500 m. In contrast, the systematic error for spherical height difference H − H* = 1 km at a distance of r = 1000 km from the evaluation point increases to 44%. Indeed, the newly derived exact Newton kernels which are of the convolution type and are represented in the tangent space moving with the evaluation point can be preferably used with little extra computational effort. E. W. Grafarend, S. Hanke. Obsahuje bibliografii |
format |
Article in Journal/Newspaper |
author |
Grafarend, Erik, 1939- Hanke, S |
author_facet |
Grafarend, Erik, 1939- Hanke, S |
author_sort |
Grafarend, Erik, 1939- |
title |
The terrain correction in a moving tangent space |
title_short |
The terrain correction in a moving tangent space |
title_full |
The terrain correction in a moving tangent space |
title_fullStr |
The terrain correction in a moving tangent space |
title_full_unstemmed |
The terrain correction in a moving tangent space |
title_sort |
terrain correction in a moving tangent space |
url |
https://kramerius.lib.cas.cz/view/uuid:6fcf33f8-88dc-411e-93d1-2e8e99eca93d https://doi.org/10.1023/A:1022088927779 |
geographic |
North Pole |
geographic_facet |
North Pole |
genre |
North Pole |
genre_facet |
North Pole |
op_relation |
https://kramerius.lib.cas.cz/view/uuid:6fcf33f8-88dc-411e-93d1-2e8e99eca93d issn:0039-3169 doi:https://doi.org/10.1023/A:1022088927779 |
op_rights |
policy:private |
op_doi |
https://doi.org/10.1023/A:1022088927779 |
_version_ |
1793769853083975680 |