Fourier geoid determination with irregular data
Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is require...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Sideris, Michael G. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1995 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 1995 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of geodesy - Springer-Verlag, 1995, 70(1995), 1-2 vom: Nov., Seite 2-12 |
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| Übergeordnetes Werk: |
volume:70 ; year:1995 ; number:1-2 ; month:11 ; pages:2-12 |
| Links: |
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| DOI / URN: |
10.1007/BF00863415 |
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| Katalog-ID: |
OLC2058931726 |
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| 245 | 1 | 0 | |a Fourier geoid determination with irregular data |
| 264 | 1 | |c 1995 | |
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| 520 | |a Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is required when only point measurements are available. This paper presents a way of computing a grid of geoid undulations N without explicitly gridding the data. The method is applicable to all FFT or FHT techniques of geoid or terrain effects determination, and it works with planar as well as spherical formulas. This method can be used not only for, e.g., computing a grid of undulations from irregular gravity anomalies Δg but it also lends itself to other applications, such as the gridding of gravity anomalies and, since the contribution of each data point is computed individually, the update of N- or Δg-grids as soon as new point measurements become available. In the case that there are grid cells which contain no measurements, the results of gravity interpolation or geoid estimation can be drastically improved by incorporating into the procedure a frequency-domain interpolating function. In addition to numerical results obtained using a few simple interpolating functions, the paper presents briefly the mathematical formulas for recovering missing grid values and for transforming values from one grid to another which might be rotated and/or scaled with respect to the first one. The geodetic problems where these techniques may find applications are pointed out throughout the paper. | ||
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| 650 | 4 | |a Fast Fourier Transform | |
| 650 | 4 | |a Grid Cell | |
| 650 | 4 | |a Point Measurement | |
| 650 | 4 | |a Gravity Anomaly | |
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10.1007/BF00863415 doi (DE-627)OLC2058931726 (DE-He213)BF00863415-p DE-627 ger DE-627 rakwb eng 550 VZ 14 ssgn Sideris, Michael G. verfasserin aut Fourier geoid determination with irregular data 1995 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1995 Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is required when only point measurements are available. This paper presents a way of computing a grid of geoid undulations N without explicitly gridding the data. The method is applicable to all FFT or FHT techniques of geoid or terrain effects determination, and it works with planar as well as spherical formulas. This method can be used not only for, e.g., computing a grid of undulations from irregular gravity anomalies Δg but it also lends itself to other applications, such as the gridding of gravity anomalies and, since the contribution of each data point is computed individually, the update of N- or Δg-grids as soon as new point measurements become available. In the case that there are grid cells which contain no measurements, the results of gravity interpolation or geoid estimation can be drastically improved by incorporating into the procedure a frequency-domain interpolating function. In addition to numerical results obtained using a few simple interpolating functions, the paper presents briefly the mathematical formulas for recovering missing grid values and for transforming values from one grid to another which might be rotated and/or scaled with respect to the first one. The geodetic problems where these techniques may find applications are pointed out throughout the paper. Fourier Transform Fast Fourier Transform Grid Cell Point Measurement Gravity Anomaly Enthalten in Journal of geodesy Springer-Verlag, 1995 70(1995), 1-2 vom: Nov., Seite 2-12 (DE-627)191686298 (DE-600)1302972-1 (DE-576)051377373 0949-7714 nnns volume:70 year:1995 number:1-2 month:11 pages:2-12 https://doi.org/10.1007/BF00863415 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_122 GBV_ILN_267 GBV_ILN_370 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2112 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4219 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4700 AR 70 1995 1-2 11 2-12 |
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10.1007/BF00863415 doi (DE-627)OLC2058931726 (DE-He213)BF00863415-p DE-627 ger DE-627 rakwb eng 550 VZ 14 ssgn Sideris, Michael G. verfasserin aut Fourier geoid determination with irregular data 1995 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1995 Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is required when only point measurements are available. This paper presents a way of computing a grid of geoid undulations N without explicitly gridding the data. The method is applicable to all FFT or FHT techniques of geoid or terrain effects determination, and it works with planar as well as spherical formulas. This method can be used not only for, e.g., computing a grid of undulations from irregular gravity anomalies Δg but it also lends itself to other applications, such as the gridding of gravity anomalies and, since the contribution of each data point is computed individually, the update of N- or Δg-grids as soon as new point measurements become available. In the case that there are grid cells which contain no measurements, the results of gravity interpolation or geoid estimation can be drastically improved by incorporating into the procedure a frequency-domain interpolating function. In addition to numerical results obtained using a few simple interpolating functions, the paper presents briefly the mathematical formulas for recovering missing grid values and for transforming values from one grid to another which might be rotated and/or scaled with respect to the first one. The geodetic problems where these techniques may find applications are pointed out throughout the paper. Fourier Transform Fast Fourier Transform Grid Cell Point Measurement Gravity Anomaly Enthalten in Journal of geodesy Springer-Verlag, 1995 70(1995), 1-2 vom: Nov., Seite 2-12 (DE-627)191686298 (DE-600)1302972-1 (DE-576)051377373 0949-7714 nnns volume:70 year:1995 number:1-2 month:11 pages:2-12 https://doi.org/10.1007/BF00863415 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_122 GBV_ILN_267 GBV_ILN_370 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2112 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4219 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4700 AR 70 1995 1-2 11 2-12 |
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10.1007/BF00863415 doi (DE-627)OLC2058931726 (DE-He213)BF00863415-p DE-627 ger DE-627 rakwb eng 550 VZ 14 ssgn Sideris, Michael G. verfasserin aut Fourier geoid determination with irregular data 1995 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1995 Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is required when only point measurements are available. This paper presents a way of computing a grid of geoid undulations N without explicitly gridding the data. The method is applicable to all FFT or FHT techniques of geoid or terrain effects determination, and it works with planar as well as spherical formulas. This method can be used not only for, e.g., computing a grid of undulations from irregular gravity anomalies Δg but it also lends itself to other applications, such as the gridding of gravity anomalies and, since the contribution of each data point is computed individually, the update of N- or Δg-grids as soon as new point measurements become available. In the case that there are grid cells which contain no measurements, the results of gravity interpolation or geoid estimation can be drastically improved by incorporating into the procedure a frequency-domain interpolating function. In addition to numerical results obtained using a few simple interpolating functions, the paper presents briefly the mathematical formulas for recovering missing grid values and for transforming values from one grid to another which might be rotated and/or scaled with respect to the first one. The geodetic problems where these techniques may find applications are pointed out throughout the paper. Fourier Transform Fast Fourier Transform Grid Cell Point Measurement Gravity Anomaly Enthalten in Journal of geodesy Springer-Verlag, 1995 70(1995), 1-2 vom: Nov., Seite 2-12 (DE-627)191686298 (DE-600)1302972-1 (DE-576)051377373 0949-7714 nnns volume:70 year:1995 number:1-2 month:11 pages:2-12 https://doi.org/10.1007/BF00863415 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_122 GBV_ILN_267 GBV_ILN_370 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2112 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4219 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4700 AR 70 1995 1-2 11 2-12 |
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10.1007/BF00863415 doi (DE-627)OLC2058931726 (DE-He213)BF00863415-p DE-627 ger DE-627 rakwb eng 550 VZ 14 ssgn Sideris, Michael G. verfasserin aut Fourier geoid determination with irregular data 1995 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1995 Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is required when only point measurements are available. This paper presents a way of computing a grid of geoid undulations N without explicitly gridding the data. The method is applicable to all FFT or FHT techniques of geoid or terrain effects determination, and it works with planar as well as spherical formulas. This method can be used not only for, e.g., computing a grid of undulations from irregular gravity anomalies Δg but it also lends itself to other applications, such as the gridding of gravity anomalies and, since the contribution of each data point is computed individually, the update of N- or Δg-grids as soon as new point measurements become available. In the case that there are grid cells which contain no measurements, the results of gravity interpolation or geoid estimation can be drastically improved by incorporating into the procedure a frequency-domain interpolating function. In addition to numerical results obtained using a few simple interpolating functions, the paper presents briefly the mathematical formulas for recovering missing grid values and for transforming values from one grid to another which might be rotated and/or scaled with respect to the first one. The geodetic problems where these techniques may find applications are pointed out throughout the paper. Fourier Transform Fast Fourier Transform Grid Cell Point Measurement Gravity Anomaly Enthalten in Journal of geodesy Springer-Verlag, 1995 70(1995), 1-2 vom: Nov., Seite 2-12 (DE-627)191686298 (DE-600)1302972-1 (DE-576)051377373 0949-7714 nnns volume:70 year:1995 number:1-2 month:11 pages:2-12 https://doi.org/10.1007/BF00863415 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_122 GBV_ILN_267 GBV_ILN_370 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2112 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4219 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4700 AR 70 1995 1-2 11 2-12 |
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10.1007/BF00863415 doi (DE-627)OLC2058931726 (DE-He213)BF00863415-p DE-627 ger DE-627 rakwb eng 550 VZ 14 ssgn Sideris, Michael G. verfasserin aut Fourier geoid determination with irregular data 1995 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1995 Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is required when only point measurements are available. This paper presents a way of computing a grid of geoid undulations N without explicitly gridding the data. The method is applicable to all FFT or FHT techniques of geoid or terrain effects determination, and it works with planar as well as spherical formulas. This method can be used not only for, e.g., computing a grid of undulations from irregular gravity anomalies Δg but it also lends itself to other applications, such as the gridding of gravity anomalies and, since the contribution of each data point is computed individually, the update of N- or Δg-grids as soon as new point measurements become available. In the case that there are grid cells which contain no measurements, the results of gravity interpolation or geoid estimation can be drastically improved by incorporating into the procedure a frequency-domain interpolating function. In addition to numerical results obtained using a few simple interpolating functions, the paper presents briefly the mathematical formulas for recovering missing grid values and for transforming values from one grid to another which might be rotated and/or scaled with respect to the first one. The geodetic problems where these techniques may find applications are pointed out throughout the paper. Fourier Transform Fast Fourier Transform Grid Cell Point Measurement Gravity Anomaly Enthalten in Journal of geodesy Springer-Verlag, 1995 70(1995), 1-2 vom: Nov., Seite 2-12 (DE-627)191686298 (DE-600)1302972-1 (DE-576)051377373 0949-7714 nnns volume:70 year:1995 number:1-2 month:11 pages:2-12 https://doi.org/10.1007/BF00863415 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OPC-GGO SSG-OPC-GEO GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_122 GBV_ILN_267 GBV_ILN_370 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2112 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4219 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4700 AR 70 1995 1-2 11 2-12 |
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Fourier geoid determination with irregular data |
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Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is required when only point measurements are available. This paper presents a way of computing a grid of geoid undulations N without explicitly gridding the data. The method is applicable to all FFT or FHT techniques of geoid or terrain effects determination, and it works with planar as well as spherical formulas. This method can be used not only for, e.g., computing a grid of undulations from irregular gravity anomalies Δg but it also lends itself to other applications, such as the gridding of gravity anomalies and, since the contribution of each data point is computed individually, the update of N- or Δg-grids as soon as new point measurements become available. In the case that there are grid cells which contain no measurements, the results of gravity interpolation or geoid estimation can be drastically improved by incorporating into the procedure a frequency-domain interpolating function. In addition to numerical results obtained using a few simple interpolating functions, the paper presents briefly the mathematical formulas for recovering missing grid values and for transforming values from one grid to another which might be rotated and/or scaled with respect to the first one. The geodetic problems where these techniques may find applications are pointed out throughout the paper. © Springer-Verlag 1995 |
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Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is required when only point measurements are available. This paper presents a way of computing a grid of geoid undulations N without explicitly gridding the data. The method is applicable to all FFT or FHT techniques of geoid or terrain effects determination, and it works with planar as well as spherical formulas. This method can be used not only for, e.g., computing a grid of undulations from irregular gravity anomalies Δg but it also lends itself to other applications, such as the gridding of gravity anomalies and, since the contribution of each data point is computed individually, the update of N- or Δg-grids as soon as new point measurements become available. In the case that there are grid cells which contain no measurements, the results of gravity interpolation or geoid estimation can be drastically improved by incorporating into the procedure a frequency-domain interpolating function. In addition to numerical results obtained using a few simple interpolating functions, the paper presents briefly the mathematical formulas for recovering missing grid values and for transforming values from one grid to another which might be rotated and/or scaled with respect to the first one. The geodetic problems where these techniques may find applications are pointed out throughout the paper. © Springer-Verlag 1995 |
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Abstract The fast Fourier transform (FFT) and, recently, the fast Hartley transform (FHT) have been extensively used by geodesists for efficient geoid determination. For this kind of efficiency, data must be given on a regular grid and, consequently, a pre-processing step of interpolation is required when only point measurements are available. This paper presents a way of computing a grid of geoid undulations N without explicitly gridding the data. The method is applicable to all FFT or FHT techniques of geoid or terrain effects determination, and it works with planar as well as spherical formulas. This method can be used not only for, e.g., computing a grid of undulations from irregular gravity anomalies Δg but it also lends itself to other applications, such as the gridding of gravity anomalies and, since the contribution of each data point is computed individually, the update of N- or Δg-grids as soon as new point measurements become available. In the case that there are grid cells which contain no measurements, the results of gravity interpolation or geoid estimation can be drastically improved by incorporating into the procedure a frequency-domain interpolating function. In addition to numerical results obtained using a few simple interpolating functions, the paper presents briefly the mathematical formulas for recovering missing grid values and for transforming values from one grid to another which might be rotated and/or scaled with respect to the first one. The geodetic problems where these techniques may find applications are pointed out throughout the paper. © Springer-Verlag 1995 |
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