Spectral analysis of the Earth’s topographic potential via 2D-DFT: a new data-based degree variance model to degree 90,000
Classical degree variance models (such as Kaula’s rule or the Tscherning-Rapp model) often rely on low-resolution gravity data and so are subject to extrapolation when used to describe the decay of the gravity field at short spatial scales. This paper presents a new degree variance model based on th...
| Main Authors: | , |
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| Format: | Journal Article |
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Springer - Verlag
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/24111 |
| _version_ | 1848751338905665536 |
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| author | Rexer, Moritz Hirt, Christian |
| author_facet | Rexer, Moritz Hirt, Christian |
| author_sort | Rexer, Moritz |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Classical degree variance models (such as Kaula’s rule or the Tscherning-Rapp model) often rely on low-resolution gravity data and so are subject to extrapolation when used to describe the decay of the gravity field at short spatial scales. This paper presents a new degree variance model based on the recently published GGMplus near-global land areas 220 m resolution gravity maps (Geophys Res Lett 40(16):4279–4283, 2013). We investigate and use a 2D-DFT (discrete Fourier transform) approach to transform GGMplus gravity grids into degree variances. The method is described in detail and its approximation errors are studied using closed-loop experiments. Focus is placed on tiling, azimuth averaging, and windowing effects in the 2D-DFT method and on analytical fitting of degree variances. Approximation errors of the 2D-DFT procedure on the (spherical harmonic) degree variance are found to be at the 10–20 % level. The importance of the reference surface (sphere, ellipsoid or topography) of the gravity data for correct interpretation of degree variance spectra is highlighted. The effect of the underlying mass arrangement (spherical or ellipsoidal approximation) on the degree variances is found to be crucial at short spatial scales. A rule-of-thumb for transformation of spectra between spherical and ellipsoidal approximation is derived. Application of the 2D-DFT on GGMplus gravity maps yields a new degree variance model to degree 90,000. The model is supported by GRACE, GOCE, EGM2008 and forward-modelled gravity at 3 billion land points over all land areas within the SRTM data coverage and provides gravity signal variances at the surface of the topography. The model yields omission errors of ~9 mGal for gravity (~1.5 cm for geoid effects) at scales of 10 km, ~4 mGal (~1 mm) at 2-km scales, and ~2 mGal (~0.2 mm) at 1-km scales. |
| first_indexed | 2025-11-14T07:51:09Z |
| format | Journal Article |
| id | curtin-20.500.11937-24111 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:51:09Z |
| publishDate | 2015 |
| publisher | Springer - Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-241112017-09-13T13:55:44Z Spectral analysis of the Earth’s topographic potential via 2D-DFT: a new data-based degree variance model to degree 90,000 Rexer, Moritz Hirt, Christian Classical degree variance models (such as Kaula’s rule or the Tscherning-Rapp model) often rely on low-resolution gravity data and so are subject to extrapolation when used to describe the decay of the gravity field at short spatial scales. This paper presents a new degree variance model based on the recently published GGMplus near-global land areas 220 m resolution gravity maps (Geophys Res Lett 40(16):4279–4283, 2013). We investigate and use a 2D-DFT (discrete Fourier transform) approach to transform GGMplus gravity grids into degree variances. The method is described in detail and its approximation errors are studied using closed-loop experiments. Focus is placed on tiling, azimuth averaging, and windowing effects in the 2D-DFT method and on analytical fitting of degree variances. Approximation errors of the 2D-DFT procedure on the (spherical harmonic) degree variance are found to be at the 10–20 % level. The importance of the reference surface (sphere, ellipsoid or topography) of the gravity data for correct interpretation of degree variance spectra is highlighted. The effect of the underlying mass arrangement (spherical or ellipsoidal approximation) on the degree variances is found to be crucial at short spatial scales. A rule-of-thumb for transformation of spectra between spherical and ellipsoidal approximation is derived. Application of the 2D-DFT on GGMplus gravity maps yields a new degree variance model to degree 90,000. The model is supported by GRACE, GOCE, EGM2008 and forward-modelled gravity at 3 billion land points over all land areas within the SRTM data coverage and provides gravity signal variances at the surface of the topography. The model yields omission errors of ~9 mGal for gravity (~1.5 cm for geoid effects) at scales of 10 km, ~4 mGal (~1 mm) at 2-km scales, and ~2 mGal (~0.2 mm) at 1-km scales. 2015 Journal Article http://hdl.handle.net/20.500.11937/24111 10.1007/s00190-015-0822-4 Springer - Verlag restricted |
| spellingShingle | Rexer, Moritz Hirt, Christian Spectral analysis of the Earth’s topographic potential via 2D-DFT: a new data-based degree variance model to degree 90,000 |
| title | Spectral analysis of the Earth’s topographic potential via 2D-DFT: a new data-based degree variance model to degree 90,000 |
| title_full | Spectral analysis of the Earth’s topographic potential via 2D-DFT: a new data-based degree variance model to degree 90,000 |
| title_fullStr | Spectral analysis of the Earth’s topographic potential via 2D-DFT: a new data-based degree variance model to degree 90,000 |
| title_full_unstemmed | Spectral analysis of the Earth’s topographic potential via 2D-DFT: a new data-based degree variance model to degree 90,000 |
| title_short | Spectral analysis of the Earth’s topographic potential via 2D-DFT: a new data-based degree variance model to degree 90,000 |
| title_sort | spectral analysis of the earth’s topographic potential via 2d-dft: a new data-based degree variance model to degree 90,000 |
| url | http://hdl.handle.net/20.500.11937/24111 |