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Reducing errors in the GRACE gravity solutions using regularization / H. Save in Journal of geodesy, vol 86 n° 9 (September 2012)
[article]
Titre : Reducing errors in the GRACE gravity solutions using regularization Type de document : Article/Communication Auteurs : H. Save, Auteur ; S. Bettadpur, Auteur ; B. Tapley, Auteur Année de publication : 2012 Article en page(s) : pp 695 - 711 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] données GRACE
[Termes IGN] gravimétrie
[Termes IGN] harmonique sphérique
[Termes IGN] levé gravimétrique
[Termes IGN] régularisation de TychonoffRésumé : (Auteur) The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which creeps into the mid and high degree and order harmonic coefficients of the Earth’s monthly gravity fields provided by GRACE. Due to the use of imperfect background models and data noise, these errors are manifested as north-south striping in the monthly global maps of equivalent water heights. In order to reduce these errors, this study investigates the use of the L-curve method with Tikhonov regularization. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems using Tikhonov regularization. However, the computational effort required to determine the L-curve is prohibitively high for a large-scale problem like GRACE. This study implements a parameter-choice method, using Lanczos bidiagonalization which is a computationally inexpensive approximation to L-curve. Lanczos bidiagonalization is implemented with orthogonal transformation in a parallel computing environment and projects a large estimation problem on a problem of the size of about 2 orders of magnitude smaller for computing the regularization parameter. Errors in the GRACE solution time series have certain characteristics that vary depending on the ground track coverage of the solutions. These errors increase with increasing degree and order. In addition, certain resonant and near-resonant harmonic coefficients have higher errors as compared with the other coefficients. Using the knowledge of these characteristics, this study designs a regularization matrix that provides a constraint on the geopotential coefficients as a function of its degree and order. This regularization matrix is then used to compute the appropriate regularization parameter for each monthly solution. A 7-year time-series of the candidate regularized solutions (Mar 2003–Feb 2010) show markedly reduced error stripes compared with the unconstrained GRACE release 4 solutions (RL04) from the Center for Space Research (CSR). Post-fit residual analysis shows that the regularized solutions fit the data to within the noise level of GRACE. A time series of filtered hydrological model is used to confirm that signal attenuation for basins in the Total Runoff Integrating Pathways (TRIP) database over 320 km radii is less than 1 cm equivalent water height RMS, which is within the noise level of GRACE. Numéro de notice : A2012-467 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-012-0548-5 Date de publication en ligne : 10/03/2012 En ligne : https://doi.org/10.1007/s00190-012-0548-5 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31913
in Journal of geodesy > vol 86 n° 9 (September 2012) . - pp 695 - 711[article]Réservation
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Code-barres Cote Support Localisation Section Disponibilité 266-2012091 RAB Revue Centre de documentation En réserve L003 Disponible Basic equations for constructing geopotential models from the gravitational potential derivatives of the first and second orders in the terrestrial reference frame / M. Petrovskaya in Journal of geodesy, vol 86 n° 7 (July 2012)
[article]
Titre : Basic equations for constructing geopotential models from the gravitational potential derivatives of the first and second orders in the terrestrial reference frame Type de document : Article/Communication Auteurs : M. Petrovskaya, Auteur ; A. Vershkov, Auteur Année de publication : 2012 Article en page(s) : pp 521 - 530 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] gradient de gravitation
[Termes IGN] harmonique sphérique
[Termes IGN] modèle de géopotentiel
[Termes IGN] repère de référence
[Termes IGN] système de référence mondialRésumé : (Auteur) This research represents a continuation of the investigation carried out in the paper of Petrovskaya and Vershkov (J Geod 84(3):165–178, 2010) where conventional spherical harmonic series are constructed for arbitrary order derivatives of the Earth gravitational potential in the terrestrial reference frame. The problem of converting the potential derivatives of the first and second orders into geopotential models is studied. Two kinds of basic equations for solving this problem are derived. The equations of the first kind represent new non-singular non-orthogonal series for the geopotential derivatives, which are constructed by means of transforming the intermediate expressions for these derivatives from the above-mentioned paper. In contrast to the spherical harmonic expansions, these alternative series directly depend on the geopotential coefficients Cn,m and Sn,m . Each term of the series for the first-order derivatives is represented by a sum of these coefficients, which are multiplied by linear combinations of at most two spherical harmonics. For the second-order derivatives, the geopotential coefficients are multiplied by linear combinations of at most three spherical harmonics. As compared to existing non-singular expressions for the geopotential derivatives, the new expressions have a more simple structure. They depend only on the conventional spherical harmonics and do not depend on the first- and second-order derivatives of the associated Legendre functions. The basic equations of the second kind are inferred from the linear equations, constructed in the cited paper, which express the coefficients of the spherical harmonic series for the first- and second-order derivatives in terms of the geopotential coefficients. These equations are converted into recurrent relations from which the coefficients Cn,m and Sn,m are determined on the basis of the spherical harmonic coefficients of each derivative. The latter coefficients can be estimated from the values of the geopotential derivatives by the quadrature formulas or the least-squares approach. The new expressions of two kinds can be applied for spherical harmonic synthesis and analysis. In particular, they might be incorporated in geopotential modeling on the basis of the orbit data from the CHAMP, GRACE and GOCE missions, and the gradiometry data from the GOCE mission. Numéro de notice : A2012-356 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-011-0535-2 Date de publication en ligne : 31/12/2011 En ligne : https://doi.org/10.1007/s00190-011-0535-2 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31802
in Journal of geodesy > vol 86 n° 7 (July 2012) . - pp 521 - 530[article]Réservation
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Code-barres Cote Support Localisation Section Disponibilité 266-2012071 RAB Revue Centre de documentation En réserve L003 Disponible ITRF2008 contribution to glacial isostatic adjustment and recent ice melting assessment / Laurent Métivier in Geophysical research letters, vol 39 n° 1 (January 2012)
[article]
Titre : ITRF2008 contribution to glacial isostatic adjustment and recent ice melting assessment Type de document : Article/Communication Auteurs : Laurent Métivier , Auteur ; Xavier Collilieux , Auteur ; Zuheir Altamimi , Auteur Année de publication : 2012 Article en page(s) : 6 p. Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Applications de télédétection
[Termes IGN] fonte des glaces
[Termes IGN] harmonique sphérique
[Termes IGN] International Terrestrial Reference Frame
[Termes IGN] modèle mathématique
[Termes IGN] rebond post-glaciaire
[Termes IGN] vitesseRésumé : (auteur) We investigate what information station vertical velocities of the ITRF2008 provide on global geodetic parameters and by extension on glacial isostatic adjustment (GIA) and recent ice melting (RIM) processes. We infer degree‐2 spherical harmonic coefficients (SHC) of the Earth figure change and theJ2 gravity rate (J˙2), which we compare with five GIA models. We find J˙2 to be (0.0 ± 2.4) × 10−11 yr−1, which is consistent with recent studies that propose a J˙2 change in the 1990s, due to RIM whose contribution to the J˙2 would be today around (3.5–4.0 ± 2.4) × 10−11 yr−1. Such results favor Peltier (2004) VM2 or Paulson et al. (2007) GIA models. The ITRF2008 SHC that are directly impacted by the GIA rotational feedback, confirm with a good precision recent results from GRACE mission that initiated a debate on GIA rotational feedback and about Peltier GIA model quality. We find a coefficient consistent with Paulson's (and other) model and more than 7 times smaller than coefficients in Peltier's models. Two explanations are possible: (1) if the model of Peltier (2004) VM2 were to be correct, then the strong rotational feedback in the model must be counteracted by a strong rotational feedback in the opposite direction generated by current ice loss, (2) if the model of Paulson et al. (2007) were to be correct, therefore GIA and RIM separately induce negligible rotational feedbacks. Both answers are quite extreme and call for more investigation on GIA modeling and rotational feedback. Numéro de notice : A2012-728 Affiliation des auteurs : LAREG (1991-2011) Thématique : POSITIONNEMENT Nature : Article DOI : 10.1029/2011GL049942 Date de publication en ligne : 14/01/2012 En ligne : https://doi.org/10.1029/2011GL049942 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=90907
in Geophysical research letters > vol 39 n° 1 (January 2012) . - 6 p.[article]Documents numériques
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ITRF2008 contribution to glacial isostatic adjustment ... - pdf éditeurAdobe Acrobat PDF Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons / Thomas Gruber in Journal of geodesy, vol 85 n° 11 (November /2011)
[article]
Titre : Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons Type de document : Article/Communication Auteurs : Thomas Gruber, Auteur ; P. Visser, Auteur ; C. Ackermann, Auteur ; M. Hosse, Auteur Année de publication : 2011 Article en page(s) : pp 845 - 860 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] analyse comparative
[Termes IGN] analyse de variance
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] données GOCE
[Termes IGN] données GRACE
[Termes IGN] géoïde gravimétrique
[Termes IGN] géoïde terrestre
[Termes IGN] harmonique sphérique
[Termes IGN] limite de résolution géométrique
[Termes IGN] orbitographie
[Termes IGN] résiduRésumé : (Auteur) Three GOCE-based gravity field solutions have been computed by ESA’s high-level processing facility and were released to the user community. All models are accompanied by variance-covariance information resulting either from the least squares procedure or a Monte-Carlo approach. In order to obtain independent external quality parameters and to assess the current performance of these models, a set of independent tests based on satellite orbit determination and geoid comparisons is applied. Both test methods can be regarded as complementary because they either investigate the performance in the long wavelength spectral domain (orbit determination) or in the spatial domain (geoid comparisons). The test procedure was applied to the three GOCE gravity field solutions and to a number of selected pre-launch models for comparison. Orbit determination results suggest, that a pure GOCE gravity field model does not outperform the multi-year GRACE gravity field solutions. This was expected as GOCE is designed to improve the determination of the medium to high frequencies of the Earth gravity field (in the range of degree and order 50 to 200). Nevertheless, in case of an optimal combination of GOCE and GRACE data, orbit determination results should not deteriorate. So this validation procedure can also be used for testing the optimality of the approach adopted for producing combined GOCE and GRACE models. Results from geoid comparisons indicate that with the 2 months of GOCE data a significant improvement in the determination of the spherical harmonic spectrum of the global gravity field between degree 50 and 200 can be reached. Even though the ultimate mission goal has not yet been reached, especially due to the limited time span of used GOCE data (only 2 months), it was found that existing satellite-only gravity field models, which are based on 7 years of GRACE data, can already be enhanced in terms of spatial resolution. It is expected that with the accumulation of more GOCE data the gravity field model resolution and quality can be further enhanced, and the GOCE mission goal of 1–2 cm geoid accuracy with 100 km spatial resolution can be achieved. Numéro de notice : A2011-470 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-011-0486-7 Date de publication en ligne : 08/06/2011 En ligne : https://doi.org/10.1007/s00190-011-0486-7 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31364
in Journal of geodesy > vol 85 n° 11 (November /2011) . - pp 845 - 860[article]Réservation
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Code-barres Cote Support Localisation Section Disponibilité 266-2011111 RAB Revue Centre de documentation En réserve L003 Disponible Wavelet modelling of the gravity field by domain decomposition methods: an example over Japan / Isabelle Panet in Geophysical journal international, vol 184 n° 1 (January 2011)
[article]
Titre : Wavelet modelling of the gravity field by domain decomposition methods: an example over Japan Type de document : Article/Communication Auteurs : Isabelle Panet , Auteur ; Yuki Kuroishi, Auteur ; Matthias Holschneider, Auteur Année de publication : 2011 Article en page(s) : pp 203 - 219 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] analyse harmonique
[Termes IGN] bruit blanc
[Termes IGN] bruit rose
[Termes IGN] harmonique sphérique
[Termes IGN] itération
[Termes IGN] Japon
[Termes IGN] modèle de géopotentiel local
[Termes IGN] potentiel de pesanteur terrestre
[Termes IGN] transformation en ondelettesRésumé : (auteur) With the advent of satellite gravity, large gravity data sets of unprecedented quality at low and medium resolution become available. For local, high resolution field modelling, they need to be combined with the surface gravity data. Such models are then used for various applications, from the study of the Earth interior to the determination of oceanic currents. Here we show how to realize such a combination in a flexible way using spherical wavelets and applying a domain decomposition approach. This iterative method, based on the Schwarz algorithms, allows to split a large problem into smaller ones, and avoids the calculation of the entire normal system, which may be huge if high resolution is sought over wide areas. A subdomain is defined as the harmonic space spanned by a subset of the wavelet family. Based on the localization properties of the wavelets in space and frequency, we define hierarchical subdomains of wavelets at different scales. On each scale, blocks of subdomains are defined by using a tailored spatial splitting of the area. The data weighting and regularization are iteratively adjusted for the subdomains, which allows to handle heterogeneity in the data quality or the gravity variations. Different levels of approximations of the subdomains normals are also introduced, corresponding to building local averages of the data at different resolution levels. We first provide the theoretical background on domain decomposition methods. Then, we validate the method with synthetic data, considering two kinds of noise: white noise and coloured noise. We then apply the method to data over Japan, where we combine a satellite-based geopotential model, EIGEN-GL04S, and a local gravity model from a combination of land and marine gravity data and an altimetry-derived marine gravity model. A hybrid spherical harmonics/wavelet model of the geoid is obtained at about 15 km resolution and a corrector grid for the surface model is derived. Numéro de notice : A2011-604 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1111/j.1365-246X.2010.04840.x Date de publication en ligne : 01/01/2011 En ligne : https://doi.org/10.1111/j.1365-246X.2010.04840.x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=91678
in Geophysical journal international > vol 184 n° 1 (January 2011) . - pp 203 - 219[article]Documents numériques
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Wavelet modelling of the gravity field .. - pdf éditeurAdobe Acrobat PDF Construction of spherical harmonic series for the potential derivatives of arbitrary orders in the geocentric Earth-fixed reference frame / M. Petrovskaya in Journal of geodesy, vol 84 n° 3 (March 2010)PermalinkPrediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data / C. Hirt in Journal of geodesy, vol 84 n° 3 (March 2010)PermalinkAssessment of a numerical method for computing the spherical harmonic coefficients of the gravitational potential of a constant density polyhedron / Olivier Jamet (2010)PermalinkWavelet modeling of the gravity field over Japan / Isabelle Panet in Bulletin of the Geographical survey institute, vol 57 (December 2009)PermalinkEfficient propagation of error covariance matrices of gravitational models: application to GRACE and GOCE / Georges Balmino in Journal of geodesy, vol 83 n° 10 (October 2009)PermalinkLocal multi-polar expansions in potential field modeling / B. Minchev in Earth, Planets and Space, vol 61 n° 10 (October 2009)PermalinkRecursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron / Dimitrios Tsoulis in Journal of geodesy, vol 83 n° 10 (October 2009)PermalinkOptima multi-step collocation: application to the space-wise approach for GOCE data analysis / M. Reguzzoni in Journal of geodesy, vol 83 n° 1 (January 2009)PermalinkPermalinkA study reference frame consistency in recent Earth gravitational models / Christopher Kotsakis in Journal of geodesy, vol 83 n° 1 (January 2009)Permalink