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Modelos armonicos no lineales para series temporales geodéticas = Non-linear harmonic models for geodetic time series / P.A. Martinez-Ortiz (2011)
Titre : Modelos armonicos no lineales para series temporales geodéticas = Non-linear harmonic models for geodetic time series Type de document : Thèse/HDR Auteurs : P.A. Martinez-Ortiz, Auteur ; J.M. Fernadiz Leal, Directeur de thèse Editeur : Alicante : Escuella politécnica superior Année de publication : 2011 Importance : 402 p. Format : 21 x 30 cm Note générale : Bibliographie Langues : Espagnol (spa) Descripteur : [Vedettes matières IGN] Géodésie
[Termes IGN] analyse harmonique
[Termes IGN] analyse spectrale
[Termes IGN] bruit blanc
[Termes IGN] bruit rose
[Termes IGN] géocentre
[Termes IGN] marée terrestre
[Termes IGN] masse de la Terre
[Termes IGN] Matlab
[Termes IGN] modèle non linéaire
[Termes IGN] positionnement par GPS
[Termes IGN] série temporelle
[Termes IGN] système de référence géodésiqueIndex. décimale : THESE Thèses et HDR Résumé : (Auteur) The dissertation addresses the development of new methods and software for the spectral analysis of scalar or vectorial time series, with emphasis in the applications of geodetic interest. The starting point can be placed in the method introduced by Harada and Fukushima for the non-linear analysis of time series, which allows the recursive detection of frequencies and their associated amplitudes and phases as well as the secular mixed Fourier terms when found in the signal. That method is extended in different ways, allowing the treatment of series affected by auto correlated noise with a power law, either evenly or unevenly spaced. This is made both at the level of frequency detection and non-linear fitting. Reduction of the computational overhead is also obtained. The theoretical work is accompanied by the developing of comprehensive and specialized software for such non-linear harmonic analysis of time series using the MATLAB programming language. Much of the tools we can find today for analyzing these periodic time series are valid only for certain types whereas the programs in the thesis can be applied to oddly spaced series in the presence of combinations of white and flicker noise. The new methods and routines are used for analyzing some interesting series as those ones describing the celestial pole offsets, the geocentre variations due to the redistribution of water mass on the Earth's surface, the excess of the length of day, continental water flux and the positions of GPS stations, among others. We estimate harmonic models that explain each one of these phenomena in the considered time domain and allow us to draw conclusions of their behavior. Note de contenu : Agradecimientos
Resumen
Abstract
I MODELOS ARMÓNICOS NO LINEALES PARA SE RÍES TEMPORALES GEODÉTICAS
1. Introducción
1.1. Objetivos y metodología
1.2. Contenidos
2. El problema de la detección de señales
2.1. Definición de serie temporal
2.1.1. Componentes de una serie temporal
2.1.2. Componente de ruido
2.2. Técnicas para el estudio de series temporales
2.2.1. Análisis clásico
2.2.2. Análisis espectral
2.2.3. Análisis wavelet
2.3. El problema de la detección de señales
2.3.1. Periodograma de Lomb
2.3.2. Dominio de frecuencia
3. Análisis armónico no lineal
3.1. Introducción
3.2. Descripción del método
3.2.1. Función objetivo y funciones base
3.2.2. Solución mínimo cuadrática
3.2.3. Optimización no lineal: Algoritmo BFGS
3.2.4. Extracción de frecuencias
3.3. Incertidumbre
3.4. Generalización
3.5. Tratamiento de los términos periódicos de corta frecuencia
4. Variaciones del polo celeste
4.1. Modelo de precesión-nutación IAU1980
4.1.1. Introducción
4.1.2. Descripción de los datos
4.1.3. Características del análisis y resultados
4.1.4. Conclusiones
4.2. Modelo de precesión-nutación IAU2000
4.2.1. Introducción
4.2.2. Descripción de los datos
4.2.3. Características del análisis y resultados
4.2.4. Conclusiones
4.3. Modelos dinámicos para la predicción a corto plazo de (óV óe)
5. Variaciones geocéntricas causadas por el flujo de agua continental 101
5.1. Introducción
5.2. Descripción de los datos
5.3. Características del análisis y resultados
5.4. Conclusiones
6. Modelos espacio-temporales para el flujo de agua continental
6.1. Introducción
6.2. Descripción de datos
6.3. Características del análisis
6.4. Resultados
6.5. Conclusiones
7. Estudio armónico del exceso en la duración del día
7.1. Introducción
7.2. Descripción de los datos
7.3. Características del análisis y resultados
7.4. Conclusiones
8. Ruido
8.1. Tipología básica
8.2. Matrices de covarianza
8.2.1. Matriz de covarianzas para un ruido blanco
8.2.2. Matriz de covarianzas para un ruido parpadeante
8.2.3. Matriz de covarianzas para un paseo aleatorio
8.3. Relación ruido-periodograma
8.4. Ruido en las observaciones GPS
9. Algoritmo FHAST
9.1. Introducción
9.2. Función objetivo
9.3. Modelo estocástico
9.3.1. Estimación de un índice espectral
9.3.2. Componente residual como combinación de varios ruidos. Es-timación de la frecuencia de transición,
9.4. Modelo funcional
9.5. Estimación de la componente de varianza
9.5.1. Condición de no negatividad
9.6. Extensión del periodograma
9.6.1. Aceleración del cálculo del periodograma
9.7. Incertidumbre
9.7.1. Parámetros lineales y no lineales del modelo funcional
9.7.2. Parámetros del modelo estocástico
9.8. Criterios de parada algorítmica
9.9. Entramado algorítmico
9.10. Simulación
10.Estudio de las series de posiciones de estaciones GPS
10.1. Introducción
10.2. Análisis de las series temporales residuales
10.3. Resultados y discusión
10.4. Conclusiones
11.Conclusiones y perspectivas
11.1. Conclusiones
11.2. Perspectivas
II EXTENDED SUMMARY: NON-LINEAR HARMO NIC MODELS FOR GEODETIC TIME SERIES
S.1. Introduction
S.2. The signal detection problem
S.2.1. Definition of time series
S.2.2. Spectral analysis
S.2.3. The signal detection problem
S.3. Non-linear harmonic analysis
S.4. Celestial Pole Offsets
S.4.1. IAU1980 Pole Offsets
S.4.2. IAU2000 Pole Offsets
S.4.3. Dynamic models for (óV,óe) prediction
S.5. Geocenter variations caused by continental water flux
S.5.1. Introduction
S.5.2. Data
S.5.3. Analysis and results
S.5.4. Conclusions
S.6. Spatio-temporal models for continental water flux
S.6.1. Introduction
S.6.2. Data
S.6.3. Methods
S.6.4. Results
S.6.5. Conclusions
S.7. Harmonio study of the length of day
S.7.1. Introduction
S.7.2. Data
S.7.3. Analysis and results
S.7.4. Conclusions
S.8. Noise
S.8.1. Typology
S.8.2. Covariance matrices
S.8.3. Relationship noise-periodogram
S.8.4. Noise in GPS observations
S.9. FHAST algorithm
S.9.1. Introduction
S.9.2. Stochastic model
S.9.3. Functional model
S.9.4. Component variance estimation
S.9.5. Modification of the periodogram
S.9.6. Stop criteria
S9.7. Algorithm
S.10. Study of the position time series of GPS stations
S.10.1.Introduction
S.10.2. Analysis and results
S.10.S.Conclusions
S.11 Conclusions and outlook
S.11.1.Conclusions
S.11.2. Outlook
III APÉNDICES
A. Ley de propagación del error
B, Acrónimos, abreviaturas y unidades
C. Modelos armónicos no lineales de algunas estaciones GPS
BibliografíaNuméro de notice : 10519 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse française Note de thèse : Bibliographie nature-HAL : Thèse DOI : sans Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=45141 Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 10519-01 30.60 Livre Centre de documentation Géodésie 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
en open access
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)
[article]
Titre : Construction of spherical harmonic series for the potential derivatives of arbitrary orders in the geocentric Earth-fixed reference frame Type de document : Article/Communication Auteurs : M. Petrovskaya, Auteur ; A. Vershkov, Auteur Année de publication : 2010 Article en page(s) : pp 165 - 178 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] champ de pesanteur local
[Termes IGN] coordonnées cartésiennes géocentriques
[Termes IGN] déviation de la verticale
[Termes IGN] Earth Gravity Model 2008
[Termes IGN] harmonique sphérique
[Termes IGN] repère de référence
[Termes IGN] trièdre local
[Termes IGN] varianceRésumé : (Auteur) The derivatives of the Earth gravitational potential are considered in the global Cartesian Earth-fixed reference frame. Spherical harmonic series are constructed for the potential derivatives of the first and second orders on the basis of a general expression of Cunningham (Celest Mech 2:207–216, 1970) for arbitrary order derivatives of a spherical harmonic. A common structure of the series for the potential and its first- and second-order derivatives allows to develop a general procedure for constructing similar series for the potential derivatives of arbitrary orders. The coefficients of the derivatives are defined by means of recurrence relations in which a coefficient of a certain order derivative is a linear function of two coefficients of a preceding order derivative. The coefficients of the second-order derivatives are also presented as explicit functions of three coefficients of the potential. On the basis of the geopotential model EGM2008, the spherical harmonic coefficients are calculated for the first-, second-, and some third-order derivatives of the disturbing potential T, representing the full potential V, after eliminating from it the zero- and first-degree harmonics. The coefficients of two lowest degrees in the series for the derivatives of T are presented. The corresponding degree variances are estimated. The obtained results can be applied for solving various problems of satellite geodesy and celestial mechanics. Copyright Springer Numéro de notice : A2010-155 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-009-0353-y Date de publication en ligne : 10/11/2009 En ligne : https://doi.org/10.1007/s00190-009-0353-y Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30350
in Journal of geodesy > vol 84 n° 3 (March 2010) . - pp 165 - 178[article]Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 266-2010031 SL Revue Centre de documentation Revues en salle Disponible Prediction 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)
[article]
Titre : Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data Type de document : Article/Communication Auteurs : C. Hirt, Auteur Année de publication : 2010 Article en page(s) : pp 179 - 190 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] Allemagne
[Termes IGN] Alpes centrales
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] déviation de la verticale
[Termes IGN] Earth Gravity Model 2008
[Termes IGN] harmonique sphérique
[Termes IGN] MNS SRTM
[Termes IGN] modèle de géopotentiel
[Termes IGN] modèle de géopotentiel local
[Termes IGN] modèle numérique de terrain
[Termes IGN] Suisse
[Termes IGN] valeur efficaceRésumé : (Auteur) This study demonstrates that in mountainous areas the use of residual terrain model (RTM) data significantly improves the accuracy of vertical deflections obtained from high-degree spherical harmonic synthesis. The new Earth gravitational model EGM2008 is used to compute vertical deflections up to a spherical harmonic degree of 2,160. RTM data can be constructed as difference between high-resolution Shuttle Radar Topography Mission (SRTM) elevation data and the terrain model DTM2006.0 (a spherical harmonic terrain model that complements EGM2008) providing the long-wavelength reference surface. Because these RTM elevations imply most of the gravity field signal beyond spherical harmonic degree of 2,160, they can be used to augment EGM2008 vertical deflection predictions in the very high spherical harmonic degrees. In two mountainous test areas—the German and the Swiss Alps—the combined use of EGM2008 and RTM data was successfully tested at 223 stations with high-precision astrogeodetic vertical deflections from recent zenith camera observations (accuracy of about 0.1 arc seconds) available. The comparison of EGM2008 vertical deflections with the ground-truth astrogeodetic observations shows root mean square (RMS) values (from differences) of 3.5 arc seconds for È and 3.2 arc seconds for È , respectively. Using a combination of EGM2008 and RTM data for the prediction of vertical deflections considerably reduces the RMS values to the level of 0.8 arc seconds for both vertical deflection components, which is a significant improvement of about 75%. Density anomalies of the real topography with respect to the residual model topography are one factor limiting the accuracy of the approach. The proposed technique for vertical deflection predictions is based on three publicly available data sets: (1) EGM2008, (2) DTM2006.0 and (3) SRTM elevation data. This allows replication of the approach for improving the accuracy of EGM2008 vertical deflection predictions in regions with a rough topography or for improved validation of EGM2008 and future high-degree spherical harmonic models by means of independent ground truth data. Numéro de notice : A2010-156 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-009-0354-x Date de publication en ligne : 12/11/2009 En ligne : https://doi.org/10.1007/s00190-009-0354-x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30351
in Journal of geodesy > vol 84 n° 3 (March 2010) . - pp 179 - 190[article]Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 266-2010031 SL Revue Centre de documentation Revues en salle Disponible Finite element method for solving geodetic boundary value problems / Z. Faskova in Journal of geodesy, vol 84 n° 2 (February 2010)
[article]
Titre : Finite element method for solving geodetic boundary value problems Type de document : Article/Communication Auteurs : Z. Faskova, Auteur ; Robert Cunderlik, Auteur ; Karol Mikula, Auteur Année de publication : 2010 Article en page(s) : pp 135 - 144 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] champ de pesanteur terrestre
[Termes IGN] Earth Gravity Model 2008
[Termes IGN] géoïde
[Termes IGN] méthode des éléments finis
[Termes IGN] problème de Dirichlet
[Termes IGN] problème des valeurs limitesRésumé : (Auteur) The goal of this paper is to present the finite element scheme for solving the Earth potential problems in 3D domains above the Earth surface. To that goal we formulate the boundary-value problem (BVP) consisting of the Laplace equation outside the Earth accompanied by the Neumann as well as the Dirichlet boundary conditions (BC). The 3D computational domain consists of the bottom boundary in the form of a spherical approximation or real triangulation of the Earth’s surface on which surface gravity disturbances are given. We introduce additional upper (spherical) and side (planar and conical) boundaries where the Dirichlet BC is given. Solution of such elliptic BVP is understood in a weak sense, it always exists and is unique and can be efficiently found by the finite element method (FEM). We briefly present derivation of FEM for such type of problems including main discretization ideas. This method leads to a solution of the sparse symmetric linear systems which give the Earth’s potential solution in every discrete node of the 3D computational domain. In this point our method differs from other numerical approaches, e.g. boundary element method (BEM) where the potential is sought on a hypersurface only. We apply and test FEM in various situations. First, we compare the FEM solution with the known exact solution in case of homogeneous sphere. Then, we solve the geodetic BVP in continental scale using the DNSC08 data. We compare the results with the EGM2008 geopotential model. Finally, we study the precision of our solution by the GPS/levelling test in Slovakia where we use terrestrial gravimetric measurements as input data. All tests show qualitative and quantitative agreement with the given solutions. Copyright Springer Numéro de notice : A2010-108 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-009-0349-7 Date de publication en ligne : 13/10/2009 En ligne : https://doi.org/10.1007/s00190-009-0349-7 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30304
in Journal of geodesy > vol 84 n° 2 (February 2010) . - pp 135 - 144[article]Exemplaires(1)
Code-barres Cote Support Localisation Section Disponibilité 266-2010021 SL Revue Centre de documentation Revues en salle Disponible Assessment 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)PermalinkLand cover classification of the North China Plain using MODIS-EVI time series / Z. Xia in ISPRS Journal of photogrammetry and remote sensing, vol 63 n° 4 (July - August 2008)PermalinkDisturbance, management, and landscape dynamics: harmonic regression of Vegetation Indices in the Lower Okavango Delta, Botswana / A.L. Neunschwander in Photogrammetric Engineering & Remote Sensing, PERS, vol 74 n° 6 (June 2008)Permalink