Just as in the era of great achievements by scientists such as Newton and Gauss, the mathematical theory of geodesy is continuing the tradition of producing exciting theoretical results, but today the advances are due to the great technological push in the era of satellites for earth observations and large computers for calculations. Every four years a symposium on methodological matters documents this ongoing development in many related underlying areas such as estimation theory, stochastic modelling, inverse problems, and satellite-positioning global-reference systems. This book presents…mehr
Just as in the era of great achievements by scientists such as Newton and Gauss, the mathematical theory of geodesy is continuing the tradition of producing exciting theoretical results, but today the advances are due to the great technological push in the era of satellites for earth observations and large computers for calculations. Every four years a symposium on methodological matters documents this ongoing development in many related underlying areas such as estimation theory, stochastic modelling, inverse problems, and satellite-positioning global-reference systems. This book presents developments in geodesy and related sciences, including applied mathematics, among which are many new results of high intellectual value to help readers stay on top of the latest happenings in the field. TOC:Gaussian Differential Geometry and Differential Geodesy.- Numerical Techniques for Large Least-Squares Problems.- Wiener Filters and Collocation in Satellite Gradiometry.- Multiresolution Data Analysis.- Use of Wavelets for the Acceleration of Iteration Schemes.- Multiscale Solution of Oblique Boundary-Value Problems by Layer Potentials.- PDF Evaluation of the Integer Ambiguity Residuals.- The Rank Deficiency in Estimation Theory.- ITRF2000: From Theory to Implementation.- GPS Permanent Network Solution.- The Estimation Theory for Random Fields in the Bayesian Context.- Application of Spherical Pseudo-Differential Operators and Spherical Wavelets for Numerical Solutions of the Fixed Altimetry-Gravimetry Boundary Value Problem.- Ellipsoidal Vertical Deflections.- Geodesy and the Problem of Ice Sheets.- Gravity Field Variability, the Geoid, and Ocean Dynamics.- SAR Interferometry for Deformation Control.
Report on the Symposium.- Gaussian Differential Geometry and Differential Geodesy.- Numerical Techniques for Large Least-Squares Problems with Applications to GOCE.- The Numerical Treatment of the Downward Continuation Problem for the Gravity Potential.- Wiener Filters and Collocation in Satellite Gradiometry.- How to Handle Colored Noise in Large Least-Squares Problems in the Presence of Data Gaps?.- Statistical Hypothesis Tests in Case of Imprecise Data.- Multiresolution Data Analysis - Numerical Realization by Use of Domain Decomposition Methods and Fast Multipole Techniques.- Integer Least-Squares.- The Use of Wavelets for the Acceleration of Iteration Schemes.- Helmert Geometry (abstract only).- Multiscale Solution of Oblique Boundary-Value Problems by Layer Potentials.- Fast Spherical Harmonic Synthesis and Co-Synthesis with Applications in Gravity Field Modeling.- Fixed Effects, Random Effects and the Mixed Model: New Results of Geodetic Estimation and Prediction Theory (abstract only).- Some Generalized Equivalency Theorems for Least-Squares Adjustment.- Procrustes Statistics to Test for Significant OLS Similarity Transformation Parameters.- PDF Evaluation of the Integer Ambiguity Residuals.- Multiple Models - Fixed, Switching, Interacting.- A Comparison of Data Weighting Methods for the Combination of Satellite and Local Gravity Data.- The Rank Deficiency in Estimation Theory and the Definition of Reference Systems.- ITRF2000: From Theory to Implementation.- Problems in the Definition of Vertical Reference Frames.- Geodetic Boundary-Value Problems and the Height Datum Problem.- GPS Permanent Network Solution: the Impact of Temporal Correlations.- A Discussion of the Use of Spherical Approximation or no Approximation in Gravity Field Modeling with Emphasison Unsolved Problems in Least-Squares Collocation.- Some Topics Related to the Solution of Boundary-Value Problems in Geodesy.- The Estimation Theory for Random Fields in the Bayesian Context: a Contribution from Geodesy.- Testing Invariance for Random Field Modeling.- A Formal Comparison Between Marych-Moritz's Series, Sansò's Change of Boundary Method and a Variational Approach for Solving Some Linear Geodetic Boundary Value Problems.- Potential Coefficients Recovery from the Spectra of the Full Space-Borne Gravity Gradient Tensor.- Application of Spherical Pseudo-Differential Operators and Spherical Wavelets for Numerical Solutions of the Fixed Altimetry-Gravimetry Boundary Value Problem.- Ellipsoidal Vertical Deflections: Regional, Continental, Global Maps of the Horizontal Derivative of the Incremental Gravity Potential.- Harmonic Maps (abstract only).- The Analytical Solutions of the Dirichlet and Neumann Boundary Value Problems with Ellipsoidal Boundary (abstract only).- Applications of Normal Mode Relaxation Theory to Solid Earth Geophysics (abstract only).- Geodesy and the Problem of Ice Sheets.- Angular Momentum in the Earth System.- Gravity Field Variability, the Geoid, and Ocean Dynamics.- Estimating Covariance Parameters in Gravity Downward Continuation.- Relating Gravity, Density, Topography and State of Stress Inside a Planet.- The A-Optimal Regularization Parameter in Uniform Tykhonov-Phillips Regularization - ?-Weighted BLE.- Response of the Earth's Crust due to Topographic Loads Derived by Inverse Isostasy.- SAR Interferometry for Deformation Control.- Changes of the Antarctic Ice Sheet Mass and the Instability of the Earth's Rotation over the Last 110 Years.- Index of Authors.- List of Participants.
Report on the Symposium.- Gaussian Differential Geometry and Differential Geodesy.- Numerical Techniques for Large Least-Squares Problems with Applications to GOCE.- The Numerical Treatment of the Downward Continuation Problem for the Gravity Potential.- Wiener Filters and Collocation in Satellite Gradiometry.- How to Handle Colored Noise in Large Least-Squares Problems in the Presence of Data Gaps?.- Statistical Hypothesis Tests in Case of Imprecise Data.- Multiresolution Data Analysis - Numerical Realization by Use of Domain Decomposition Methods and Fast Multipole Techniques.- Integer Least-Squares.- The Use of Wavelets for the Acceleration of Iteration Schemes.- Helmert Geometry (abstract only).- Multiscale Solution of Oblique Boundary-Value Problems by Layer Potentials.- Fast Spherical Harmonic Synthesis and Co-Synthesis with Applications in Gravity Field Modeling.- Fixed Effects, Random Effects and the Mixed Model: New Results of Geodetic Estimation and Prediction Theory (abstract only).- Some Generalized Equivalency Theorems for Least-Squares Adjustment.- Procrustes Statistics to Test for Significant OLS Similarity Transformation Parameters.- PDF Evaluation of the Integer Ambiguity Residuals.- Multiple Models - Fixed, Switching, Interacting.- A Comparison of Data Weighting Methods for the Combination of Satellite and Local Gravity Data.- The Rank Deficiency in Estimation Theory and the Definition of Reference Systems.- ITRF2000: From Theory to Implementation.- Problems in the Definition of Vertical Reference Frames.- Geodetic Boundary-Value Problems and the Height Datum Problem.- GPS Permanent Network Solution: the Impact of Temporal Correlations.- A Discussion of the Use of Spherical Approximation or no Approximation in Gravity Field Modeling with Emphasison Unsolved Problems in Least-Squares Collocation.- Some Topics Related to the Solution of Boundary-Value Problems in Geodesy.- The Estimation Theory for Random Fields in the Bayesian Context: a Contribution from Geodesy.- Testing Invariance for Random Field Modeling.- A Formal Comparison Between Marych-Moritz's Series, Sansò's Change of Boundary Method and a Variational Approach for Solving Some Linear Geodetic Boundary Value Problems.- Potential Coefficients Recovery from the Spectra of the Full Space-Borne Gravity Gradient Tensor.- Application of Spherical Pseudo-Differential Operators and Spherical Wavelets for Numerical Solutions of the Fixed Altimetry-Gravimetry Boundary Value Problem.- Ellipsoidal Vertical Deflections: Regional, Continental, Global Maps of the Horizontal Derivative of the Incremental Gravity Potential.- Harmonic Maps (abstract only).- The Analytical Solutions of the Dirichlet and Neumann Boundary Value Problems with Ellipsoidal Boundary (abstract only).- Applications of Normal Mode Relaxation Theory to Solid Earth Geophysics (abstract only).- Geodesy and the Problem of Ice Sheets.- Angular Momentum in the Earth System.- Gravity Field Variability, the Geoid, and Ocean Dynamics.- Estimating Covariance Parameters in Gravity Downward Continuation.- Relating Gravity, Density, Topography and State of Stress Inside a Planet.- The A-Optimal Regularization Parameter in Uniform Tykhonov-Phillips Regularization - ?-Weighted BLE.- Response of the Earth's Crust due to Topographic Loads Derived by Inverse Isostasy.- SAR Interferometry for Deformation Control.- Changes of the Antarctic Ice Sheet Mass and the Instability of the Earth's Rotation over the Last 110 Years.- Index of Authors.- List of Participants.
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