1 Introduction 2 Coordinate Systems and Transformations 3 Gravity Field Quantities 3.1 Gravity field quantities in the spatial domain 3.2 Gravity field quantities in the spectral domain 3.3 Bouguer gravity field 4 Parameters, Data and Models 4.1 Parameters 4.2 Input data and models 4.2.1 Terrestrial datasets 4.2.2 Planetary and lunar datasets 5 Gravity Maps 5.1 Terrestrial gravity maps 5.2 Planetary and lunar gravity maps 6 Theory of Heights 6.1 Definitions of physical heights 6.2 Definitions of the geoid height and the height anomaly 6.3 Approximate definitions of orthometric heights 7 Geoid-to-quasigeoid Separation 7.1 Geoid-to-quasigeoid separation (accurate definition) 7.2 Computation in the spatial domain 7.2.1 Topographic component 7.2.2 Non-topographic component 7.3 Computation in the spectral domain 7.3.1 Topographic term (of uniform density) 7.3.2 Topographic term (of anomalous density) 7.3.3 Non-topographic term 7.3.4 Normal gravity term 7.3.5 Full spectral expression 7.4 Approximate definitions of the geoid-to-quasigeoid separation 7.5 Discussion of numerical aspects 7.6 Geoid-to-quasigeoid separation offshore 8 Comparison of Methods 8.1 Numerical analysis and results 8.1.1 Classical solution 8.1.2 Sj?berg』s solution 8.1.3 Accurate solution 8.2 Comparison of results 8.2.1 Topographic contribution differences 8.2.2 Non-topographic contribution differences 8.2.3 Complete differences 8.2.4 Contribution of terrain geometry 8.3 Sensitivity analysis 8.4 Discussion of results 9 Analysis of Gravity in the Definition of Heights 9.1 Differences between normal and normal-orthometric heights 9.2 Numerical analysis and results 9.2.1 Spectral analysis 9.2.2 Correlation analysis 9.3 Discussion of results
10 Effect of Topographic Density of the Geoid 10.1 Numerical analysis and results 10.1.1 Individual contributions to the geoid-to-quasigeoid separation 10.1.2 Choice of the average topographic density 10.2 Geoid errors due to density uncertainties 10.3 Discussion of results 11 Geoid-to-quasigeoid Separation Offshore 11.1 Numerical analysis and results 11.1.1 Methodology 11.1.2 Results 11.2 Error analysis and discussion of results 12 Height Systems in Planetary Geodesy 12.1 Physical heights for telluric planets (and moons) 12.2 Numerical realization and results 12.2.1 Topographic models 12.2.2 Accurate geoid and orthometric heights 12.2.3 Approximate geoid and orthometric heights 12.2.4 Comparison of accurate and approximate results 12.2.5 Regional study: Martian topographic features 12.2.6 Regional study: Lunar topographic features 12.3 Discussion of results 13 Molodensky』s Concept in Planetary Geodesy 13.1 Methodology 13.2 Results 13.3 Discussion of results 14 Concluding Summary References Appendix A: Topographic Potential for External Convergence Domain Appendix B: Anomalous Topographic Potential for External Convergence Domain Appendix C: Anomalous Topographic Potential for Internal Convergence Domain Appendix D: Contribution of Uniform Topographic Density Appendix E: Contribution of Anomalous Lateral Topographic Density Appendix F: Contribution of Lakes and Glaciers Appendix G: Sub-geoid Mass Density Contribution Appendix H: Contribution of Inland Topography (offshore) Appendix I: Contribution of Polar Glaciers (offshore) Appendix J: Contribution of Mean Dynamic Topography (offshore) Appendix K: Contribution of Sub-geoid Masses (offshore) Appendix L: FFT Technique for Spherical Harmonic Analysis and Synthesis Appendix M: Inverse Solutions to Boundary Value Problems Appendix N: Conditionality of Inverse Solutions to Boundary Value Problems Appendix O: Numerical Analysis of Conditionality of Inverse Solutions Appendix P: Analytical Solution of Green Integrals Appendix Q: Weak Singularity of Green Integrals in A Direct Gravity Inversion Appendix R: Far-zone Contributions to A Direct Gravity Inversion Appendix S: Molodensky Truncation Coefficients for Green Integrals Appendix T: Least-squares Estimation Model Appendix U: Iterative Method of Conjugate Gradients with Pre-conditioning Appendix V: Regularization
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