目前大地水准测量和沿水准线的重力测量实现水准网的国家，实际使用的是赫尔默特正射高度或莫洛登斯基正常高度。如何实现垂直基准统一是目前面临的主要问题。《Definition and Realization of Height Systems in Terrestrial and Planetary Science Applications（地球和行星科学应用中高程系统的定义与实现）》对赫尔默特正射高度和莫洛登斯基法向高度之间的转换进行了数值研究。结果表明，赫尔默特对正射高度的定义并不准确。为了减少由于应用赫尔默特正射高度产生的较大误差，提出了一种精确的正射高度计算方法。在精确定义的基础上，给出了正射高度和法向高度之间的关系，并总结了计算这种关系的数值方法。《Definition and Realization of Height Systems in Terrestrial and Planetary Science Applications（地球和行星科学应用中高程系统的定义与实现）》将数值方法扩展到行星科学应用中，特别是对地球行星（和卫星）的物理高度的研究，同时对数值结果进行了讨论。
目錄：
Contents1 Introduction 12 Coordinate Systems and Transformations 133 Gravity Field Quantities 153.1 Gravity field quantities in the spatial domain 153.2 Gravity field quantities in the spectral domain 183.3 Bouguer gravity field 194 Parameters， Data and Models 244.1 Parameters 244.2 Input data and models 254.2.1 Terrestrial datasets 254.2.2 Planetary and lunar datasets 275 Gravity Maps 305.1 Terrestrial gravity maps 305.2 Planetary and lunar gravity maps 346 Theory of Heights 406.1 Definitions of physical heights 406.2 Definitions of the geoid height and the height anomaly 426.3 Approximate definitions of orthometric heights 437 Geoid-to-quasigeoid Separation 457.1 Geoid-to-quasigeoid separation (accurate definition) 457.2 Computation in the spatial domain 477.2.1 Topographic component 507.2.2 Non-topographic component 517.3 Computation in the spectral domain 537.3.1 Topographic term (of uniform density) 547.3.2 Topographic term (of anomalous density) 567.3.3 Non-topographic term 587.3.4 Normal gravity term 597.3.5 Full spectral expression 597.4 Approximate definitions of the geoid-to-quasigeoid separation 607.5 Discussion of numerical aspects 637.6 Geoid-to-quasigeoid separation offshore 668 Comparison of Methods 698.1 Numerical analysis and results 698.1.1 Classical solution 708.1.2 Sj？berg’s solution 738.1.3 Accurate solution 748.2 Comparison of results 788.2.1 Topographic contribution differences 808.2.2 Non-topographic contribution differences 828.2.3 Complete differences 838.2.4 Contribution of terrain geometry 848.3 Sensitivity analysis 868.4 Discussion of results 889 Analysis of Gravity in the Definition of Heights 919.1 Differences between normal and normal-orthometric heights 919.2 Numerical analysis and results 929.2.1 Spectral analysis 1069.2.2 Correlation analysis 1089.3 Discussion of results 10910 Effect of Topographic Density of the Geoid 11110.1 Numerical analysis and results 11310.1.1 Individual contributions to the geoid-to-quasigeoid separation 11410.1.2 Choice of the average topographic density 12110.2 Geoid errors due to density uncertainties 12210.3 Discussion of results 12411 Geoid-to-quasigeoid Separation Offshore 12711.1 Numerical analysis and results 12711.1.1 Methodology 12711.1.2 Results 12811.2 Error analysis and discussion of results 13212 Height Systems in Planetary Geodesy 13412.1 Physical heights for telluric planets (and moons) 13612.2 Numerical realization and results 13712.2.1 Topographic models 13812.2.2 Accurate geoid and orthometric heights 14112.2.3 Approximate geoid and orthometric heights 14512.2.4 Comparison of accurate and approximate results 14512.2.5 Regional study: Martian topographic features 14812.2.6 Regional study: Lunar topographic features 14812.3 Discussion of results 15013 Molodensky’s Concept in Planetary Geodesy 15413.1 Methodology 15513.2 Results 15513.3 Discussion of results 16114 Concluding Summary 163References 170Appendix A: Topographic Potential for External Convergence Domain 187Appendix B: Anomalous Topographic Potential for External Convergence Domain 189Appendix C: Anomalous Topographic Potential for Internal Convergence Domain 192Appendix D: Contribution of Uniform Topographic Density 194Appendix E: Contribution of Anomalous Lateral Topographic Density 195Appendix F: Contribution of Lakes and Glaciers 196Appendix G: Sub-geoid Mass Density Contribution 197Appendix H: Contribution of Inland Topography (offshore) 198Appendix I: Contribution of Polar Glaciers (offshore) 200Appendix J: Contribution of Mean Dynamic Topography (offshore) 202Appendix K: Contribution of Sub-geoid Masses (offshore) 204Appendix L: FFT Technique for Spherical Harmonic Analysis and Synthesis 205Appendix M: Inverse Solutions to Boundary Value Problems 207Appendix N: Conditionality of Inverse Solutions to Boundary Value Problems 210Appendix O: Numerical Analysis of Conditionality of Inverse Solutions 215Appendix P: Analytical Solution of Green Integrals 221Appendix Q: Weak Singularity of Green Integrals in A Direct Gravity Inversion 223Appendix R: Far-zone Contributions to A Direct Gravity Inversion 225Appendix S: Molodensky Truncation Coefficients for Green Integrals 228Appendix T: Least-squares Estimation Model 230Appendix U: Iterative Method of Conjugate Gradients with Pre-conditioning 232Appendix V: Regularization 233
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