This volume gathers the proceedings of the IX Hotine-Marussi Symposium on Mathematical Geodesy, which was held from 18 to 22 June 2018 at the Faculty of Civil and Industrial Engineering, Sapienza University of Rome, Italy. Since 2006, the Hotine-Marussi Symposia series has been produced under the auspices of the Inter-Commission Committee on Theory (ICCT) within the International Association of Geodesy (IAG). The ICCT has organized the last four Hotine-Marussi Symposia, held in Wuhan (2006) and Rome (2009, 2013 and 2018). The overall goal of the ICCT and Hotine-Marussi Symposia has always been to advance geodetic theory, as reflected in the 25 peer-reviewed research articles presented here.
The IX Hotine-Marussi Symposium was divided into 10 topical sessions covering all aspects of geodetic theory including reference frames, gravity field modelling, adjustment theory, atmosphere, time series analysis and advanced numerical methods. In total 118 participants attended the Symposium and delivered 82 oral and 37 poster presentations. During a special session at the Accademia Nazionale deiLincei, the oldest scientific academy in the world, six invited speakers discussed interactions of geodesy with oceanography, glaciology, atmospheric research, mathematics, Earth science and seismology.
Part I: Gravity field modelling and height systems.- Orbit Optimization for Future Gravity Field Missions: Influence of the Time Variable Gravity Field Models in a Genetic Algorithm Approach.- Comparison of Criteria for the Identification of Correlated Orders in GRACE Spherical Harmonic Coefficients.- Second- and Third-Order Derivatives of the Somigliana-Pizzetti Reference Gravity Field.- On the Advantage of Normal Heights.- Green's Function Method Extended by Successive Approximations and Applied to Earth's Gravity Field Recovery.- On Combining the Directional Solutions of the Gravitational Curvature Boundary-Value Problem.- Part II: Theory of modern geodetic reference frames.- Review of Reference Frame Representations for a Deformable Earth.- Impacts of the LARES and LARES-2 Satellite Missions on the SLR Terrestrial Reference Frame.- Permanent GNSS Network Optimization Considering Tectonic Motions.- Part III: Estimation theory and inverse problems in geodesy.- Adjustment of Gauss-Helmert Models with Autoregressive and Student Errors.- How Abnormal Are the PDFs of the DIA Method: A quality description in the context of GNSS.- Controlling the Bias within Free Geodetic Networks.- Regularized Solutions of the Two Layers Inverse Gravimetric Problem in the Space of Bounded Variation Functions.- Converted Total Least Squares Method and Gauss-Helmert Model with Applications to Coordinate Transformations.- A Bayesian Nonlinear Regression Model Based on T-Distributed Errors.- The GNSS for Meteorology (G4M) Procedure and Its Application to Four Significant Weather Events.- Part IV: Advanced numerical methods in geodesy.- Modelling the Gravitational Field by Using CFD Techniques.- Surface Loading of a Self-Gravitating, Laterally Heterogeneous Elastic Sphere -Preliminary Result for the 2D Case.- Using Structural Risk Minimization to Determine the Optimal Complexity of B-Spline Surfaces for Modelling Correlated Point Cloud Data.- On the Numerical Implementation of a Perturbation Method for Satellite Gravity Mapping.- Non-Recursive Representation of an Autoregressive Process within the Magic Square.- A Bootstrap Approach to Testing for Time-Variability of AR Process Coefficients in Regression Time Series with t-Distributed White Noise Components.- Identification of suspicious data for robust estimation of stochastic processes.- Quality and Distribution of Terrestrial Gravity Data for Precise Regional Geoid Modelling: A Generalized Setup.- Part VI: Interactions of geodesy and mathematics.- Geodesy and Mathematics: Interactions, Acquisitions, and Open Problems.