Geoid modeling for the Future Circular Collider at CERN

The Future Circular Collider (FCC) at CERN is a next-generation particle accelerator in the planning phase, with a proposed circumference of approximately 91 km and an average depth of 300 m below the surface. Its realization requires an exceptionally precise geodetic infrastructure to ensure the accurate alignment of accelerator components. In particular, a regional geoid model with a precision of 1 cm is needed to support the vertical reference system of the FCC, while sub-millimeter accuracy over sliding windows of a few hundred meters is ultimately required for the alignment of the components inside the tunnel. Existing national and global geoid models do not meet these stringent requirements due to inconsistencies in national datums, heterogeneous data coverage, and limited spatial resolutions. This thesis addresses these challenges by developing, validating, and assessing a dedicated high-precision regional geoid model for the FCC region. The research combines gravity observations, global geoid models, and topographic datasets using the Remove-Compute-Restore approach based on radial basis functions, implemented in the GROOPS software toolkit to compute the FCC geoid and quasigeoid. To enable validation of these solutions, a 45 km long validation profile was established, extending from Meyrin (Switzerland) to Annecy (France), and integrating GNSS, leveling, gravity, and deflections of the vertical measurements. The comparisons confirmed a standard deviation of 1.3 to 1.7 cm between the FCC solution and the independent datasets. Along the projected FCC tunnel, the current precision was estimated to be approximately 1.1 mm over 225 m, providing an important benchmark for future sub-millimeter modeling efforts. Further analyses quantified the influence of auxiliary datasets and modeling assumptions on the geoid solution. Systematic differences among digital elevation models resulted in geoid height variations of up to 3.5 cm in bias and 6 mm in standard deviation, highlighting the significance of digital elevation model quality even in relatively flat terrain. A geoid closed-loop simulator was developed to assess error propagation under controlled conditions. Simulations demonstrated that a gravity observation spacing finer than 1 km is required to maintain sub-centimeter accuracy and that incorrect density assumptions can introduce systematic geoid biases at the centimeter level. These results confirm that data consistency and gravity data spacing are key to achieve sub-millimeter precision required for the final alignment of the FCC. Finally, a comprehensive review of current and emerging techniques for gravity field determination, including quantum gravimeters and chronometric leveling, was conducted to guide the design of future measurement campaigns in the FCC region. Overall, this thesis established the first geoid model dedicated to the FCC region and provided the methodological foundation and validation framework required for sub-centimeter geoid modeling in support of the FCC at CERN.