Geodesy

Geodesy is the science of measuring and modelling the Earth’s shape, gravity field and rotational dynamics. It underpins everything from precise navigation and mapping to the monitoring of sea-level rise, tectonic movements and mass redistribution in the land–ocean–atmosphere system. Modern geodesists combine observations from terrestrial networks, airborne surveys and, crucially, satellite missions to determine a global reference frame, define the geoid (an equipotential surface approximating mean sea level) and track variations in Earth orientation and gravity. These efforts rely on high-precision timekeeping, advanced inversion methods and sophisticated modelling of signal propagation through the atmosphere. By integrating geometry, gravity and rotation, geodesy delivers centimetre- to millimetre-scale accuracy at the global scale, supporting applications in hazard assessment, resource exploration, climate science and infrastructure planning.

Research from Nature Portfolio

Recent studies have exploited gravity data to resolve crustal interfaces and lithospheric structure with unprecedented detail. In one investigation, gravity anomalies from the GOCE satellite were used to map the topography and fold amplitude of the Mohorovičić discontinuity beneath Tibet, revealing directional ranges orthogonal to surface strain and Moho depths twice that of normal continental crust. Another work produced high-resolution gravity gradient grids at multiple satellite altitudes, capturing directional signals that improve lithospheric modelling and uncertainty reduction in geophysical inversions. Advances in computational efficiency have also emerged: a midpoint quadrature method combined with two-dimensional fast Fourier transforms now permits rapid three-dimensional gravity and magnetic modelling with arbitrary density or susceptibility distributions, cutting computation time and memory use by two orders of magnitude compared with conventional approaches.

Research from all publishers

Theoretical analyses have refined our understanding of spherical harmonic series approximations of the external gravitational potential. Asymptotic formulas now predict error bounds and divergence behaviour beneath the Brillouin sphere, guiding optimal truncation degrees and quantifying depth-dependent error growth. In marine gravity recovery, an improved triple-collocation integration has merged multi-mission altimeter-derived gravity grids, including the latest ICESat-2 data, yielding a unified anomaly field that outperforms individual mission products in shallow and offshore waters. On the analytical front, novel closed-form expressions for the gravitational potential and its up to third-order derivatives have been derived for tesseroids, spherical zonal bands and shells. These solutions serve both as high-precision benchmarks for numerical integration schemes and as a foundation for investigating superposition error elimination in tesseroid discretization.

Geodesy publication trend

The graph below shows the total number of articles in geodesy across all publications each year (not limited to Nature Index journals).

Technical terms

Geoid: An equipotential surface of Earth’s gravity field that approximates mean sea level and serves as a reference for heights.

International Terrestrial Reference Frame (ITRF): A global coordinate system realised by geodetic observations (GNSS, VLBI, SLR, DORIS) that defines positions and velocities of reference stations.

Gravity anomaly: The difference between measured gravity acceleration and a smooth reference model, used to infer subsurface mass variations.

Spherical harmonics: A set of orthogonal functions on the sphere used to represent the global gravity potential as a degree-ordered series.

Tesseroid: A three-dimensional volume element on a spherical shell, employed in forward modelling to compute gravitational effects for regional domains.

References

1. Moho topography, ranges and folds of Tibet by analysis of global gravity models and GOCE data. Scientific Reports (2015).
2. Satellite gravity gradient grids for geophysics. Scientific Reports (2016).
3. Fast 3D gravity and magnetic modelling using midpoint quadrature and 2D FFT. Scientific Reports (2023).
4. Divergence beneath the Brillouin sphere and the phenomenology of prediction error in spherical harmonic series approximations of the gravitational field. Reports on Progress in Physics (2024).
5. An improved triple collocation-based integration of multiple gravity anomaly grids from satellite altimetry: Contribution of ICESat-2. Remote Sensing of Environment (2023).
6. Analytical Solutions for Gravitational Potential up to Its Third-order Derivatives of a Tesseroid, Spherical Zonal Band, and Spherical Shell. Surveys in Geophysics (2023).
7. Geodesy.