Gravity Field Modeling Techniques

Gravity field modelling encompasses a suite of mathematical and observational methods designed to characterise Earth’s gravity variations from global to regional scales. At its core lies potential theory, where the gravitational potential is expanded in spherical harmonics to describe long-wavelength structure, while high-resolution variations are captured through terrestrial and marine gravity measurements. Satellite gravimetry missions employ low-low satellite tracking and satellite-to-satellite altimetry to resolve the medium- to long-wavelength field, whereas radar altimeters infer marine gravity anomalies from ocean surface topography. Terrestrial surveys and airborne measurements furnish short-wavelength detail, often integrated with satellite data via least squares collocation or regularisation techniques. Forward modelling with volume elements, such as tesseroids, enables precise computation of gravitational effects, while inversion methods recover subsurface mass distributions. Advances in computational resources and analytical asymptotic formulations have sharpened estimates of truncation error and divergence behaviour in spherical harmonic series. Combined global models now achieve resolutions down to a few kilometres by merging satellite, airborne and ground data, underpinning geophysical, oceanographic and geodetic applications.

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Recent theoretical work has elucidated the asymptotic behaviour and divergence of truncated spherical harmonic expansions beneath the so-called Brillouin sphere, providing explicit formulae for prediction error bounds in both potential and its radial derivative. Validation with high-precision synthetic data highlights optimum truncation degrees and quantifies how error amplitudes grow with depth and harmonic degree, guiding the selection of series truncation for global and local studies.

In marine gravity recovery, an improved triple collocation integration merges multiple altimeter-derived gravity anomaly grids from diverse missions into a unified high-resolution field. By combining grids through statistical error estimation and least squares collocation, the method yields enhanced marine gravity accuracy across varying depths and proximities to coastlines, demonstrating the benefit of systematic multi-mission fusion for global oceanic applications.

On the analytical front, new closed-form expressions for gravitational potential and its derivatives up to third order have been derived for tesseroids, spherical zonal bands and shells. These solutions enable precise forward modelling at satellite altitudes, reveal superposition error cancellation effects under spherical symmetry, and establish benchmarks for evaluating numerical integration schemes across different grid resolutions and quadrature orders.

Gravity Field Modeling Techniques publication trend

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

Technical terms

Gravitational potential: Scalar function representing the work per unit mass required to move a test mass from infinity to a point in the gravity field.

Spherical harmonics: Orthogonal functions on the sphere used to decompose the global gravity field into degree-dependent components.

Satellite altimetry: Technique measuring sea surface height variations to infer marine gravity anomalies via the geoid-tide relationship.

Least squares collocation: Statistical interpolation method combining heterogeneous gravity data sets while accounting for their error covariances.

Tesseroid: Three-dimensional volume element defined on a spherical shell, employed in forward modelling of local gravitational effects.

References

1. 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).
2. An improved triple collocation-based integration of multiple gravity anomaly grids from satellite altimetry: Contribution of ICESat-2. Remote Sensing of Environment (2023).
3. Analytical Solutions for Gravitational Potential up to Its Third-order Derivatives of a Tesseroid, Spherical Zonal Band, and Spherical Shell. Surveys in Geophysics (2023).