Geophysical applicability of atomic clocks: direct continental geoid mapping

The geoid is the true physical figure of the Earth, a particular equipotential surface of the gravity field of the Earth that accounts for the effect of all subsurface density variations. Its shape approximates best (in the sense of least squares) the mean level of oceans, but the geoid is more difficult to determine over continents. Satellite missions carry out distance measurements and derive the gravity field to provide geoid maps over the entire globe. However, they require calibration and extensive computations including integration, which is a non-unique operation. Here we propose a direct method and a new tool that directly measures geopotential differences on continents using atomic clocks. General Relativity Theory predicts constant clock rate at sea level, and faster (resp. slower) clock rate above (resp. below) sea level. The technology of atomic clocks is on the doorstep of reaching an accuracy level in clock rate that is equivalent to 1 cm in determining equipotential surface (including geoid) height. We discuss the value and future applicability of such measurements including direct geoid mapping on continents, and joint gravity and geopotential surveying to invert for subsurface density anomalies. Our synthetic calculations show that the geoid perturbation caused by a 1.5 km radius sphere with 20% density anomaly buried at 2 km depth in the crust of the Earth is already detectable by atomic clocks of achievable accuracy. Therefore atomic clock geopotential surveys, used together with relative gravity data to benefit from their different depth sensitivities, can become a useful tool in mapping density anomalies within the Earth.

💡 Research Summary

The paper proposes a novel, direct method for mapping the continental geoid by exploiting the extreme frequency stability of modern atomic clocks. Traditional geoid determination relies on satellite laser ranging and gravimetric data, which must be integrated to recover the geopotential field. This integration is mathematically non‑unique, requires extensive calibration, and suffers from reduced accuracy over land where ocean‑based reference surfaces are unavailable.

General Relativity predicts that a clock’s rate depends on the gravitational potential: clocks run slower in deeper potential wells and faster at higher potentials. Quantitatively, the fractional frequency shift Δf/f equals the geopotential difference ΔW divided by c² (the speed of light squared). Consequently, measuring the frequency difference between two clocks placed at distinct locations yields the absolute geopotential difference without any integration.

State‑of‑the‑art optical lattice and ion clocks have already demonstrated fractional uncertainties approaching 10⁻¹⁸, which corresponds to a height resolution of roughly 1 cm in geopotential terms (ΔW ≈ 0.01 m² s⁻²). The authors use synthetic forward modelling to assess detectability of a realistic subsurface anomaly: a sphere 1.5 km in radius, 20 % denser (or lighter) than the surrounding crust, buried at a depth of 2 km. This body generates a gravity anomaly of about 0.1 mGal and a geopotential perturbation of ≈0.01 m² s⁻². Both magnitudes are above the detection thresholds of current atomic clocks and gravimeters, implying that such a feature could be identified by a combined survey.

A key advantage of clock‑based geopotential measurements is their complementary depth sensitivity compared with gravity. Gravity is most responsive to shallow density variations and decays rapidly with depth, whereas geopotential integrates contributions from the entire mass column, retaining sensitivity to deeper structures. By jointly inverting clock‑derived ΔW and gravity Δg data, one can resolve the vertical distribution of density anomalies with higher fidelity than either dataset alone.

Practical deployment considerations are discussed. Optimal inter‑clock spacing is on the order of a few to several tens of kilometres, balancing atmospheric and temperature‑induced systematic errors against the need for a measurable potential difference. Integration times of several hours to days are required to average down white frequency noise to the 10⁻¹⁸ level. Precise positioning and baseline determination are achieved through GNSS, while clock synchronization can be maintained via fiber‑optic links or satellite time transfer (e.g., the ACES mission). Existing and planned international clock networks (ITOC, ACES, ELT‑Clock) provide the necessary infrastructure for large‑scale geoid surveys.

The authors conclude that atomic‑clock geopotential surveys represent a transformative tool for continental geodesy. As clock technology pushes toward 10⁻¹⁹ fractional uncertainty, the achievable height resolution will fall below 1 cm, opening the possibility of mapping subtle geoid undulations caused by tectonic processes, mantle convection, or fluid migration. Such high‑resolution geoid data, combined with traditional gravimetry, could improve models of crustal density structure, enhance earthquake hazard assessments, and aid resource exploration. Future work should focus on field experiments to validate the concept, develop robust data‑fusion algorithms, and refine error budgets for realistic operational environments.