Determination of a high spatial resolution geopotential model using atomic clock comparisons

G. Lion,I. Panet,C. Guerlin,S. Bize,P. Wolf,P. Delva

doi:10.1007/s00190-016-0986-6

Abstract

Recent technological advances in optical atomic clocks are opening new perspectives for the direct determination of geopotential differences between any two points at a centimeter-level accuracy in geoid height. However, so far detailed quantitative estimates of the possible improvement in geoid determination when adding such clock measurements to existing data are lacking. We present a first step in that direction with the aim and hope of triggering further work and efforts in this emerging field of chronometric geodesy and geophysics. We specifically focus on evaluating the contribution of this new kind of direct measurements in determining the geopotential at high spatial resolution (approx 10 km). We studied two test areas, both located in France and corresponding to a middle (Massif Central) and high (Alps) mountainous terrain. These regions are interesting because the gravitational field strength varies greatly from place to place at high spatial resolution due to the complex topography. Our method consists in first generating a synthetic high-resolution geopotential map, then drawing synthetic measurement data (gravimetry and clock data) from it, and finally reconstructing the geopotential map from that data using least squares collocation. The quality of the reconstructed map is then assessed by comparing it to the original one used to generate the data. We show that adding only a few clock data points (less than 1% of the gravimetry data) reduces the bias significantly and improves the standard deviation by a factor 3. The effect of the data coverage and data quality on the results is investigated, and the trade-off between the measurement noise level and the number of data points is discussed.

Highlights

Chronometry is the science of the measurement of time
Here, we investigate to what extent clocks could contribute to fill the gap between the satellite and nearsurface gravity spectral and spatial coverages in order to improve our knowledge of the geopotential and gravity field at all wavelengths
If we increase the number of gravity data at high spatial resolution, we reduce the modeling error, which solves the problem of data interpolation; inversely, the modeling error will be more important if we have a poor coverage and gaps

Summary

Introduction

As the time flow of clocks depends on the surrounding gravity field through the relativistic gravitational redshift predicted by Einstein (Landau and Lifshitz 1975), chronometric geodesy considers the use of clocks to directly determine Earth’s gravitational potential differences. The performances of optical clocks had not been sufficient to make applications in practice for the determination of Earth’s gravity potential. Chou et al (2010) demonstrated the ability of the new generation of atomic clocks, based on optical transitions, to sense geoid height differences with a 30-cm level of accuracy. An accuracy of 2.1 × 10−18 (JILA, Nicholson et al 2015) has been obtained, equivalent to geopotential differences of 0.2 m2s−2, or 2 cm on the geoid. Other related work using optical fiber or coaxial cable time-frequency transfer can be found in (Shen 2013; Shen and Shen 2015)

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