A Geodetic Determination of the Gravitational Potential Difference Toward a 100-km-Scale Clock Frequency Comparison in a Plate Subduction Zone

Abstract

Recent advances in the developments of optical atomic clocks have enabled 10−18-level frequency comparisons between fibre-linked clocks. Therefore, chronometric leveling with an uncertainty on the order of 1 cm has become possible, based on the general theory of relativity. Since measurement uncertainty does not deteriorate with increasing fibre length, applications of chronometric leveling in geodesy, particularly unification of height reference systems, have been actively studied. In Japan, a frequency comparison is under experimentation using a fibre link connecting two optical lattice clocks approximately 100 km apart. This study estimates both the potential difference between these two clock sites with a geodetic method and its uncertainty to verify the results of chronometric leveling, which will be obtained in the near future. We use orthometric heights derived from leveling surveys repeated for monitoring crustal deformation. When discussing an uncertainty at the 1-cm level in height, the effects of temporal variations in the gravitational potential on the height measurement need to be considered due to various geophysical phenomena, including tides. Our results show that the uncertainty in the height measurements by geodetic leveling is the largest and that tidal potential changes during the height measurements can cause systematic errors of a few mm. The effects due to variations in the nontidal ocean bottom pressure and atmospheric pressure are more than an order of magnitude smaller than the tidal effects at this spatial scale. An upper limit of groundwater effects is also estimated. In a future comparison with clocks with an uncertainty on the order of 10−19, tidal potential changes and groundwater effects must be more rigorously evaluated.

Algorytm regulacji geometrycznych sieci niwelacyjnych

“…5. A huge weak point of the classical approach of the adjustment of the highest order levelling networks is a strong correlation between the standard errors of the adjusted geopotential numbers / heights of the nodal benchmarks and their remoteness from the datum point [6,[11][12]. Analyzing the data included in the second and the sixth columns in table 1 and table 2, one can calculate that the correlation coefficients between the standard errors of the adjusted heights of the benchmarks and their remoteness from the datum point in Qulunkyla are 0.96 and 0.98, respectively for the data in table 1 and table 2.…”

“…The highest order geometric levelling has been used as a main method for establishing of height system for state territories [1, 2] since the last decades of the 19 th century. The method is also widely applied for verification of monitoring of the recent vertical movements of the Earth's crust [3,4], verification and calibration of GNSS measurement [5] and chronometric levelling results [6]. The importance of the precise geometric levelling for civil engineering activities is also well-known [7].…”

“…The duration of measurement of a state levelling network is usually years, but in some cases and decades [1,8]. During the campaign time there are many natural processes, which lead to deterioration of levelling networks and their accuracy, e.g., the recent vertical movements of the Earth's crust [3], tidal effects [6], etc. Therefore, the fast measurement of a levelling network has (a) reflection on the accuracy of the network.…”

Geometryczne dane niwelacyjne i niektóre błędy systematyczne w ich przetwarzaniu

“…Equations ( 3) and (6) give the relation between the power parameter p and standard errors of the adjusted heights of the nodal benchmarks in a levelling network. Moreover, the standard error per unit weight µ is also affected by the Inverse Distance Weighting power parameter p. This relation is given by equation (7).…”

“…The highest order geometric levelling has been used as a main method for establishing of height system for state territories [1][2][3][4] or even for a whole continent [1, [4][5] since the last decades of 19 th century. The method is also widely applied for validation of gravimetric geoid [5] and quasigeoid models [6], verification of chronometric levelling results [7], monitoring of the recent vertical movements of the Earth's crust [3], verification and calibration of GNSS antennas [8], etc. The importance of the precise geometric levelling for civil engineering activities is also well-known [9].…”