Quarter-diurnal tides observed with a long-base water-tube tiltmeter in the Grand Duchy of Luxembourg

We analyzed 7 years of Earth tide measurements performed with a 43 m long water-tube tiltmeter in the Underground Laboratory for Geodynamics in Walferdange (Luxembourg).The high performances of this instrument lead to diurnal and semi-diurnal tidal measurements in excellent accordance with the models. The results of the Earth tide harmonic analysis show the lowest standard deviations (STDV) among all the results obtained with other tiltmeters in Walferdange. For instance, the high signal-to-noise ratio (SNR) allows an estimation of the amplitude of the M2 wave with a STDV as small as 3 μasec (i.e., a SNR of 1700 for this wave) and a phase uncertainty less than 0.024°, which represents 3 s only.In addition it was possible to successfully separate and obtain a significant estimate of some of the small constituents of the ter- and quarter-diurnal bands such as 2MK3, M3, MN4, M4 and MS4. The presence of these very small waves (with amplitudes of less than a few microarcseconds) is most likely due to the effects of the shallow-water tides known to be remarkable in the North Sea (distance of 300 km). This represents the first clear observation of tilt induced by the non-linear tides in the North Sea and it might become a complementary tool for the validation of non-linear tide models.