Tidal Love and Shida numbers estimated by geodetic VLBI

Frequency-dependent Love and Shida numbers, which characterize the Earth response to the tidal forces, were estimated in a global adjustment of all suitable geodetic Very Long Baseline Interferometry (VLBI) sessions from 1984.0 to 2011.0. Several solutions were carried out to determine the Love and Shida numbers for the tidal constituents at periods in the diurnal band and in the long-period band in addition to values of the Love and Shida numbers common for all tides of degree two. Adding up all twelve diurnal tidal waves that were estimated, the total differences in displacement with respect to the theoretical conventional values of the Love and Shida numbers calculated from an Earth model reach 1.73 ± 0.29 mm in radial direction and 1.15 ± 0.15 mm in the transverse plane. The difference in the radial deformation following from the estimates of the zonal Love numbers is largest for the semi-annual tide Ssa with 1.07 ± 0.19 mm.

•Space geodetic estimates of complex frequency-dependent Love and Shida numbers of degree two.•Love and Shida numbers from 27 years of geodetic VLBI observations with unprecedented accuracy.•Love and Shida numbers for solid Earth tides notably improved in terms of precision and accuracy.•Small deviation of Love and Shida numbers of solid Earth tides from their conventional values.