The fortnightly and monthly zonal tides in the Earth's rotation from 1962 to 1988

SUMMARY The fortnightly (Mf) and monthly (M,) zonal waves in the Earth’s rotation have been analysed in order to derive their scaling factor k/C (or tidal effective Love number k) from several UT1-TAI time series as derived by different techniques (optical astrometry: OA, Very Long Baseline Interferometry: VLBI, and Satellite Laser Ranging: SLR), which are available at the Central Bureau of the IERS (International Earth Rotation Service) during the period from 1962.0 to 1989.3. The derived value for this factor from the astrometric data shows significant timedependent discrepancies with the theoretical values from 1962 to 1982, as appeared in previous analyses on shorter intervals (Capitaine 1982; Hefty 1982; Capitaine & Guinot 1985). Discrepancies of the same order of magnitude also appear in the 1 yr estimates for these factors from SLR or VLBI UT1 time series from 1977 to 1983. Since 1984, using higher precision and more regular SLR or VLBI data, the estimated values for the tidal factor are significantly improved, and there is a good agreement between the 1 yr estimated values from the different techniques, within their corresponding formal errors. The present study clearly shows, as previously suggested by Lambeck & Cazenave (1974) and tested by Merriam (1984) and then by Luo et al. (1987) on limited estimates, that the derivation of the effective Love number k from the zonal waves in UT1 is significantly improved when the data are, at first, corrected for the atmospheric angular momentum effect, especially in the case of the monthly wave. Some anomalous discrepancies with the theoretical value still exist for a few 1 yr estimates of this tidal factor using SLR or VLBI UT1 time series corrected for the atmospheric effect, which may be explained by the remaining unmodelled effects in the range 5-100 days, increasing with the period. The estimated value for (k/C)M, and for (Ic/C)~, from 5yr intervals of the most accurate and regular VLBI and SLR data are consistent with the theoretical value (k/C = 0.944) corresponding to an elastic Earth with a fluid core and equilibrium oceans, plus the additional ‘in phase’ and ‘out of phase’ frequency-dependent contribution for the non-equilibrium oceans as computed by Brosche et al. (1989). Such a result indicates that Yoder, William & Parke’s (1981) model for the tidal scaling parameter now needs significant correction for the ocean tide response. These estimated values for (k/C) are also consistent with the theoretical evaluations for the frequency-dependent effect of anelasticity of the mantle of the long-period Love numbers (Wahr & Bergen 1986: lower bound, Dehant 1987).