GPS‐observed vertical ocean tide loading displacements show in Cornwall, southwest England, and in Brittany, northwest France, discrepancies of 2–3 mm with predicted values based on the isotropic Preliminary Reference Earth Model for the main tidal harmonic M2, yet in central Europe the agreement is better than 0.5 mm. By comparison of ocean tide models and validation with tide gauge observations, we demonstrate that the uncertainties in the former are too small to cause this disagreement. Furthermore, we find that different local models of the crust and different global elastic reference models derived from seismological observations can only reduce the observed discrepancies to 1–2 mm, which still exceeds the GPS observational uncertainty of 0.2–0.4 mm. It is customary to use the elastic properties of the Earth as given by seismic models. Previously, there has been insufficient evidence to determine how to modify these properties during the transformation from seismic to tidal frequencies to account for possible anelastic dispersion in the asthenosphere, and so this effect has been ignored. If we include this effect, then our discrepancies reduce further to 0.2–0.4 mm. This value is of the same order as the sum of the remaining errors due to uncertainties in the ocean tide models and in the GPS observations themselves. This research provides evidence in western Europe of a reduction of around 8–10% of the seismic shear modulus in the asthenosphere at tidal frequencies. In addition, we find that the asthenosphere absorption band frequencies can be represented by a constant quality factor Q.
GPS has been extensively used to estimate tidal ground displacements, but the accuracy of this has not been systematically verified. Using more than 20 sites distributed across western Europe, we show that postprocessed kinematic precise point positioning GPS with appropriately tuned process noise constraints is capable of recovering synthetic tidal displacements inserted into real data, with a typical accuracy of 0.2 mm depending on the time series noise. The kinematic method does not result in erroneous propagation of signals from one coordinate component to another or to the simultaneously estimated tropospheric delay parameters. It is robust to the likely effects of day‐to‐day equipment and reference frame changes, and to outages in the data. A minimum data span of 4 years with at least 70% availability is recommended. Finally, we show that the method of reducing apparent coordinate time series noise by constraining the tropospheric delay to values previously estimated in static batch GPS analysis, in fact, results in the suppression of true tidal signals. Using our kinematic GPS analysis approach, periodic displacements can be reliably observed at the 0.2 mm level, which is suitable for the testing and refinement of ocean tide and solid Earth response models.
SUMMARY O1 and M2 observations from well‐calibrated spring gravimeters and superconducting gravimeters from the Global Geodynamics Project (GGP) are used to test models of the Earth's body tide and 10 ocean tide models. It is shown that some of the ocean tide models give anomalous results in various parts of the world. For example, the Schwiderski ocean tide model gives discrepancies in several areas and the FES series of ocean tide models have problems in the western Pacific (China, Japan and Australia). The majority of the high‐quality tidal gravity measurements in Europe are in close agreement with the Dehant, Defraigne and Wahr (DDW) elastic and inelastic body tide models. The gravimetric factors for the DDW elastic and inelastic models only differ by 0.12 per cent and the present calibration accuracy does not allow us to distinguish between these models, but does reduce the previous upper bound on inelastic gravimetric factors. The European observations give a phase lag of a few hundredths of a degree for the O1 body gravity tide, which is consistent with the Mathews inelastic body tide model. At some European and worldwide stations the gravimetric factors differ by up to 0.3 per cent from the DDW model and it is suggested that further checks on the gravimeter calibrations are required. Accurate determinations of instrumental phase lags are now easier to achieve and the imaginary (out‐of‐phase) component of tidal gravity can be used for accurate tests of this component of ocean tide models.
S U M M A R YTwo independent continuous global positioning system (CGPS) processing strategies, based on a double-difference regional network and a globally transformed precise point positioning solution, provide horizontal and vertical crustal motion estimates for Great Britain. Absolute gravity and geological information from late Holocene sea level data further constrain the vertical motion estimates. For 40 CGPS stations we estimate station velocities and associated uncertainties using maximum likelihood estimation, assuming the presence of white and coloured noise. Horizontal station velocity estimates agree to <1 mm yr −1 between the two CGPS processing strategies and closely follow predicted plate motions. Residual velocities, generally <1 mm yr −1 , follow no regular pattern, that is, there is no discernible internal deformation, nor any dependence on station monumentation or time-series length. Vertical station velocity estimates for the two CGPS processing strategies agree to ∼1 mm yr −1 , but show an offset of ∼1 mm yr −1 with respect to the absolute gravity (AG) estimates. We attribute this offset to a bias related to known issues in current CGPS results and correct for it by AG-alignment of our CGPS estimates of vertical station velocity. Both CGPS estimates and AG-aligned CGPS estimates of present-day vertical crustal motions confirm the pattern of subsidence and uplift in Great Britain derived from Holocene sea level data for the last few thousand years: ongoing subsidence on Shetland, uplift in most areas of Scotland, and subsidence in large areas of England and Wales.
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