Summary The admittance function and coherence relating gravity and topography are important constraints on the elastic thickness (Te) of the lithosphere. Forsyth (1985) modelled them with a lithosphere loaded both externally by topography and internally by density contrasts such as initial undulations on the Moho. His approach has yielded thicknesses as high as 150 km for the continental lithosphere. McKenzie & Fairhead (1997) argued that this method can only supply an upper bound on Te because the response is biased by ‘noise’ due to density variations in the upper crust. We have used Forsyth's approach to analyse the effect of shallow heterogeneities such as sedimentary basins and igneous intrusions, simulating them by a thin layer with a laterally variable density. The information content of the admittance and coherence is concentrated in the wavenumbers at which the two responses roll‐off to half their zero‐wavenumber values. These two parameters are used to explore the interdependence of the retrieved elastic thickness and internal/external loading ratio f. Provided the internal load is less than 10 per cent of the external, it does indeed bias the response so that Te is overestimated. However, for predominantly internal loads, the reverse is the case, and the value of Te obtained by assuming equal internal and external loads is actually a lower bound. It is particularly important to allow for the flexure due to upper‐crustal loads when the lithosphere is old and topography subdued due to prolonged erosion. Application of our approach to McKenzie & Fairhead's (1997) Western Australia data shows that the loading ratio depends strongly on wavenumber, but that it is still possible to use the response data to constrain Te, which must be at least 90 km if the results obtained by conventional spectral estimation are accepted, at least 40 km using the multitaper method.
The theory, causes, observations, and possible applications of seismic anisotropy in the Earth have developed considerably since the previous state of the art paper was published in 1977. The behaviour of waves in layered anisotropic media is now much better understood and the evidence for seismic anisotropy indicates that anisotropy is likely to be present throughout much of the crust and upper mantle. The top few hundred kilometres of the mantle appears to be anisotropic with the orientations aligned by the present or palaeo stress-field. The upper part of the crust is frequently anisotropic, probably due to cracks differentially aligned by the non-lithostatic stresses. The possibility of being able to monitor crack geometry by seismic techniques opens a wide range of applications in currently important activities.
S U M M A R YThis paper describes a new rationale for computing a gravimetric geoid and reports that the resulting geoid model, EDIN2000, is now good enough to resolve previously contradictory estimates for mean sea surface topography (MSST) around Great Britain. For at least 30 yr, it has been known that MSST derived from tide gauges, levelling and oceanography were mutually inconsistent and differed by an order of magnitude. When combined with an altimetric mean sea surface, EDIN2000 is also able to map realistic MSST over the northwest European shelf, and identify and quantify mean currents flowing in the deep ocean parallel to the shelf edge.When compared with 11 GPS referenced tide gauges on the British mainland our estimate of MSST has a standard deviation of only 0.03 m and its variation with latitude is not significantly different from zero. For these sites, long distance levelling errors are larger than geoid errors. We identify a systematic jump (by 0.24 ± 0.05 m) in the levelled transfer of Ordnance Datum Newlyn, affecting all sites in Great Britain to the north of latitude 53 • N. Even after this correction, the variability of levelling remains larger than that of the geoid and GPS, implying a more complex structure to the levelling error than a simple step.Away from coasts we find that the best way to validate marine gravity data is their ability to predict MSST with low local variability when combined with altimetric mean sea level. There is a large reduction in MSST variability when marine gravity data are subjected to an anti-aliased adjustment of the mismatch where ship tracks cross. We also report two MSST model comparisons from a shelf seas and a deep ocean model, both of high resolution. There is quantitative and qualitative agreement between our geoid-derived MSST and the model predictions, indicating significant improvements compared with earlier geoid models. We also show that with the improved accuracy of geoid-based MSST, it will become necessary to validate models and observations at matching epochs.
In the Nordic seas, we combine a computation of absolute surface current flow derived from geodetic data with in situ historical hydrographic data to estimate the absolute volume, heat, and salt transports as a function of depth. Our mean dynamic topography (MDT) is calculated from marine, airborne and satellite gravimetry, combined with satellite altimetry, using a new algorithm called the iterative combination method (ICM). Residual noise in the gravimetric geoid is the limit on MDT resolution and is suppressed using a Gaussian filter with a width at half‐peak amplitude of 59 km. Detailed and coherent flow paths for surface geostrophic currents are clearly identified. ICM MDT was used as fixed boundary condition to transform historical hydrography into absolute estimates of volume, heat, and salt transport, replacing the assumption of an isobaric surface at a predetermined depth. For the inflow of Atlantic Water (potential temperature Θ > 6°C) through the Faroe‐Shetland Channel into the Nordic seas, we obtain time‐averaged fluxes between 1993 and 1996 of 3.5 Sv (volume), 121 TW (heat), and 124 × 106 kg s−1 (salt), very close to reported observations from acoustic Doppler current profiler moorings and conductivity‐temperature‐depth data. For the Svinøy section, we obtain a northward transport of Atlantic Water (S > 35.0, T > 5.0°C) of 3.9 Sv in the eastern branch of the Norwegian Atlantic Current comparable with reported measurements of 4.2 Sv. Similarly good agreement is found for the Hornbanki and Iceland‐Faroe Ridge sections and for monitoring Atlantic Water outflow across the Barents Sea Opening to the Arctic shelf.
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