Temporal Gravity Variations near Shrinking Vatnajökull Ice Cap, Iceland

Repeated gravity measurements were carried out from 1991 until 1999 at sites SE of Vatnajökull, Iceland, to estimate the mass flow and deformation accompanying the shrinking of the ice cap. Published GPS data show an uplift of about 13 ± 5 mm/a near the ice margin. A gravity decrease of –2 ± 1 μGal/a relative to the Höfn base station, was observed for the same sites. Control measurements at the Höfn station showed a gravity decrease of –2 ± 0.5 µGal/a relative to the station RVIK 5473 at Reykjavík (about 250 km from Höfn). This is compatible, as a Bouguer effect, with a 10 ± 3 mm/a uplift rate of the IGS point at Höfn and an uplift rate of ~20 mm/a near the ice margin. Although the derived gravity change rates at individual sites have large uncertainties, the ensemble of the rates varies systematically and significantly with distance from the ice. The relationship between gravity and elevation changes and the shrinking ice mass is modelled as response to the loading history. The GPS data can be explained by 1-D modelling (i.e., an earth model with a 15-km thick elastic lithosphere and a 7·10¹⁷ Pa·s asthenosphere viscosity), but not the gravity data. Based on 2-D modelling, the gravity data favour a low-viscosity plume in the form of a cylinder of 80 km radius and 10¹⁷ to 10¹⁸ Pa·s viscosity below a 6 km-thick elastic lid, embedded in a layered PREM-type earth, although the elevation data are less well explained by this model. Strain-porosity-hydrology effects are likely to enhance the magnitude of the gravity changes, but need verification by drilling. More accurate data may resolve the discrepancies or suggest improved models.     

Differential concentration of Technetium-99 (99Tc) in common intertidal molluscs with different food habits

Concentration of ⁹⁹Tc has been measured in fucoids and molluscs, sampled in a sheltered intertidal at the southwest coast of Norway from February to November 2006. The concentrations of ⁹⁹Tc in molluscs differed significantly between species. The filtering bivalve Mytilus edulis had the lowest concentrations with averages of 2.3-5.9 Bq kg⁻¹ d.w., while the herbivorous gastropods Littorinalittorina, Littorina obtusata and Patella vulgata had higher concentrations. P. vulgata and L. obtusata had the highest concentrations, 40-47 and 26-30 Bq kg⁻¹ d.w., respectively. L. obtusata has a specialized habit of living, and prefers to feed on fucoids. P. vulgata can graze extensively on the fucoid Ascophyllum nodosum when available. Fucoids are known to have very high uptake of ⁹⁹Tc, and this was also found in the present study. The high ⁹⁹Tc-concentrations of L. obtusata and P. vulgata are most likely due to their habit of feeding on fucoids.     

Unbiased vs biased estimation of GPS phase ambiguities from dual-frequency code and phase observables

With access to dual-frequency pseudorange and phase Global Positioning System (GPS) data, the wide-lane ambiguity can easily be fixed. Advantage is taken of this information in the linear combination of the above four observables for base ambiguity estimation (i.e. of N ₁ and N ₂). Starting points for our analysis are the Best Linear Unbiased Estimators BLUE₁ and BLUE₂. BLUE₁ is the best one (with minimum mean square error, MSE) if the ionosphere effect is negligible. If this is not the case, BLUE₂ has the smallest variance, but not necessarily the least mean square error. Hence, both estimators may suffer from a non-optimal treatment of the ionosphere bias. BLUE₁ ignores possible ionosphere bias, while BLUE₂ compensates for this bias in a less favourable way by eliminating it at the price of increased noise. As an alternative, linear estimators are derived, which make a compromise between the ionosphere bias and the random observation errors. This leads to the derivation of the Best Linear Estimator (BLE) and the Restricted Best Linear Estimator (RBLE) with minimum MSE. The former is generally not very useful, while the RBLE is recommended for practical use. It is shown that the MSE of the RBLE is limited by the variances of BLUE₁ and BLUE₂, i.e.

Higher-degree reference field in the generalized Stokes-Helmert scheme for geoid computation

In this paper we formulate two corrections that have to be applied to the higher-degree reference spheroid if one wants to use it in conjunction with the Stokes-Helmert scheme for geoid determination. We show that in a precise geoid determination one has to apply the correction for the residual topographical potential and the correction for the earth ellipticity. Both these corrections may reach several decimetres; we show how their magnitudes vary within Canada and we give their global ranges.     

A refined conversion from normal height to orthometric height

The difference between orthometric and normal heights (or the height anomaly and the geoid height) is usually approximated by a term consisting of the Bouguer anomaly times elevation divided by normal gravity. We derive an improved formula, which includes a topographic roughness term (terrain correction) and a term due to the lateral variation of topographic density, for the practical application of this conversion. It is shown that for high mountainous areas with rough topography these two terms are of the same order as the Bouguer anomaly related term. Already for elevations of a few hundred metres they could reach the order of a centimetre. In addition, for the more precise computations in high mountainous areas, a term related with the downward continuation of topographic potential from the surface to sea level could be significant.     

On the error of analytical continuation in physical geodesy

Analytical continuation of gravity anomalies and height anomalies is compared with Helmert's second condensation method. Assuming that the density of the terrain is constant and known the latter method can be regarded as correct. All solutions are limited to the second power of H/R, where H is the orthometric height of the terrain and R is mean sea-level radius. We conclude that the prediction of free-air anomalies and height anomalies by analytical continuation with Poisson's formula and Stokes's formula goes without error. Applying the same technique for geoid determination yields an error of the order of H², stemming from the failure of analytical continuation inside the masses of the Earth.