Tidal gravity and ocean tide loading in Europe

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The results are presented from tidal gravity measurements at five sites in Europe using LaCoste and Romberg ET gravimeters. Improvements that we have made to the accuracies of these gravimeters are discussed. It is shown that the 'standard' calibration of the International Center for Earth Tides, used for worldwide tidal gravity profiles, is 1.2 per cent too high. The M₂ and O₁ observations are compared with model calculations of the Earth's body tide and ocean tide loading and it is shown that there is a very significant improvement in the agreement between observations and models compared to that obtained with previous tidal gravity measurements. For O₁, where the ocean tide loading and attraction in central Europe is only 0.4 per cent of the body tide, our measurements verify that the Dehant-Wahr anelastic body tide model gravimetric factor is accurate to 0.2 per cent. It is also shown that the effects of lateral heterogeneities in Earth structure on tidal gravity are too small to explain the large anomalies in previously published tidal gravity amplitudes. The observations clearly show the importance of conserving tidal mass in the Schwiderski ocean tide model. For sites in central Europe, the M₂ and O₁ observations and the models are in agreement at the 0.1 μgal (10⁻⁹ m s⁻²) level and tidal corrections to this accuracy can now be made to absolute gravity measurements.     

The Residual Water Flow through the Solent, South England

Summary. A reduced equation of motion is used to compute the residual velocity and the residual transport through the West Solent from the water levels recorded over an eight-month period at tide gauges at either end of the channel. A coefficient of bottom friction of 5·0 × 10⁻³ is assumed. There was a spring-neap variation and a significant correlation of fluctuations in the residual velocity with meteorological conditions. Westward residual velocities occurred at spring tides with low barometric pressure and south-westerly winds. Eastward residual velocities occurred at neap tides with high pressure and north-easterly winds. Because of the progressive nature of the tidal wave the long term residual transport appeared to be towards the west and the flushing time for the Solent system was long for considerable periods. The maximum velocities experienced during a tidal cycle half way along the channel are towards the west with a probability of values exceeding 160 cm s⁻¹ for 10 min in 5·4 days.     

The tidal dynamics of the Irish and Celtic Seas

Summary. Current meter data collected over periods of more than 14 day from the Irish and Celtic Seas are harmonically analysed and presented in maps of tidal stream information. Making use of the analysed current data, and by constructing time series of frictional and inertial stresses which are also harmonically analysed, harmonic constituents of the surface tidal slopes at current meter stations are obtained. Using these with data collected from offshore tide gauges, and in conjunction with coastal tide data, cotidal maps are drawn with some confidence for M ₂, S ₂, O ₁ and K ₁, the M ₂ chart resolving the discrepancy which exists between the different charts of the Celtic Sea already produced. Cotidal maps for M ₃ and M ₄ are also presented.
The mean over a tidal cycle of the energy flux for M ₂, S ₂ and O ₁ is also presented in the form of the total energy flux in these constituents which crosses different sectional lines. A flux of 44 × 10⁶ kW is observed to enter the Celtic Sea from the Atlantic and this is compared with previous estimates. An energy budget is also performed for M ₂, including all the effects of astronomical forcing and Earth tides to enable comparison to be made between the true energy inflow and the estimated frictional dissipation. Finally, comparison is made between the mean of the instantaneous energy flux and the sum of the energy fluxes associated with the major harmonics.     

A diurnal resonance in the ocean tide and in the Earth's load response due to the resonant free 'core nutation'

Summary. The luni-solar forced nutations and body tide are believed to be resonant at frequencies near (1 + 1/460) cycle sidereal day⁻¹ as seen from the rotating Earth. This resonance is due to the Earth's rotating, elliptical fluid core. We show here that tides in the open ocean and the Earth's response to those tides must also be resonant at (1 + 1/460) cycle day⁻¹. We examine these resonant oceanic effects on the Earth's nutational motion and on the body tide. Effects on the forced nutations might be as large as 0.002 arcsec at 18.6 yr. The effects on the observed resonance in the body tide are more important. For tidal gravity, for example, the difference between K ₁ and 0 ¹ which is usually used to determine the resonance, can be perturbed by 30 per cent or more due to the oceanic resonance effects.     

Geodetic observations of ice flow velocities over the southern part of subglacial Lake Vostok, Antarctica, and their glaciological implications

In the austral summer seasons 2001/02 and 2002/03, Global Positioning System (GPS) data were collected in the vicinity of Vostok Station to determine ice flow velocities over Lake Vostok. Ten GPS sites are located within a radius of 30 km around Vostok Station on floating ice as well as on grounded ice to the east and to the west of the lake. Additionally, a local deformation network around the ice core drilling site 5G-1 was installed.
The derived ice flow velocity for Vostok Station is  2.00 m a⁻¹± 0.01 m a⁻¹  . Along the flowline of Vostok Station an extension rate of about 10⁻⁵ a⁻¹ (equivalent to 1 cm km⁻¹ a⁻¹) was determined. This significant velocity gradient results in a new estimate of 28 700 years for the transit time of an ice particle along the Vostok flowline from the bedrock ridge in the southwest of the lake to the eastern shoreline. With these lower velocities compared to earlier studies and, hence, larger transit times the basal accretion rate is estimated to be 4 mm a⁻¹ along a portion of the Vostok flowline. An assessment of the local accretion rate at Vostok Station using the observed geodetic quantities yields an accretion rate in the same order of magnitude. Furthermore, the comparison of our geodetic observations with results inferred from ice-penetrating radar data indicates that the ice flow may not have changed significantly for several thousand years.     

North Atlantic Water in the Barents Sea Opening, 1997 to 1999

North Atlantic Water (NAW) is an important source of heat and salt to the Nordic seas and the Arctic Ocean. To measure the transport and variability of one branch of NAW entering the Arctic, a transect across the entrance to the Barents Sea was occupied 13 times between July 1997 and November 1999, and hydrography and currents were measured. There is large variability between the cruises, but the mean currents and the hydrography show that the main inflow takes place in Bjørnøyrenna, with a transport of 1.6 Sv of NAW into the Barents Sea. Combining the flow field with measurements of temperature and salinity, this results in mean heat and salt transports by NAW into the Barents Sea of 3.9×10¹³ W and 5.7×10⁷ kg s⁻¹, respectively. The NAW core increased in temperature and salinity by 0.7 °C yr⁻¹ and 0.04 yr⁻¹, respectively, over the observation period. Variations in the transports of heat and salt are, however, dominated by the flow field, which did not exhibit a significant change.     

Glaciers in Svalbard: mass balance, runoff and freshwater flux

Gain or loss of the freshwater stored in Svalbard glaciers has both global implications for sea level and, on a more local scale, impacts upon the hydrology of rivers and the freshwater flux to fjords. This paper gives an overview of the potential runoff from the Svalbard glaciers. The freshwater flux from basins of different scales is quantified. In small basins (A < 10 km²), the extra runoff due to the negative mass balance of the glaciers is related to the proportion of glacier cover and can at present yield more than 20% higher runoff than if the glaciers were in equilibrium with the present climate. This does not apply generally to the ice masses of Svalbard, which are mostly much closer to being in balance. The total surface runoff from Svalbard glaciers due to melting of snow and ice is roughly 25 ± 5 km³ a⁻¹, which corresponds to a specific runoff of 680 ± 140 mm a⁻¹, only slightly more than the annual snow accumulation. Calving of icebergs from Svalbard glaciers currently contributes significantly to the freshwater flux and is estimated to be 4 ± 1 km³ a⁻¹ or about 110 mm a⁻¹.     

Accumulation Rate Measurements at Taylor Dome, East Antarctica: Techniques and Strategies for Mass Balance Measurements in Polar Environments

Accumulation rate measurements on the East Antarctic plateau are challenging due to both spatial and temporal variability. Annual stratigraphy is often not reliably or consistently preserved in the firn, and so accumulation cannot be determined from snow pit stratigraphy. We present a suite of accumulation rate measurements collected over several seasons at Taylor Dome, East Antarctica. We compare net accumulation results from direct burial rate measurements and β -activity firn cores along a 35 km traverse. The two methods are consistent and show that the net accumulation varies from greater than 10 cm a⁻¹ to about 1 cm a⁻¹ (ice equivalent) southwest to northeast across the dome. We map the depth of shallow radar layering to interpolate and extrapolate these point-location measurements and show that considerable variations occur over kilometer scales resulting from subtle surface topography. We also present accumulation rates estimated from concentration of the cosmogenic isotope ¹⁰Be and from activity profiles of ²¹⁰Pb. Finally, satellite passive microwave data are used to estimate spatially averaged accumulation rates on the regional to continental scale to provide a context for these local observations. We show that robust mass balance measurements in this environment must rely on spatial and/or temporal averaging.     

Oxygen consumption in Macrotrachela musculosa and Trichotria truncata (Rotatoria) from the High Arctic

Oxygen consumption by rotifers Macrotrachela musculosa and Trichotria truncata from Spitsbergen tundra (77°N) was measured using the method of Cartesian divers. The metabolic rate of M. musculosa was: 0.205 10⁻³mm³ 0₂ per g 10⁻⁶ per hour at 2°C, 0.201 10⁻⁶mm³ at 6°C and 0.616 10⁻³mm³ 0₂ per g 10⁻⁶ per hour at 10°C. The metabolic rate of Trichotria truncata at 6° was 0.103 10⁻³mm³ per g 10⁻⁶ per hour. The relation between body weight and oxygen consumption by M. musculosa at 2°C is expressed with the equation R = 0.18W^0.67, with R – oxygen consumption in mm³10⁻³ per individual per hour and W – wet weight of an animal in g 10⁻⁶.     

40Ar-39Ar incremental heating studies on the Tudor Gabbro, Grenville Province, Ontario: its bearing on the North American apparent polar wander path in late Proterozoic times

Summary. ⁴⁰Ar-³⁹Ar incremental heating studies have been carried out on samples taken from the Tudor Gabbro, Grenville Province, Ontario. In an earlier K-Ar study, these rocks have yielded an isochron age of ∼700 Ma together with very high initial argon ratios. Age spectrum plots on whole-rock samples, in general, display a saddle-shaped character, with two of them exhibiting minima close to 700 Ma. No clear plateaus are observed for these rocks. A hornblende separate records the time ∼1110 Ma at which the stock finally cooled through the ∼590°C isotherm. The Tudor Gabbro was probably intruded into an area undergoing middle-amphibolite facies meta-morphism about 1180 Ma ago. The age spectra of two whole-rock samples together with that of their plagioclase separates, suggest that the stock cooled to ∼200–250°C at about 720 Ma. Slow cooling, averaging about 1°C Ma⁻¹ is indicated for this section of the Grenville Province for the period 1100–700 Ma. If the age of the Tudor Gabbro's palaeomagnetic pole position is taken to be 720 Ma, the Hadrynian Track Hypothesis leads to very high polar wander rates of > 20cm a⁻¹ for the period 820–720 Ma. If this hypothesis is rejected, the average drift rate for this period would be ∼4 cm a⁻¹, in much better agreement with published values of ∼5 cm a⁻¹ for the period 1400–820 Ma.     

Long-period geomagnetic variations and mantle conductivity: an inversion using Bailey's method

Summary. We have implemented an algorithm which is based on Bailey's solution of the inverse problem of electromagnetic induction in the Earth. The study was motivated by recent determinations of very long period data and also benefited from recent redeterminations of high frequency data. The algorithm has been successfully tested to provide reliable estimates of conductivity down to a depth of 2000 km, using synthetic data in the period range from 4 days to 11 years. Smooth data sets, which are required for the inversion, were constructed from various sources. At a given depth, the range of inverted models is less than one order of magnitude. Due to the lack of high frequency data, the conductivity of the upper 600 km of the mantle, which is found to be of the order of 10⁻¹Ω⁻¹ m⁻¹, may be overestimated. The algorithm performs well in the middle mantle, where conductivity rises steadily from 1 to 50 Ω⁻¹ m⁻¹. The lack of very low frequency data and limitations of the algorithm prevent one from obtaining meaningful estimates in the lower mantle. However, the study of the propagation of the late 1960s secular variation acceleration provides an estimate of the mean conductivity of the whole mantle. Thus, a complete mantle profile can be constructed. It is found that deep mantle conductivity probability does not exceed a few hundred Ω⁻¹ m⁻¹.     

Mass Movement of Mancos Shale Crust Near Caineville, Utah: A 30-year Record

Rates of soil creep were studied periodically over a 30-year period in southeastern Utah on Mancos Shale badland slopes averaging 35 degrees. More intensive studies were carried out over a 10-year period on slopes averaging 40 degrees. On the 35 degree slope the average rate of movement was 2.71 cm yr⁻¹.On the 40 degree slopes, rates varied from 3.14 to 5.94 cm yr⁻¹.
Individual rates of movement varied widely, but average movement of a given line was consistent. No statistical differences in rates of movement were found between north- and south-facing slopes.
About two-thirds of the total movement occurred during the winter/spring period; episodes of rapid movement coincided with years in which storms deposited at least 0.6 cm of precipitation per day for at least two consecutive days. Downslope rotation of nails indicates that creep involves only the top few centimeters of soil.     

Deglaciation effects on the rotation of the Earth

Summary. The viscoelastic response of the Earth to the mass displacements caused by late Pleistocene deglaciation and concomitant sea level changes is shown to be capable of producing the secular motion of the Earth's rotation pole as deduced from astronomical observations. The calculations for a viscoelastic Earth yield a secular motion in the direction of 72° W meridian which is in excellent agreement with observed values. The average Newtonian viscosity and the relaxation time obtained from polar motion data are about (1.1 ± 0.6)10²³ poise (P) and 10⁴ (1 ± 0.5) yr. The non-tidal secular acceleration of the Earth can also be attributed to the viscoelastic response to deglaciation and results in an independent viscosity estimate of 1.6 × 10²³ P with upper and lower limits of 1.1 × 10²³ and 2.8 × 10²³ P. These values are in agreement with those based on the polar drift analysis and indicate an average mantle viscosity of 1–2 × 10²³ P.     

Micromonas pusilla (Prasinophyceae) as part of pico-and nanoplankton communities of the Barents Sea

Micromonas pusilla (Butcher) Manton & Parke appears to be a prominent member of the Barents Sea picoplankton community as revealed by the serial dilution culture method. Cell numbers frequently exceeded 10⁷ cells 1⁻¹, though they usually varied between 10³and 10⁶ cells l⁻¹. A number of other identified and unidentified taxa were recorded and quantified. Distribution relative to the marginal ice zone is reported.     

Distribution of Chemical Constituents in Superimposed Ice from Austre Brøggerbreen, Spitsbergen

10 m and 2.3 m ice cores were obtained on Austre Brøggerbreen, Spitsbergen in Svalbard (78°53 ' N, 11°56 ' E, 450 m a.s.l.) in September 1994 and in March 1995, respectively. Stratigraphy, bulk density, pH, electrical conductivity, and major ions were obtained from the core samples.
The chemical effect of meltwater percolation through snow/ice is examined. Good correlation between Cl⁻ and Na⁺ was obtained. The ratio of Cl⁻ to Na⁺ was 1.14 which was nearly the same value as in bulk sea water. However, the variation of Cl⁻/Na⁺ shows that higher ratio occured in the bubble-free ice. Furthermore the Cl⁻ ions remain in higher concentration than SO ₄ ²⁻ or Na⁺ ions.     

Crustal and upper mantle structure of the northwestern North Island, New Zealand, from seismic refraction data

The crustal and upper mantle structure of the northwestern North Island of New Zealand is derived from the results of a seismic refraction experiment; shots were fired at the ends and middle of a 575 km-long line extending from Lake Taupo to Cape Reinga. The principal finding from the experiment is that the crust is 25 ± 2 km thick, and is underlain by what is interpreted to be an upper mantle of seismic velocity 7.6 ± 0.1 km s⁻¹, that increases to 7.9 km s⁻¹ at a depth of about 45 km. Crustal seismic velocities vary between 5.3 and 6.36 km s⁻¹ with an average value of 6.04 km s⁻¹. There are close geophysical and geological similarities between the north-western North Island of New Zealand and the Basin and Range province of the western United States. In particular, the conditions of low upper-mantle seismic velocities, thin crust with respect to surface elevation, and high heat-flow (70–100 mW m⁻²) observed in these two areas can be ascribed to their respective positions behind an active convergent margin for about the past 20 Myr.     

Estimating the crust permeability from fluid-injection-induced seismic emission at the KTB site

During the hydraulic-fracturing experiment in the German Continental Deep Drilling Borehole (KTB) in December 1994, microseismic activity was induced. Here we develop a technique for estimating permeability using the spatio-temporal distribution of the fluid-injection-induced seismic emission. The values we have obtained for the KTB experiment (0.25times10^-16 to 1.0times10^-16 1.0times10^-16 m²) are in a very good agreement with the previous hydraulic-type permeability estimates from KTB deep-observatory studies. In addition, our estimates of the hydraulic diffusivity support the previously calculated value for the upper crust, which is of the order of 1 m² s^-1. However, this estimate now relates to the depth range 7.5-9 km.     

The effect of polar wander on the tides of a hemispherical ocean

Summary. A numerical model is constructed of the tides in a hemispherical ocean driven by the forces corresponding to the Y₂^–2 equilibrium tide. The model is used to study how tidal dissipation is affected by changes in the position of the ocean relative to the Earth's rotational axis and to test a hypothesis concerning the Gerstenkorn event.
As the position of the Earth's axis is varied with respect to the ocean, the model shows changes in the dissipation rate due to the changing position and importance of individual resonances of the ocean. However, a cooperative effect is also observed which results, for an ocean of depth 4400 m, in broad frequency bands near 10 rad day⁻¹ and-6 rad day⁻¹ in which the dissipation rate remains high.
The cooperative effect is found to arise from the existence, in an unbounded ocean, of resonances at these frequencies which match the tidal forces. When ocean boundaries are introduced, the new resonances near these frequencies contain a large component of the underlying resonance and as a result are themselves a good match to the driving forces.
For the real ocean, these findings imply that changes in the position of the pole, and also possibly changes in the shape of the ocean, will on average have little effect on the energy dissipated by the tides. However in the past changes in the mean depth and area of the ocean or the increased rotation rate of the Earth may have resulted in a smaller dissipation rate.     

On the penetration of a hot diapir through a strongly temperature-dependent viscosity medium

Summary. The ascent of a hot spherical body through a fluid with a strongly temperature-dependent viscosity has been studied using an axisymmetric finite element method. Numerical solutions range over Peclet numbers of 10⁻¹– 10³ from constant viscosity up to viscosity variations of 10⁵. Both rigid and stress-free boundary conditions were applied at the surface of the sphere. The dependence of drag on viscosity variation was shown to have no dependence on the stress boundary condition except for a Stokes flow scaling factor. A Nusselt number parameterization based on the stress-free constant viscosity functional dependence on the Peclet number scaled by a parameter depending on the viscosity structure fits both stress-free and rigid boundary condition data above viscosity variations of 100. The temperature scale height was determined as a function of sphere radius. For the simple physical model studied in this paper pre-heating is required to reduce the ambient viscosity of the country rock to less than 10²² cm² s⁻¹ in order for a 10 km diapir to penetrate a distance of several radii.     

Magnetic and viscous coupling at the core–mantle boundary: inferences from observations of the Earth's nutations

Dissipative core–mantle coupling is evident in observations of the Earth's nutations, although the source of this coupling is uncertain. Magnetic coupling occurs when conducting materials on either side of the boundary move through a magnetic field. In order to explain the nutation observations with magnetic coupling, we must assume a high (metallic) conductivity on the mantle side of the boundary and a rms radial field of 0.69 mT. Much of this field occurs at short wavelengths, which cannot be observed directly at the surface. High levels of short-wavelength field impose demands on the power needed to regenerate the field through dynamo action in the core. We use a numerical dynamo model from the study of Christensen & Aubert (2006) to assess whether the required short-wavelength field is physically plausible. By scaling the numerical solution to a model with sufficient short-wavelength field, we obtain a total ohmic dissipation of 0.7–1 TW, which is within current uncertainties. Viscous coupling is another possible explanation for the nutation observations, although the effective viscosity required for this is 0.03 m² s⁻¹ or higher. Such high viscosities are commonly interpreted as an eddy viscosity. However, physical considerations and laboratory experiments limit the eddy viscosity to 10⁻⁴ m² s⁻¹, which suggests that viscous coupling can only explain a few percent of the dissipative torque between the core and the mantle.