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1.
The effect of polar wander on the tides of a hemispherical ocean   总被引：1，自引：0，他引：1  
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.  相似文献   

2.
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.  相似文献   

3.
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.  相似文献   

4.
The tidal dynamics of the Irish and Celtic Seas   总被引：1，自引：0，他引：1  
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.  相似文献   

5.
Summary. Recent results from the analysis of postglacial rebound data suggest that the viscosity of the Earth's mantle increases through the transition region. Models which fit both relative sea-level and free air gravity data have viscosities which increase from a value near 1022 poise in the upper mantle beneath the lithosphere to a value of about 1023 poise in the lower mantle. In this paper we analyse the effect of deglaciation upon the Earth's rotation and thereby show that the observed secular trend (polar wander) evident in the ILS—IPMS pole path, and measurements of the non-tidal acceleration of the length of day, are both consistent with the viscosity profile deduced from postglacial rebound. The two analyses are therefore mutually reinforcing.  相似文献   

6.
b
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.  相似文献   

7.
We have used tidal gravity measurements from six stations in central Europe to investigate the resonance in the diurnal tidal band, caused by inertial coupling between the mantle and outer core of the Earth. By the use of stacking it was possible to determine the eigenfrequency and quality factor of this eigenmode, commonly called the 'nearly diurnal free-wobble'. We assessed the effect of systematic errors from the ocean correction to the tidal measurements employing a Monte-Carlo method. The observed eigenfrequency is 1 + 1/(434 ± 7) cycles per sidereal day, and is significantly higher than predicted by theories. The observed quality factor is (2.8 ± 0.5) × 103.  相似文献   

8.
The fossil record of the variation of the solar day and the synodic month with geological time is examined for evidence of the steady contraction of the Earth postulated by Lyttleton to explain a discrepancy between the apparent secular accelerations of the Sun and Moon. Data for the Phanerozoic and the Precambrian agree in showing that a change in the Earth's moment of inertia as large as that suggested by Lyttleton is only consistent with the fossil record if the secular change in the gravitational constant Ġ/ G ≥+ 4 × 10–11/yr. A variation of G of this magnitude appears to be ruled out by a recent analysis of lunar occultation observations utilizing Atomic Time.  相似文献   

9.
From a large collection of Ethiopian flood basalts (~30  Myr old) sampled for magnetostratigraphy, 40Ar/39Ar geochronology and geochemical investigations, 47 samples were selected in order to test their suitability for Thellier palaeointensity experiments. Only 17 samples from eight individual flows yielded reliable palaeointensity estimates, with flow-mean virtual dipole moments ranging from 3.0 to 10.5 × 1022  A  m2 .
  A critical review of the Oligocene palaeointensity data set, including these new Ethiopian data, indicates an Oligocene mean virtual dipole moment of 5.1 ± 2.5 × 1022  A  m2 for the complete data set. After applying mild selection criteria, the reduced data set yields a mean value of only 4.6 ± 1.9 × 1022  A  m2 . This value is significantly lower than the present-day field strength but is higher than the Mesozoic dipole low mean field. This low Oligocene field might be in agreement with the high palaeosecular variation and rather high non-dipole field invoked around 30  Ma. However, the Oligocene data set is largely dependent on the palaeointensity determinations from Armenia, obtained mainly from baked contacts, which show amazingly low dispersion at both flow and between-flow levels. More data are needed to reduce the weight of these determinations on the mean value and avoid a possible bias.  相似文献   

10.
Summary. A systematic approach is suggested for modelling the development of sedimentary basins. The theory, which partitions basin formation into initiating and isostatic adjustment processes, is applicable to all modes of basin formation if these processes are linear, or can he represented with sufficient accuracy in an incrementally linear form.
The dynamics of regional isostatic adjustment are characterized by the Heaviside space-time Green functions for the response of elastic and viscoelastic (Maxwell) thin plate models of the lithosphere. It is shown, by convolving the Heaviside—Green functions with cylindrical surface loads, that the rate of isostatic adjustment on a viscoelastic lithosphere is a function of the wavelength of the surface load, long wavelengths being compensated most rapidly.
Six archetypal initiating processes for sedimentary basin development are presented. These processes are those responsible for the subsidence of the Earth's surface which creates a depression in which water and sediments collect. Isostatic amplification of subsidence by sediment and water loads is cast in the form of an integral equation with isostatic Heaviside—Green functions as kernel.
Specific examples, the basins that result from a graben initiating process, are compared with the largest scale structure of the North Sea Basin, a basin that is known to be underlain by a graben system. A model, in which a 50-km wide graben subsides exponentially with a time constant of 5 × 107yr during the interval 180–100 Myr bp , is shown to be consistent with the largest scale structure of the North Sea Basin if the underlying lithosphere is viscoelastic with a flexural rigidity of ∼5 × 1025 Nm and relaxation time constant ∼ 106 yr.  相似文献   

11.
Summary. The power spectrum of the Earth's spin has important components with periods ranging from a few days to at least a few thousand years, and probably to the age of the Earth. The secular acceleration, as the term is used here, refers to the components with periods longer than three centuries. In the year 600, the secular acceleration was —19.9 ± 0.8 parts in 109 per century, while the value at the present time is less than half this size. The spin acceleration has important contributions from tidal friction and from an effect that is proportional to the square of the magnetic dipole moment. When these contributions are subtracted from the observed acceleration, we are left with a contribution that amounts to +41 parts in 109 per century. This amount probably results from an unknown combination of changes in the size of the core, in the amount of glaciation, and in the size of the gravitational constant.  相似文献   

12.
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.  相似文献   

13.
Summary. Tidal gravity measurements have been made at six sites in Britain with two nulled LaCoste and Romberg Earth tide gravitymeters. The M 2 observations from these and two further sites are compared with calculations of the tidal loading from the seas around the British Isles and the major oceans. Models of the M 2 marine tides are convolved with Green's functions for appropriate radially stratified Earth models. The differences between the M 2 observations and the theoretical calculations are less than 0.6 μ gals and it is shown that these differences contain further information concerning the errors in the marine tide models. The M 2 marine tides on the north-west European continental shelf are reasonably well known and this allows a useful test of the feasibility of using tidal gravity measurements for the inverse ocean tide problem in areas where the ocean tides are less well known. The differential gravity loading signal between pairs of gravity stations is shown to be important for considerations of the uniqueness and accuracy of the inverse problem. M 2 tidal gravity loading maps for the British Isles and Europe have been produced which are of use in making corrections to various geodetic measurements.  相似文献   

14.
Summary. The thermal effect of a rapid injection of hot magmas into the lower part of the lithosphere is modelled as an increase in heat production through the invaded region. The change in surface heat flow and the uplift resulting from the thermal expansion are determined in three-dimensional axially symmetric geometry: they are expressed as the space time convolutions of a Green's function with the anomalous heat production.
The anomalies with shorter wavelength (compared to the lithospheric thickness) are attenuated. This filtering affects the surface uplift more than the heat flow anomaly; the attenuation effect is larger when only the lower part of the lithosphere is invaded.
The uplift time constant is of the same order as the heat conduction time if the lower lithosphere is invaded by magmas at a moderate rate (i.e. the rate of injection does not exceed the equivalent of 0.1 per cent of the lithospheric volume in 106yr). Fifty per cent of the total uplift takes place in about 80 × 106yr for a lithosphere 100 km thick. The uplift is slightly faster when the whole lithosphere is invaded. The heat flow anomaly is delayed when the lower part of the lithosphere is invaded.
The spatial extent and the timing of the uplift and heat flow anomalies are critical in determining the mechanism's feasibility. Magma injections explain rapid uplifts [> 100 m (106 yr)−1] only if the magma is supplied at a very high rate (i.e. at least 10 per cent of the lithosphere volume per 106yr). It is a feasible mechanism for uplifts that occur over longer periods of time (≊ 30 × 106yr) such as those that seem to have occurred when the African plate came to rest with respect to the mantle.  相似文献   

15.
The geomagnetic field intensity during Archaean times is evaluated from a palaeomagnetic and chronological study of a dolerite dyke intruded into the 3000 Ma Nuuk Gneisses at Nuuk (64.2°N, 51.7°W), west Greenland. Plagioclase from the dolerite dyke yields a mean K-Ar age of 2752 Ma. Palaeomagnetic directions after thermal demagnetization of the dyke and the gneiss reveal a positive baked-contact test, indicating that the high-temperature-component magnetization of the dyke is primary. Thellier experiments on 12 dyke specimens yield a palaeointensity value of 13.5±4.4 μT. The virtual dipole moment at ca. 2.8 Ga is 1.9±0.6 × 1022 Am2, which is about one-quarter of the present value. The present study and other available data imply that the Earth's magnetic field at 2.7 ∼ 2.8 Ga was characterized by a weak dipole moment and that a fairly strong geomagnetic field similar to the present intensity followed the weak field after ca. 2.6 Ga.  相似文献   

16.
We present an approximate method to estimate the resolution, covariance and correlation matrix for linear tomographic systems Ax = b that are too large to be solved by singular value decomposition. An explicit expression for the approximate inverse matrix A − is found using one-step backprojections on the Penrose condition AA −≈ I , from which we calculate the statistical properties of the solution. The computation of A − can easily be parallelized, each column being constructed independently.
The method is validated on small systems for which the exact covariance can still be computed with singular value decomposition. Though A − is not accurate enough to actually compute the solution x , the qualitative agreement obtained for resolution and covariance is sufficient for many purposes, such as rough assessment of model precision or the reparametrization of the model by the grouping of correlating parameters. We present an example for the computation of the complete covariance matrix of a very large (69 043 × 9610) system with 5.9 × 106 non-zero elements in A . Computation time is proportional to the number of non-zero elements in A . If the correlation matrix is computed for the purpose of reparametrization by combining highly correlating unknowns x i , a further gain in efficiency can be obtained by neglecting the small elements in A , but a more accurate estimation of the correlation requires a full treatment of even the smaller A ij . We finally develop a formalism to compute a damped version of A −.  相似文献   

17.
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.  相似文献   

18.
Inference of mantle viscosity from GRACE and relative sea level data   总被引：12，自引：0，他引：12  
Gravity Recovery And Climate Experiment (GRACE) satellite observations of secular changes in gravity near Hudson Bay, and geological measurements of relative sea level (RSL) changes over the last 10 000 yr in the same region, are used in a Monte Carlo inversion to infer-mantle viscosity structure. The GRACE secular change in gravity shows a significant positive anomaly over a broad region (>3000 km) near Hudson Bay with a maximum of ∼2.5 μGal yr−1 slightly west of Hudson Bay. The pattern of this anomaly is remarkably consistent with that predicted for postglacial rebound using the ICE-5G deglaciation history, strongly suggesting a postglacial rebound origin for the gravity change. We find that the GRACE and RSL data are insensitive to mantle viscosity below 1800 km depth, a conclusion similar to that from previous studies that used only RSL data. For a mantle with homogeneous viscosity, the GRACE and RSL data require a viscosity between  1.4 × 1021  and  2.3 × 1021  Pa s. An inversion for two mantle viscosity layers separated at a depth of 670 km, shows an ensemble of viscosity structures compatible with the data. While the lowest misfit occurs for upper- and lower-mantle viscosities of  5.3 × 1020  and  2.3 × 1021  Pa s, respectively, a weaker upper mantle may be compensated by a stronger lower mantle, such that there exist other models that also provide a reasonable fit to the data. We find that the GRACE and RSL data used in this study cannot resolve more than two layers in the upper 1800 km of the mantle.  相似文献   

19.
This paper investigates possible long-period oscillations of the earth's fluid outer core. Equations describing free oscillations in a stratified, self-gravitating, rotating fluid sphere are developed using a regular perturbation on the equations of hydrodynamics. The resulting system is reduced to a finite set of ordinary differential equations by ignoring the local horizontal component of the earth's angular velocity vector, Ω, and retaining only the vertical component. The angular dependence of the eigensolutions is described by Hough functions, which are solutions to Laplace's tidal equation.
The model considered here consists of a uniform solid elastic mantle and inner core surrounding a stratified, rotating, inviscid fluid outer core. The quantity which describes the core's stratification is the Brunt—Väisälä frequency N , and for particular distributions of this parameter, analytical solutions are presented. The interaction of buoyancy, and rotation results in two types of wave motion, the amplitudes of which are confined predominantly to the outer core: (1) internal gravity waves which exist when N 2 > 0, and (2) inertial oscillations which exist when N 2<4Ω2. For a model with a stable density stratification similar to that proposed by Higgins & Kennedy (1971), the resulting internal gravity wave eigenperiods are all at least 8 hr, and the fundamental modes have periods of at least 13 hr. A model with an unstable density stratification admits no internal gravity waves but does admit inertial oscillations whose eigenperiods have a lower bound of 12hr.  相似文献   

20.
we have obtained one year of measurements from a subsurface instrumented mooring carrying two current meters and one bottom pressure recorder in the strait between Nordaustlandet and Kvitøya in the northeastern Svalbard archipelago. The observations show a mixed tide with typical amplitudes 0.4 db and 10cm sec−1. The semidiurnal tide is characterized by a progressive wave propagating toward the south. together with a cross-channel baroclinic mode. The annual average (non-tidal) current is less than 2cm sec−1 toward the north-east, suggesting that the transport into the Arctic Ocean is approximately 0.2 × 106m3s−1.  相似文献   

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