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1.
A rigorous singular perturbation theory is developed to estimate the electric field E produced in the mantle M by the core dynamo when the electrical conductivity σ in M depends only on radius r, and when | r?rln σ| ? 1 in most of M. It is assumed that σ has only one local minimum in M, either (a) at the Earth's surface ?V, or (b) at a radius b inside the mantle, or (c) at the core-mantle boundary ?K. In all three cases, the region where σ is no more than e times its minimum value constitutes a thin critical layer; in case (a), the radial electric field Er ≈ 0 there, while in cases (b) and (c), Er is very large there. Outside the critical layer, Er ≈ 0 in all three cases. In no case is the tangential electric field ES small, nearly toroidal, or nearly calculable from the magnetic vector potential A as ?? tAS. The defects in Muth's (1979) argument which led him to contrary conclusions are identified. Benton (1979) cited Muth's work to argue that the core-fluid velocity u just below ?K can be estimated from measurements on ?V of the magnetic field B and its time derivative . A simple model for westward drift is discussed which shows that Benton's conclusion is also wrong.In case (a), it is shown that knowledge of σ in M is unnecessary for estimating ES on ?K with a relative error | r?r 1 nσ| ?1from measurements of ES on ?V and knowledge of ? tB in M (calculable from ? tB on ?V if σ is small). Then, in case (a), u just below ?K can be estimated as . The method is impractical unless the contribution to ES on ?V from ocean currents can be removed.The perturbation theory appropriate when σ in M is small is considered briefly; smallness of σ and of | r?r ln σ| ?1 a independent questions. It is found that as σ → 0, B approaches the vacuum field in M but E does not; the explanation lies in the hydromagnetic approximation, which is certainly valid in M but fails as σ → 0. It is also found that the singular perturbation theory for | r?r ln σ| ?1 is a useful tool in the perturbation calculations for σ when both σ and | r?r ln σ| ?1 are small. 相似文献
2.
The magnetic field in the Earth's mantle is computed using a depth-dependent electrical conductivity, of form σ = σa( r/ a) ?α, and an approximation scheme in which the electromagnetic time constant of the mantle is assumed small compared with the time scales of the secular variation, and in which the induced currents and fields are obtained iteratively. We first associate the toroidal fields in the mantle with motions at the core surface ( r = a) which create the observed geomagnetic field by flux rearrangement, and compute the resulting couple, Γ, parallel to the geographical axis. Using only zonal core motions, and values σa = 3 × 10 3ω?1m?1, α = 30 for the conductivity profile, we find that the toroidal induced fields create a couple, ΓT, that over most of this century has been roughly ten times greater than the poloidal part, ΓS, of Γ, and has the same sign. The total couple, Γ, has fluctuations of order 10 18 Nm as required for the observed decade fluctuations in the length of the day. Its average is ~ ?1.5 × 10 18 Nm, i.e., it is too large to remain unbalanced. We suppose that an equally important couple in the opposite sense is created by flux leakage from the core, and we estimate the necessary gradient of toroidal field in the core to be of order ?0.5 Gs km ?1 at the core surface. During the course of the data analysis needed for the present work, we found some evidence for a torsional wave in the Earth's core with a period of ~ 60 y. 相似文献
3.
There has been renewed interest lately in the possibility that at least a part of the Earth's liquid core may be stably stratified. A gravitationally stable region would permit the existence of inertia-gravity or gravity-inertia waves in addition to the Rossby and Kelvin waves which exist due to rotational effects and which are well known in oceanography and atmospheric dynamics. These wave motions are of interest because their periods are dependent on the density stratification as specified by the buoyancy frequency N which in turn determines the amplitude of large-scale radial motions in the core.The waves have too high a frequency to be connected dynamically to the magnetic field in the core, but if they do exist they may be detectable by sensitive long-period gravimeters at the Earth's surface. This paper examines the available evidence for the frequency regimes, excitation and damping mechanisms of the core waves. It is concluded that although the waves may exist theoretically, their detection and interpretation as a method for determining N is a difficult proposition. 相似文献
4.
The case is presented that the efficiency of variable viscosity convection in the Earth's mantle to remove heat may depend only very weakly on the internal viscosity or temperature. An extensive numerical study of the heat transport by 2-D steady state convection with free boundaries and temperature dependent viscosity was carried out. The range of Rayleigh numbers ( Ra) is 10 4?10 7 and the viscosity contrast goes up to 250000. Although an absolute or relative maximum of the Nusselt number ( Nu) is obtained at long wavelength in a certain parameter range, at sufficiently high Rayleigh number optimal heat transport is achieved by an aspect ratio close to or below one. The results for convection in a square box are presented in several ways. With the viscosity ratio fixed and the Rayleigh number defined with the viscosity at the mean of top and bottom temperature the increase of Nu with Ra is characterized by a logarithmic gradient β = ?ln( Nu)/ ? ln( Ra) in the range of 0.23–0.36, similar to constant viscosity convection. More appropriate for a cooling planetary body is a parameterization where the Rayleigh number is defined with the viscosity at the actual average temperature and the surface viscosity is fixed rather than the viscosity ratio. Now the logarithmic gradient β falls below 0.10 when the viscosity ratio exceeds 250, and the velocity of the surface layer becomes almost independent of Ra. In an end-member model for the Earth's thermal evolution it is assumed that the Nusselt number becomes virtually constant at high Rayleigh number. In the context of whole mantle convection this would imply that the present thermal state is still affected by the initial temperature, that only 25–50% of the present-day heat loss is balanced by radiogenic heat production, and the plate velocities were about the same during most of the Earth's history. 相似文献
5.
An expression for the inviscid horizontal velocity field at the surface of the Earth's core necessary to account for the poloidal main magnetic field and its secular variation seen at the Earth's surface is derived for an insulating mantle in the limit of infinite core conductivity. The starting point of derivation is Ohm's law rather than the magnetohydrodynamic induction equation. Maps of the resulting motion for epoch 1965.0 at different truncation levels are presented and discussed. 相似文献
6.
The correlation discovered by Hide and Malin between the variable parts of the Earth's gravitational field and magnetic field (suitably displaced in longitude) was tentatively and qualitatively explained by them in terms of the influence on both fields of irregularities (or “surface bumps”) at the core-mantle interface. In this paper, a quantitative analysis of this phenomenon is developed, through study of an idealised problem in which conducting fluid occupying the region z < η( x) flows over the surface z = η( x) in the presence of a magnetic field ( B0,0,0), the whole system rotating with angular velocity (0,0,Ω). It is assumed that so that perturbation methods are applicable. Determination of the magnetic potential in the “mantle” region z < η( x) requires solution of the full hydromagnetic problem in the fluid. It is shown that three wave modes are excited, two of which (for values of the parameters of the problem of geophysical interest) have a boundary layer character. Phase interactions between these modes lead to a shift and a distortion of the magnetic pattern relative to the gravitational pattern. The correlation between the gravitational potential and the magnetic potential (shifted by a distance x0) is determined on the plane as a function of x0/ d and the curves obtained are qualitatively similar to that based on the observed data; the maximum correlation obtained varies between 0.67 and 1, depending on values of the parameters of the problem, and is about 0.72 for reasonable estimates of these parameters in the geophysical context. 相似文献
7.
The vertical geoelectric field measured at Vostok, Antarctica (78.5°S, 107°E, L=75.0) over the 13 month interval May 1979–May 1980 is correlated with the interplanetary magnetic field (IMF) components By and Bz at times when Vostok is connected to the dayside magnetosphere. No significant association with IMF Bx is found. The interaction of the solar wind and the Earth’s magnetic field generally results in anti-sunward plasma flow in the high-latitude, polar ionosphere driven by a dawn-to-dusk, cross polar cap potential difference pattern. Using the IZMEM model to infer the contribution of the cross polar cap potential difference to the potential difference between the ionosphere and the ground at Vostok for the measured IMF conditions, we show that this provides a viable mechanism for the IMF associations found. We demonstrate that the direct association of the geoelectric field with the cross polar cap potential difference is independent of a result (Park, 1976. Solar magnetic sector effects on the vertical atmospheric electric field at Vostok, Antartica. Geophysical Research Letters 3(8), 475–478) showing an 15% decrease in the vertical geoelectric field measured at Vostok, 1–3 days after the passage of IMF sector boundaries. Evidence is also presented supporting the Park result, for which a mechanism is yet to be confirmed. 相似文献
8.
When the proto-Earth was growing by the accretion of planetesimals and its mass became greater than about 0.1 ME, where ME is the present Earth's mass, an appreciable amount of gas of the surrounding solar nebula was attracted towards the proto-Earth to form an optically thick, dense atmosphere. We have studied the structure of this primordial atmosphere under the assumptions that (1) it is spherically symmetric and in hydrostatic equilibrium, and (2) the net energy outflow (i.e., the luminosity) is constant throughout the atmosphere and is given by GMM/R with M = M/106yr or M/107yr where M and R are the mass and the radius of the proto-Earth, respectively.The results of calculations show that the temperature at the bottom of the atmosphere, namely, at the surface of the proto-Earth increases greatly with the mass of the proto-Earth and it is about 1500°K for M = 0.25 ME. This high temperature is due to the blanketing effect of the opaque atmosphere. Thus, as long as the primordial solar nebula was existing, the surface temperature of the proto-Earth was kept high enough to melt most of the materials and, hence, the melted iron sedimented towards the center to form the Earth's core. 相似文献
9.
A crucial step in the investigation of the energetics of motions in the Earth's core and the generation of the geomagnetic field by the hydromagnetic dynamo process is the estimation of the average strength of the magnetic field B = Bp + BT in the core. Owing to the probability that the toroidal field BT in the core, which has no radial component, is a good deal stronger than the poloidal field Bp, direct downward extrapolation of the surface field to the core-mantle interface gives no more than an extreme lower limit to . This paper outlines the indirect methods by which can be estimated, arguing that is probably about 10 ?2 T (100 Γ) but might be as low as 10 ?3 T (10 Γ) or as high as 5 × 10 ?2 T (500 Γ). 相似文献
10.
The mean tangential stresses at a corrugated interface between a solid, electrically insulating mantle and a liquid core of magnetic diffusivity λ are calculated for uniform rotation of both mantle and core at an angular velocity Ω in the presence of a corotating magnetic field B. The core and mantle are assumed to extend indefinitely in the horizontal plane. The interface has the form z = η( x, y), where z is the upward vertical distance and x, y are the zonal and latitudinal distances respectively. The function η( x, y) has a planetary horizontal length scale (i.e. of the order of the radius of the Earth) and small amplitude and vertical gradient. The liquid core flows with uniform mean zonal velocity U0 relative to the mantle. Ω and B possess vertical and horizontal components.The vertical (poloidal) component Bp is uniform and has a value of 5 G while the horizontal (toroidal) field BT = Bpαz, where α is a constant. When |α| ? 1, the mean horizontal stresses are found to have the same order of magnitude (10 ?2 N m ?2) as those inferred from variations in the decade fluctuations in the length of the day, although the exact numerical values depend on the orientation of Ω as well as on the wavenumbers in the zonal and latitudinal directions.The influence of the steepness (as measured by α) of the toroidal field on the stresses is investigated to examine whether the constraint that the mean horizontal stresses at the core-mantle interface be of the order of 10 ?2 N m ?2 might provide a selection mechanism for the behaviour of the toroidal field in the upper reaches of the outer core of the Earth. The results indicate that the restriction imposed on α is related to the value assigned to the toroidal field deep into the core. For example, if |α| ? 1 then the tangential stresses are of the right order of magnitude only if the toroidal field is comparable with the poloidal field deep in the core. 相似文献
11.
The forces and overturning moments exerted by second order waves on large vertical circular cylinders are analysed. The mathematical equations governing the physical system are the three-dimensional Laplace's equation satisfied by the velocity potential ?( x, y, z, t) and the boundary conditions, namely the dynamic boundary condition which is obtained from the Bernoulli's equation, kinematic boundary condition, radiation condition, bottom boundary condition and the zero radial velocity condition on the surface of the cylinder. The non-linearity of the mathematical problem is evidenced in the free surface boundary conditions viz. dynamic and kinematic boundary conditions. Analytical solutions are obtained using the perturbation technique. These solutions are compared with various experimental data. The comparison shows favourable agreement between the theory and the experimental results. 相似文献
12.
Mean atomic weight profiles for the lunar mantle have been calculated from velocity-density systematic relations using lunar density and seismic velocity models. Despite large variability among the models, the calculation including Poisson's ratio yields a range of mean atomic weight values between 22 and 23 g mol ?1 below 150 km. A similar calculation for the Earth's mantle produces a mean atomic weight of 21.1 ±0.4 g mol ?1. This suggests that the Moon cannot be derived directly from the Earth's mantle, or that it has had a differentiation history different from the Earth's. The lunar require an Fe mole fraction between 0.25 and 0.33 for a pure olivine mantle, or between 0.33 and 0.45 for pure pyroxene.The present profiles are 0.5–3.0 g mol ?1 higher than those calculated from lunar compositional models based on lunar rock compositions and petrology and assumed lunar histories, indicating inadequacies in either the seismic or compositional models, or in both. The mean atomic weight approach provides a method of comparing the consistency of seismic and compositional models of planetary interiors. 相似文献
13.
Vertical eddy diffusivities ( Kv's) have been estimated at fourteen widely separated locations from fourteen 222Rn profiles and two 228Ra profiles measured near the ocean floor as part of the Atlantic and Pacific GEOSECS programs. They show an inverse proportionality to the local buoyancy gradient [(g/?)(?? pot/?z)] calculated from hydrographic measurements. The negative of the constant of proportionality is the buoyancy flux [?Kv(g/?)(??pot/?z)] which has a mean of ?4 × 10 ?6 cm 2/sec 3. Our results suggest that the buoyancy flux varies very little near the ocean floor. Kv's for the interior of the deep Pacific calculated from the relationship Kv = (4 × 10?6cm2/sec3)/[(g/?)(??pot/?z)] agree well with published estimates. Kv's calculated for the pycnocline are one to two orders of magnitude smaller than upper limits estimated from tritium and 7Be distributions.Heat fluxes calculated with the model Kv's obtained from the 222Rn profiles average 31 μcal cm ?2 sec ?1 in the Atlantic Ocean and 8 μcal cm ?2 sec ?1 in the Pacific Ocean. 相似文献
14.
Thermodynamic conditions (first of all, temperature) are the main dynamic factors in the transformation process of ferrous
to ferric iron (TFFI). TFFI usually takes place within a temperature range of 473–843 K (most active at temperatures above
673 K) and does not require presence of the oxidizing agents above 673 K. Analysis of the chemical composition of different
rocks and minerals indicates that only for some sedimentary rocks is the relative content of ferrous iron oxide less than
its value in magnetite, and this value is minimal for oceanic sediments. The relative content of ferrous iron oxide in oceanic
magmatic rocks exceeds this value in continental magmatic rocks and depends on the rate of rock cooling. An investigation
of the role of the titanium oxide content of different rocks on stability of ferrous iron oxide against its transformation
to ferric iron oxide shows that a significant correlation ( r = 0.79) does exist between the relative content of ferrous iron oxide and ratio of TiO 2/Fe 2O 3. Temperature within the solar nebula at location of the Earth was within the temperature range of the TFFI. During the Earth
accretion and its early evolution, ferric iron oxide was unstable and most likely did not exist. The first magnetic minerals
containing ferric iron could have appeared only after the Earth’s surface had cooled below ∼843 K. The formation of the first
Algoma-type banded iron formations could be used as a marker of the Earth’s surface cooling below ∼843 K. 相似文献
15.
A second-order hydrostatic theory is developed on the assumption that the trace of the Earth's inertia tensor, its mass and mean radius are invariant under any process causing deviations from the hydrostatic state.The hydrostatic flattening and the zonal coefficients of the hydrostatic gravitational field are obtained as ??1 = 299.638, J2 = 1072.618 × 10 ?6 and J4 = ?2.992 × 10 ?6, respectively.The internal theory using the preliminary reference earth model (PREM) of Dziewonski and Anderson (1981) yields ??1 = 299.627, J2 = 1072.701 × 10 ?6 and J4 = ?2.992 × 10 ?6. The agreement between these and the hydrostatic values indicate that PREM is suitable as a reference model as it represents the spheroidal density distribution in a state of zero non-hydrostatic stress while satisfying the fundamental geodetic observations of the invariant quantities.The small discrepancy between the hydrostatic flattening and the value deduced from PREM suggests that the density is underestimated at large depths and/or it is slightly overestimated in shallow regions of the Earth.The discrepancies between the hydrostatic and observed quantities persist after the removal of the accountable effects of isostatically compensated topography, permanent tidal deformation and the present mass anomalies associated with the Late-Pleistocene deglaciation. These ‘corrected’ discrepancies point to a triaxial non-hydrostatic figure which cannot be explained by the delayed response of the Earth to tidal deceleration. 相似文献
16.
Slow changes in the magnetic field are believed to originate in the core of the Earth. Interpretation of these changes requires knowledge both of the vertical component of the field and of its rate of change at the core-mantle boundary (CMB). While various spherical harmonic models show some agreement for the field at the CMB, those for secular variation (SV) do not. SV models depend heavily on annual means at relatively few and poorly distributed magnetic observatories. In this paper, the SV at the CMB is modelled by fitting 15-year differences in the annual means of the X, Y and Z components (from 1959 to 1974). The model is made unique by imposing the constraint that be a minimum, using the method of Shure et al. (1982). If SV is attributed to motions of core fluid, then this model will yield, in some sense, the slowest core motions. The null space is determined by the distribution of observations, and therefore, to be consistent, only those observatories have been retained which recorded almost continuously throughout the interval 1959–1974.The method allows misfit between the model and the observations. The best value for the misfit can be derived from estimates of errors in the data, or alternatively, because larger misfit leads to smoother models (i.e., smaller ), the best value can be estimated subjectively from the final appearance of the model. Both procedures have their counterparts in the conventional spherical harmonic expansion approach, when smoothing is achieved by lowering the truncation level. The new proposal made in this paper is to use objective criteria for determining the misfit, based on the assumption that diffusion is negligible, in which event all integrals will vanish when Si is a region on the CMB bounded by a contour of zero vertical component of field. For the 1965 definitive model which is adopted here, and for most other contemporary models, there are six such areas, giving five independent integrals (the integrals over the six regions must sum to zero if ? · B = 0). Tabulating these integrals for various choices of the misfit gives minimum values near 2 nT y ?1. It is impossible to achieve this good a fit to the data using a reasonable model derived by truncating the spherical harmonic expansion. The value 2 nT y ?1 corresponds to errors of ~ 20 nT in individual annual means, which is rather larger than expected from the scatter in the data. 相似文献
17.
Jupiter's field is strongly dipolar but with relatively large high order moments compared to the Earth's. In situ magnetic field data allow us to interpret most of the Earth-based microwave observations of Jupiter, with the exception of Branson's hot spot. Decametric emissions have a complex rotational pattern which has been stable since 1950; their agreement with the spacecraft magnetic fields is much less satisfactory than that of the microwaves. We conclude that the extrapolation of magnetic fields from the spacecraft to the surface of Jupiter is in error by 40% in the Southern Hemisphere.Saturn's radio emissions show complexities similar to Jupiter's. They are strongly asymmetric about the rotational axis, although Saturn's Field is nearly axisymmetric. Their strong asymmetry suggests strong longitudinal variations in the magnetic field a few thousand kilometers from the cloud tops, in conflict with the field measured aboard Pioneer 11.The magnetic fields within a few thousand kilometers of either Jupiter's or Saturn's cloud tops are probably unknown. It is discouraging that more is not known about the fields after a total of 7 encounters. Perhaps the Galileo probe can test usefully models of the Jupiter field, even if its measurements refer to just one trajectory through the clouds. An arguable case can be made that the giant planets exhibit complexity of magnetic structure similar to the Sun. 相似文献
18.
Field variations in the region of the eruptive event on June 7, 2011 are studied based on vector measurements of the photospheric magnetic field by the SDO/HMI instrument. Variations of the modulus (B), the radial (Br) and the transverse (Bt) components of the magnetic induction, and the inclination angle (α) of the field lines to the radial direction from the center of the Sun are analyzed. It is found that, in the part of the flare region near the polarity inversion line (PIL) after the onset of the flare, the magnitude and the transverse component of the magnetic induction as well as the angles α abruptly increase. During the slow rise of filament near its channel, the inclination angles of the field lines decrease. It is shown that diverging flare ribbons are above the regions of the photosphere with local maxima of the field modulus and with deep minima of the inclination angles of the field lines at all stages of their existence over their entire length with the exception of small areas. It is established that the azimuth decreases after the onset of the flare near the PIL of the photospheric magnetic field, which means an increase in the shear. On the contrary, at a distance from the PIL there is a slight decrease in the shear. 相似文献
19.
The negative and positive fronts of the IMF B z component arrived at intervals of 3 h during a strong magnetic storm of May 15, 2005. The occurrence of Pc5 pulsations at these three characteristic instants has been considered based on the WIND satellite magnetic data. Pulsations originated not only during sudden compression SC of the magnetosphere but also during the B z sign reversal from positive to negative. The IMF B z sign reversal from negative to positive did not affect the development of pulsations. It is assumed that Pc5 pulsations observed after the negative IMF B z front are related to the development of surface waves at the magnetopause as a result of impulsive reconnection of field lines. 相似文献
20.
The advantages of the approximation of the Earth's magnetic field by means of the field of the so-called natural magnetic sources are discussed. The shifting of these natural magnetic sources, determined for different epochs, is used to forecast the Earth's magnetic field and to draw conclusions about the motion of the corresponding part of the Earth. On the basis of the representation of the Earth's magnetic field from several past geological epochs as a field of one optimum dipole a new theory about the Earth's evolution is proposed. 相似文献
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