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1.
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 B 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 B. This paper outlines the indirect methods by which B can be estimated, arguing that B 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   

2.
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   

3.
The value of the acoustic Grüneisen parameter, γa, in the earth's interior has been computed using data from recent models obtained by inversion of normal data. In this paper we emphasize the data from the PEM model of the earth because there has been sufficient smoothing of the seismic data so that the derivatives d ln νs/d ? and d ln νp/d ? can be well defined at all depths.The results for the lower mantle show that γa decreases exponentially from 1.3 to 1.0, and there are several consistent cross-checks of the limiting values. We find γa is about 1.5 for the inner core and outer core. These results confirm, in broad outline, the results of others who computed γ for the core by entirely different methods. They also confirm a higher value of γ in the inner core. The value of γa in the lower mantle follows a ρ?1.35 law, which is reminiscent of the expirical law γρ = constant, commonly used in shock-wave analyses.  相似文献   

4.
Recently observed secular acceleration impulses (SAI) of the geomagnetic field are interpreted in terms of organized motions of the outer core layers. Such motions have planetary dimensions (5000 km) and a large amplitude (3 × 10?4 m s?1) and are established in very short times (less than one year). The correlation of SAI observed in the Northern Hemisphere with minima in the Earth's rotation rate (around 1840, 1905 and 1970) is shown to be consistent with a simple model involving electromagnetic coupling of the weakly conducting (of the order of 100 ω?1 m?1) mantle, of a coherent outer core layer (thickness 100 to a few hundred kilometres) and of the rest of the core. The magnitude of the torque which acts suddenly on both parts of the core at the time of the impulses is estimated.  相似文献   

5.
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 ?tB. 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 1nσ|?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 ?r×ES/Br. 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   

6.
Virtually all dynamo models may be expected to give rise to a permanent differential rotation between mantle and core. Weak conductivity in the mantle permits small leakage currents which couple to the radial component of the magnetic field, producing a Lorentz torque. Mechanical equilibrium is achieved when a zero net torque is established at a critical rotation rate. An estimate of the drift is determined easily given the magnetic field structure predicted by any dynamo model. The result for the drift rate at the core-mantle interface along the equator is given by the product of three factors
Uφ1=UφRλ*L*
The first of these is a geometrical factor which depends only on the structural character of the field. For a variety of model fields, this factor ranges from 16 to 35. The second factor is the ratio of r.m.s. toroidal to poloidal field. This ratio is an (implicitly) adjustable parameter of both α2 and α-ω dynamos, and is a measure of the relative efficiency of the generation process for each component. The third (dimensional) term is the ratio of core magnetic diffusivity to core radius, 10?4 cm s?1.The result is essentially independent of the value of mantle diffusivity and its effective depth. The sign of the result may be positive or negative. For α2 dynamos a westward drift is produced by choosing α > 0 in the Northern Hemisphere, which constitutes a dynamical assertion about the dynamo process. For an r.m.s. toroidal field of the order of 15 Gs, based on fairly general considerations, a drift rate comparable to observation is expected.  相似文献   

7.
An examination of the westward drift of the geomagnetic field indicates that the drift velocity is almost independent of latitude, suggesting a uniform rigid rotation of spherical shape. When the geomagnetic field is separated into standing and drifting components and expressed in a spherical harmonic series, a lack of sectorial terms is noted in the standing field. It is shown that these features are well explained by a stratified core model.The core is supposed to be stratified near the surface where toroidal fluid motions are predominant. In the deeper part, the fluid motion is two-dimensional, forming Taylor columns. A simplified core model is assumed to represent these features, in which the core is divided into two parts, an outer spherical shell that rotates westwards at a uniform rate of 0.3° y?1 and a central sphere in which the two-dimensional columnar motions reside. The toroidal motions in the outer spherical interact with the dipole field to induce the drifting field, whereas the columnar motions generate the standing field through interaction with a toroidal field. It follows that a small velocity as 5 × 10?3 cm s?1 for the stratified motion is sufficient to create the observed drifting field.  相似文献   

8.
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9.
Motivated by the high degree of correlation between the variable parts of the magnetic and gravitational potentials of the Earth discovered by Hide and Malin (using a harmonic analysis approach and utilizing the geomagnetic data) when one field is suitably displaced relative to the other, Moffatt and Dillon (1976) studied a simple planar model in an attempt to find a quantitative explanation for the suggestion that this high degree of correlation may be due to the influences produced by bumps on the core-mantle interface. Moffatt and Dillon assumed that the core-mantle interface was z = η(x) where |?η/?χ| ? 1 and such that in the core [z < η(x)] a uniform flow (U0, 0, 0) prevails in the presence of a uniform ‘toroidal’ field (B0, 0, 0); (here z is the vertical coordinate and x is the eastward distance). The whole system rotates uniformly about the vertical with angular velocity Ω. The present work extends the model discussed by Moffatt and Dillon to include a horizontal component of angular velocity ΩH and a uniform small poloidal field Bp. In addition, the uniform toroidal field is here replaced by one which vanishes everywhere in the mantle and increases linearly, from zero on the interface, with z. It is shown that the presence of ΩH and Bp, together with the present choice of toroidal magnetic field, has a profound effect both on the correlation between the variable parts of the magnetic and gravitational fields of the Earth, and on how far the disturbances caused by the topography of the interface [which is necessarily three-dimensional i.e. z = η(x, y) here] can penetrate into the liquid core. In particular it is found that the highest value of the correlation function is +0.79 which corresponds to a situation in which the magnetic potential is displaced both latitudinally and longitudinally relative to the gravitational potential.  相似文献   

10.
The contribution of multiple scattering to the coda waves for three-dimensional elastic medium is investigated by extending the computational procedures developed earlier for the two-dimensional medium. It is shown that the effects of multiple scattering start to become important at a shorter lapse time,t c = 0.65(n 0σu)?1, than in the two-dimensional case (t c = 0.8(n 0σu)?1).  相似文献   

11.
A simple new method is described for extracting, from magnetic observations taken at Earth's surface, the vertical growth rate of vertical motion, ?u/?r, at special isolated points on the top surface of Earth's liquid core. The technique utilizes only the radial component of the frozen-flux induction equation and it requires information only on the radial magnetic field, Br, its horizontal gradient, and its secular variations, ?Br/?t, at the core-mantle boundary.  相似文献   

12.
Preliminary reference Earth model   总被引：29，自引：0，他引：29  
A large data set consisting of about 1000 normal mode periods, 500 summary travel time observations, 100 normal mode Q values, mass and moment of inertia have been inverted to obtain the radial distribution of elastic properties, Q values and density in the Earth's interior. The data set was supplemented with a special study of 12 years of ISC phase data which yielded an additional 1.75 × 106 travel time observations for P and S waves. In order to obtain satisfactory agreement with the entire data set we were required to take into account anelastic dispersion. The introduction of transverse isotropy into the outer 220 km of the mantle was required in order to satisfy the shorter period fundamental toroidal and spheroidal modes. This anisotropy also improved the fit of the larger data set. The horizontal and vertical velocities in the upper mantle differ by 2–4%, both for P and S waves. The mantle below 220 km is not required to be anisotropic. Mantle Rayleigh waves are surprisingly sensitive to compressional velocity in the upper mantle. High Sn velocities, low Pn velocities and a pronounced low-velocity zone are features of most global inversion models that are suppressed when anisotropy is allowed for in the inversion.The Preliminary Reference Earth Model, PREM, and auxiliary tables showing fits to the data are presented.  相似文献   

13.
Various rock magnetic techniques were applied to characterize magnetically the samples of a soil profile taken from west-central Minnesota. There is a marked change in magnetic properties as a function of depth in the core. X-ray analysis and Curie temperature measurements carried out on the magnetic fractions indicate that magnetite is the dominant iron oxide in both the top soil and the subsoil. The intensity of anhysteretic remanent magnetization (ARM) decreases sharply as the depth increases. In contrast, the stability of ARM was found to be higher for the subsoil. The surface soil sample was capable of acquiring a significant amount of viscous remanent magnetization (VRM). The VRM acquisition coefficient (Sa) of the subsoil (Sa= 3.18 × 10?6emu g?1, 3.18 × 10?6A m2 kg?1) was about ten times weaker than that of the top soil sample (Sa = 3.868 × 10?7emu g?1, 3.868 × 10?7A m2 kg?1). The magnetic domain state indicator, the ratio of coercivity of remanence to coercive force, Hcr/Hc, was 1.5 and 3.85 for the top soil and subsoil, respectively. It appears that the observed variations in magnetic properties down the present soil core is due only to a difference in grain size. We conclude that the magnetic grains in surface soil samples were more single-domain (SD) like whereas the magnetite grains in the subsoil samples were more likely in pseudo-single-domain (PSD) or small multidomain (MD) range. The observed lower stability for the surface soil samples is attributed to the presence of superparamagnetic grains whose presence was confirmed by transmission electron micrographs.  相似文献   

14.
Summary In Paper III (Mohandis [1]2) we considered the sudden introduction of amagnetic dipole in the earth's core to act as a source of disturbance to the exitation field taken as a poloidal one. A symmetrical case was considered where the dipole axis is placed parallel to the original field and perpendicular to the earth's mantle. In the present work, we consider an unsymmetric case where the axis of themagnetic dipole is placed perpendicular to both the mantle and the exitation field which is taken as a toroidal one. A mathematical study is made for the resulting fluid motion in the core as well as for the generated hydromagnetic perturbations in both the mantle and the earth's fluid core. A more powerful method has been adopted than those used in previous cases.  相似文献   

15.
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 104?107 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   

16.
The thermal expansion of stishovite has been determined by an X-ray camera technique in a temperature range of 18 – 600°C at an atmospheric pressure. The thermal-expansion coefficients along the crystallographic a- and c-axes at 300 K are αa = (6.0 ± 0.6) · 10?6K?1 and αc = (1.4 ± 0.5) · 10?6K?1, respectively. The volume coefficient at 300 K is αν = (13.5 ± 0.6) · 10?6K?1.  相似文献   

17.
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 m's 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   

18.
The Hf isotope composition of original igneous or detrital zircons in high-grade metamorphic rocks can be used to trace protolith origin, but metamorphic effect on the Hf isotope composition of newly grown domains remains to evaluate. We report a detailed in situ combined study of intragrain U-Pb and Lu-Hf isotopes in zircons from granitic gneiss and eclogite in the Dabie orogen of China that experienced ultrahigh-pressure eclogite-facies metamorphism. The results show correlations in 206Pb / 238U age, initial Hf isotope composition, and Th / U and Lu / Hf ratios between the domains of different origins. The metamorphic domains are characterized by low Th / U and Lu / Hf ratios but high ?Hf(t) values relative to the igneous core and mantle of pre-metamorphic ages. Positive correlations are observed between Th / U and Lu / Hf ratios, pointing to the similar effect of metamorphism on both U-Th-Pb and Lu-Hf isotope systems. Thus the metamorphic domains are distinguished from the igneous core and mantle by their low Lu / Hf ratios that are less than 0.001 for the granitic gneiss and less than 0.0001 for the eclogite. Despite differences in both protolith age and geochemical source between granitic gneiss and eclogite, rim ?Hf(t) values are variably 3.1 to 13.5 greater than core ?Hf(t) values when calculated at timing of protolith formation. This indicates that the zircon overgrowth was associated with a metamorphic medium that has high 176Hf / 177Hf but low 176Lu / 177Hf ratios. While the metamorphic domains contain more radiogenic Hf isotopes than the original igneous core and mantle, their Lu / Hf ratios are significantly lower than those of core and mantle. Therefore, the metamorphic zircons acquired their initial Hf isotope ratios from metamorphic fluids that have high 176Hf / 177Hf ratios but low Lu / Hf ratios with sound variability depending on the Lu-Hf isotope compositions of pre-existing and co-precipitating phases.  相似文献   

19.
The 2017 Guptkashi earthquake occurred in a segment of the Himalayan arc with high potential for a strong earthquake in the near future. In this context, a careful analysis of the earthquake is important as it may shed light on source and ground motion characteristics during future earthquakes. Using the earthquake recording on a single broadband strong-motion seismograph installed at the epicenter, we estimate the earthquake’s location (30.546° N, 79.063° E), depth (H?=?19 km), the seismic moment (M0?=?1.12×1017 Nm, M w 5.3), the focal mechanism (φ?=?280°, δ?=?14°, λ?=?84°), the source radius (a?=?1.3 km), and the static stress drop (Δσ s ~22 MPa). The event occurred just above the Main Himalayan Thrust. S-wave spectra of the earthquake at hard sites in the arc are well approximated (assuming ω?2 source model) by attenuation parameters Q(f)?=?500f0.9, κ?=?0.04 s, and fmax?=?infinite, and a stress drop of Δσ?=?70 MPa. Observed and computed peak ground motions, using stochastic method along with parameters inferred from spectral analysis, agree well with each other. These attenuation parameters are also reasonable for the observed spectra and/or peak ground motion parameters in the arc at distances ≤?200 km during five other earthquakes in the region (4.6?≤?M w ?≤?6.9). The estimated stress drop of the six events ranges from 20 to 120 MPa. Our analysis suggests that attenuation parameters given above may be used for ground motion estimation at hard sites in the Himalayan arc via the stochastic method.  相似文献   

20.
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   

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