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1.
Abou-Bakr K. Ibrahim 《Pure and Applied Geophysics》1971,91(1):114-133
Summary Using the Haskell matrix formulation, theoretical reflection coefficient curves have been calculated for a multi-layered core-mantle boundary for comparison with observational data. Two cases are considered, first when the shear velocity in the core is equal to zero and second when the core has a finite rigidity. If the velocity contrast is large between the imbedded layer and the mantle, the reflection coefficient curves for the multi-layered medium are irregular in shape as compared to those for two half-spaces, representing the core and the mantle, respectively. The reflection coefficient curves show an oscillatory character if the imbedded layer is thick and has a high velocity contrast.The observational data consist of short-period vertical-component seismograph records ofP andPcP from nuclear explosions in the Aleutian chain, Nevada, Novaya Zemlya, Kazakh and Sahara. Attenuation and geometrical spreading are taken into consideration. Four different models for the quality factorQ are applied to the observational data. The data are found to be much affected by theQ-model used for the corrections.Based on proposedQ-values, a model for the core-mantle boundary is found, characterized by two low-velocity layers at the bottom of the mantle. The thicknesses are 16.10 km (outer layer) and 19.96 km (inner layer), the compressional wave velocities 12.17 km/sec and 10.94 km/sec and the shear wave velocities are 6.29 km/sec and 5.33 km/sec, respectively. A better fit to this model is found when in addition the shear velocity in the outer core is 2.20 km/sec and the density ratio at the core-mantle boundary is 1.07. In other words, the observations favour a layer of finite rigidity in the outer core rather than a fluid one. 相似文献
2.
Abou-Bakr K. Ibrahim 《Pure and Applied Geophysics》1971,91(1):95-113
Summary The aim of this paper is to present the formulations which can be used in calculating reflection and transmission coefficients when the rigidity in the core is taken into consideration. The theoretical curves presented can be used as a guide for studies of the physical parameters of the core-mantle boundary. It is hoped that these curves may lead to a clarification of the great differences between observed data and theoretical calculations, when the geometrical spreading and attenuation are taken into account.The Thomson-Haskell matrix formulations are used to calculate the reflection and transmission coefficients for a multi-layered medium imbedded between two half-spaces representing the solid mantle and a rigid core. A rigid core is defined here as having a rigidity in the range 1010<<1011 cgs units. For five proposed models of the core-mantle boundary the rigidity in the core is varied and the results are compared with those for a liquid core. 相似文献
3.
Introduction The fluid outer core separates the solid inner core from the solid elastic mantle, and as a result, makes the free and forced movement of this mechanical system more complicated and profuse. As the elastic mantle, the free oscillations may occur within the Earths fluid outer core (FOC) due to excitation of a strong and deep earthquake (Crossley, 1975b; Friedlander, Siegmann, 1982; Shen, 1983; Friedlander, 1985). However, compared with the oscillations of the elastic mantle, i… 相似文献
4.
The elasto-gravitational deformation response of the Earth’s solid parts to the perturbations of the pressure and gravity
on the core-mantle boundary (CMB) and the solid inner core boundary (ICB), due to the dynamical behaviors of the fluid outer
core (FOC), is discussed. The internal load Love numbers, which are formulized in a general form in this study, are employed
to describe the Earth’s deformation. The preliminary reference Earth model (PREM) is used as an example to calculate the internal
load Love numbers on the Earth’s surface, CMB and ICB, respectively. The characteristics of the Earth’s deformation variation
with the depth and the perturbation periods on the boundaries of the FOC are also investigated. The numerical results indicate
that the internal load Love numbers decrease quickly with the increasing degree of the spherical harmonics of the displacement
and depend strongly on the perturbation frequencies, especially on the high frequencies. The results, obtained in this work,
can be used to construct the boundary conditions for the core dynamics of the long-period oscillations of the Earth’s fluid
outer core.
Foundation item: State Natural Science Foundation of China (40174022 and 49925411) and the Projects from Chinese Academy of Sciences (KZCX2-106
and KZ952-J1-411). 相似文献
5.
6.
David E. Loper 《Physics of the Earth and Planetary Interiors》1975,11(1):43-60
The feasibility of a precessionally driven dynamo is investigated. The relative orientation of the angular-velocity vectors of the mantle and core and the precession vector of the earth are determined from a torque balance. The core and mantle are acted upon by separate gravitational torques and mutual interaction torques resulting from pressure, viscous and magnetic stresses at the core-mantle interface. The viscous and magnetic torques are determined using the results of a detailed analysis of the Ekman-Hartmann and magnetic diffusion layers generated at the core-mantle interface by the misalignment of the mantle and core angular-velocity vectors. The dissipative torques are found to be weaker by a factor of 10?4 than those estimated by Malkus (1968) and Stacey (1973), resulting in only 3.5 · 107 W being extracted from the rotational kinetic energy of the earth by these mechanisms. Furthermore, it is found that all of this energy is dissipated in the boundary layers at the core-mantle interface and none is available to drive the geodynamo. 相似文献
7.
The effect of oceanic loading Δg in the vertical component of gravity is assessed in two different models of the Earth, namely, the PREM model and the European
model IASP91. For this purpose, we considered the Molodensky boundary problem which describes the deformations of the gravitating
elastic compressible sphere. We derived the equation that links the boundary conditions on the surface and at the bottom of
the mantle, and calculated the load Love numbers for the studied models. By the example of the territory of Western Europe,
it is shown that the value of the correction, Δg, noticeably depends on the applied seismic models of the upper mantle and the lithosphere. 相似文献
8.
This article commences by surveying the basic dynamics of Earth's core and their impact on various mechanisms of core-mantle coupling. The physics governing core convection and magnetic field production in the Earth is briefly reviewed. Convection is taken to be a small perturbation from a hydrostatic, “adiabatic reference state” of uniform composition and specific entropy, in which thermodynamic variables depend only on the gravitational potential. The four principal processes coupling the rotation of the mantle to the rotations of the inner and outer cores are analyzed: viscosity, topography, gravity and magnetic field. The gravitational potential of density anomalies in the mantle and inner core creates density differences in the fluid core that greatly exceed those associated with convection. The implications of the resulting “adiabatic torques” on topographic and gravitational coupling are considered. A new approach to the gravitational interaction between the inner core and the mantle, and the associated gravitational oscillations, is presented. Magnetic coupling through torsional waves is studied. A fresh analysis of torsional waves identifies new terms previously overlooked. The magnetic boundary layer on the core-mantle boundary is studied and shown to attenuate the waves significantly. It also hosts relatively high speed flows that influence the angular momentum budget. The magnetic coupling of the solid core to fluid in the tangent cylinder is investigated. Four technical appendices derive, and present solutions of, the torsional wave equation, analyze the associated magnetic boundary layers at the top and bottom of the fluid core, and consider gravitational and magnetic coupling from a more general standpoint. A fifth presents a simple model of the adiabatic reference state. 相似文献
9.
基于PREM模型，利用非自转、球型分层、各向同性、理想弹性（SNREI）地球的形变理论，讨论了地球在不同驱动力作用下的形变特征．采用地球位移场方程的4阶Runge Kutta数值积分方法，解算了在表面负荷和日月引潮力作用下地球表面和内部形变和扰动位，并给出了地球表面的负荷Love数和体潮Love数．结果表明在固体内核中的形变很小，液核中低阶(n＜10)负荷位移随半径的变化非常复杂．当负荷阶数超过10时，地核中的形变和扰动位都很小，地球的响应主要表现为弹性地幔中的径向位移，且随深度增加急剧减弱，负荷阶数越高这种衰减的速度越快．SNREI地球的地表负荷Love数和体潮Love数与信号频率的依赖关系很弱．在计算体潮Love数的过程中，采用了SNREI地球的运动方程，同时考虑了由于地球自转和椭率引起的核幔边界附加压力，这一近似处理方法获得的结果能很好地符合地球表面重力潮汐实际观测结果． 相似文献
10.
S. M. Molodensky 《Izvestiya Physics of the Solid Earth》2006,42(5):357-361
The amplitudes and phases of forced nutation and diurnal earth tides depend significantly on the moment of forces between the liquid core and mantle of the Earth, resulting from the differential rotation of the core. The solution to the dynamic problem of rotation of an imperfectly elastic mantle with an imperfectly liquid core and an ocean indicates that the predominant role is played by the so-called core-mantle inertial coupling (related to the effect of hydrodynamic pressure in the liquid core on the ellipsoidal core-mantle boundary). The magnitude of this coupling depends significantly not only on the dynamic flattening of the liquid core but also on the elastic and inelastic properties of the mantle, as well as on the amplitudes and phases of oceanic tides. In this paper, the effects of oceanic tides on the magnitude of inertial coupling between the liquid core and the mantle and on the period and damping decrement of free nearly diurnal nutation are estimated. 相似文献
11.
《Physics of the Earth and Planetary Interiors》2005,148(2-4):109-130
In an effort to resolve the current conflict between geochemical requirements for an apparently isolated mantle reservoir and recent geophysical evidence for whole-mantle convection, we investigate the possibility that the region above the core-mantle boundary, termed D″, serves as an early-isolated, rare-gas- and incompatible-element-bearing reservoir, and we propose a mechanism for its formation that is a likely outcome of Earth accretion models. In these models, the most cataclysmic event in Earth history, the moon-forming giant impact on the proto-Earth of a Mars-size planet (perhaps as early as 4540 Ma ago) was followed by accretion of smaller bodies long afterwards (until ∼3900 Ma). Some collisions probably triggered melting, metal segregation and degassing. However, the small bodies, fragments, particles, dust, including those of chondrite-like composition, existed on near-earth orbits, were irradiated by intense solar wind, and finally fell on an early-formed, incompatible-element-enriched basaltic crust without causing extensive melting. The respective regions of the crust, loaded with chondrite-like debris, were therefore significantly enriched in iron. When this mixed material was subducted, the bulk density of the subducted lithosphere exceeded that of the bulk silicate mantle, which had already lost its metallic iron to the core. Segregation of this denser material at the base of the mantle was facilitated by the high temperatures at the core-mantle boundary, which greatly reduce the viscosity, as was quantitatively modelled by Christensen and Hofmann (Christensen, U.R., Hofmann, A.W., 1994. Segregation of subducted oceanic-crust in the convecting mantle. J. Geophys. Res.-Solid Earth 99 (B10), 19867–19884). Assuming a basalt/chondrite mass ratio of about 4/1, we obtain a density contrast of ∼7%, which would stabilize the subducted material between the metal core and silicate mantle.Mass balance considerations and preliminary results of geochemical modelling of the above scenario (similar to that performed by Tolstikhin and Marty [Tolstikhin, I.N., Marty, B., 1998. The evolution of terrestrial volatiles, A view from helium, neon, argon and nitrogen isotope modeling. Chem. Geol. 147, 27–52]) show the potential geochemical importance of D″. (1) Modelling of Pu–U–I–Xe isotope systematics predicts formation of this reservoir early in Earth history, ∼100 Ma after formation of the Solar system. (2) The total amount of heat-generating U, Th, K (and other highly incompatible elements) in D″ exceeds 20% of the Earth inventory, and a similar portion of terrestrial heat is being transferred from the core + D″ into the base of the overlying convecting mantle. (3) D″ is enriched in solar implanted rare gases because the small (re)-accreting debris with high surface/mass ratios will have been subjected to intense radiation by the early sun. (4) Rare gases diffuse from D″ into the overlying mantle and are then transferred into upwelling plumes, which originate above D″. In addition, small amounts of D″ material may be entrained by the mantle convective flow as was recently discussed by Schott et al. [Schott, B., Yuen, D.A., Braun, A., 2002. The influences of composition and temperature-dependent rheology in thermal-chemical convection on entrainment of the D″ layer. Physics Earth Planet. Inter. 129, 43–65]. From the rare-gas modelling it follows that initially (∼4500 Ma ago) D″ could have been more massive by a factor of ∼1.2 than at present (about 2 × 1026 g). The present-day mass flux from D″ into the convecting mantle is estimated to be ≤0.05 × 1016 g year−1, a factor of ∼100 less than the rate of ridge magmatism. This small contribution of D″ material makes it difficult to trace fingerprints of D″ even using such sensitive tracers as Pb isotope ratios. (5) The density contrast that stabilizes D″ is maintained by its higher intrinsic density due to the iron-rich chondrite-like component. Subduction of this material, its entrainment by convective mantle flow and mixing could also account for the preservation of the chondritic relative abundances of siderophile elements in the mantle. If D″ is partially molten, the density contrast may be caused by a high-density melt fraction. 相似文献
12.
Recognition that the cooling of the core is accomplished by conduction of heat into a thermal boundary layer (D″) at the base of the mantle, partly decouples calculations of the thermal histories of the core and mantle. Both are controlled by the temperature-dependent rheology of the mantle, but in different ways. Thermal parameters of the Earth are more tightly constrained than hitherto by demanding that they satisfy both core and mantle histories. We require evolution from an early state, in which the temperatures of the top of the core and the base of the mantle were both very close to the mantle solidus, to the present state in which a temperature increment, estimated to be ～ 800 K, has developed across D″. The thermal history is not very dependent upon the assumption of Newtonian or non-Newtonian mantle rheology. The thermal boundary layer at the base of the mantle (i.e., D″) developed within the first few hundred million years and the temperature increment across it is still increasing slowly. In our preferred model the present temperature at the top of the core is 3800 K and the mantle temperature, extrapolated to the core boundary without the thermal boundary layer, is 3000 K. The mantle solidus is 3860 K. These temperatures could be varied within quite wide limits without seriously affecting our conclusions. Core gravitational energy release is found to have been remarkably constant at ～ 3 × 1011 W. nearly 20% of the core heat flux, for the past 3 × 109 y, although the total terrestrial heat flux has decreased by a factor of 2 or 3 in that time. This gravitational energy can power the “chemical” dynamo in spite of a core heat flux that is less than that required by conduction down an adiabatic gradient in the outer core; part of the gravitational energy is used to redistribute the excess heat back into the core, leaving 1.8 × 1011 W to drive the dynamo. At no time was the dynamo thermally driven and the present radioactive heating in the core is negligibly small. The dynamo can persist indefinitely into the future; available power 1010 y from now is estimated to be 0.3 × 1011 W if linear mantle rheology is assumed or more if mantle rheology is non-linear. The assumption that the gravitational constant decreases with time imposes an implausible rate of decrease in dynamo energy. With conventional thermodynamics it also requires radiogenic heating of the mantle considerably in excess of the likely content of radioactive elements. 相似文献
13.
As is known, the secular deceleration of the Earth's diurnal rotation is explained mainly by the tidal friction in the ocean. Below we consider this mechanism in some detail, taking into account also elastic deformations of the mantle under the action of ocean loading and the interaction between the tide-generating body, ocean tidal wave, liquid outer core, and solid inner core. It is shown that elastic displacements of the core-mantle boundary under the action of ocean loading are of about the same amplitude and phase as the elastic loading displacements of the Earth's outer surface. As a result, side by side with the mechanism of secular deceleration of diurnal rotation of the mantle, there are also (1) the opposite mechanism of secular acceleration of diurnal rotation of the outer liquid core and of the solid inner core and (2) the mechanism of excitation of differential rotation in the liquid core. Taking these effects into account, we compare theoretical and modern observed data on the eastward drift of the solid inner core. It is shown that the best agreement may be obtained if the turbulent viscosity of the liquid core is about 2 × 10
3
Poise 相似文献
14.
旋转椭球型地球的固体地幔与液态地核间相互作用而产生的逆向本征模通常称之为地球自由核章动,自由核章动的品质因子（Q值）能有效反映核幔边界层能量耗散特征,与核幔边界的黏滞度密切相关.本文首次利用全球地球动力学计划网络23个台站27组高密度采样的高精度超导重力仪器观测数据,采用迭积技术,确定了自由核章动参数Q值,进而计算了核幔边界的黏滞系数.数值结果说明获得的核幔边界动力学黏滞系数达到103 Pa·s量级,与加拿大科学家Smylie等利用VLBI观测资料获得的最新结果一致,这说明重力技术是有效应用于研究地球深内部结构的重要手段之一. 相似文献
15.
We analyze the present-day data on the periods of free oscillations and amplitudes of the forced nutations of the Earth for evaluating the admissible range of the mass and moment of inertia for the liquid core. The initial model for this study is taken in the form of the model distribution of density and mechanical Q parameters of the mantle suggested in (Molodenskii, 2010; 2011a; 2011b). This model was constructed by the steepest descent method in the space of 64 parameters, which determine the distribution of density and parameters of mechanical Q in the mantle, liquid outer core, and solid inner core of the Earth. We assumed the Q parameter of the mantle and inner solid core to be constant and sought for the density variations for the simplest two-parameter model of the piecewise-linear functions with the jumps on the boundary between the liquid core and the mantle and at the olivine-spinel phase transition at a depth of 670 km in the mantle. After this, the computations were repeated for the other distributions of Q (which were also assumed to be unchanged) that correspond to their limiting admissible values. Using this approach, we managed to find the most probable values of the mass and moment of inertia of the liquid core and determine the admissible range of their values. According to our estimates, the ratios of the mass and moments of inertia of the liquid core to the mass and moment of inertia of the whole Earth fall in the intervals 0.317996 ± 0.00065 and 0.110319 ± 0.00022, respectively. These values are lower than the corresponding values for the PREM model (0.322757 and 0.112297) by (1.48 ± 0.30)% and (1.76 ± 0.35)%, respectively. The interpretation of these results requires the revision and thorough analysis of the data on the admissible temperature range of the liquid core and (or) its chemical composition. 相似文献
16.
Shock observations on melting of iron by Brown and McQueen with the inner core boundary (ICB) density contrast estimated by Masters are used with the assumption that the light ingredient of the outer core is oxygen to calculate the boundary temperature TICB = (5000 ± 900) K. Adiabatic extrapolation to the core-mantle boundary (CMB) gives TICB = (3800 ± 800) K. The temperature increment across the D″ layer is not well constrained, but is estimated to be TD″ = (800 ± 400) K and a slightly superadiabatic extrapolation to 670 km gives T670 + = (2300 ± 950) K. This is only about 300 K higher than the extrapolation to the same level from the upper mantle, T670? = (1970 ± 150) K. The difference is far too small to make a viable mid-mantle boundary layer. Remaining unceertainties are too large to discount such a boundary layer with certainty, but agreement of our new temperature profile with temperatures deduced from equation of state studies on the lower mantle and core encourages the view that we are converging to a well-determined temperature profile for the Earth. 相似文献
17.
Constraints on rigid zones and other distinct layers at the top of the outer core using CMB underside reflected PKKP waves 
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下载免费PDF全文 Clear PKKP, a P wave reflects off the core-mantle boundary on the core side, is recorded by the transcontinental USArray from two deep earthquakes occurred in South America and Tonga, and one intermediate-depth earthquake in the Hindu Kush region. We compare the PKKP waveforms with the direct P waves to investigate the fine structures near the core-mantle boundary, with a primary focus on the core side. We find no evidence for the existence of a sedimentary layer of lighter elements with a thickness above a few hundreds of meters beneath the reflection points of the two deep events, which are located at the Ninety-East Ridge and South Africa. On the other hand the PKKP wave duration of the Hindu Kush event is almost twice as long as that of the P wave, suggesting that multiple reflections may be occurring at the core-mantle boundary located beneath the Antarctic, which is located inside the so-called tangent cylinder of the outer core. The tangent cylinder is an imaginary cylindrical region suggested by geodynamics studies, which has different flow pattern and may have a higher concentration in lighter elements as compared to the rest of the outer core. One possible explanation of the elongated PKKP is a thin distinct layer with a thickness of a few kilometers at the top of the outer core, suggesting that precipitation of lighter elements may occur at the core-mantle boundary. Our data also indicate an extremely low QP of 312, approximately 40% of the PREM average (~780), within the large-scale low-velocity anomaly in the lowermost mantle beneath Pacific. 相似文献
18.
Although vigorous mantle convection early in the thermal history of the Earth is shown to be capable of removing several times the latent heat content of the core, we are able to construct a thermal evolution model of the Earth in which the core does not solidify. The large amount of energy removed from the model Earth's core by mantle convection is supplied by the internal energy of the core which is assumed to cool from an initial high temperature given by the silicate melting temperature at the core-mantle boundary. For the smaller terrestrial planets, the iron and silicate melting temperatures at the core-mantle boundaries are more comparable than for the Earth, and the cores of these planets may not possess enough internal energy to prevent core solidification by mantle convection. Our models incorporate temperature-dependent mantle viscosity and radiogenic heat sources in the mantle. The Earth models are constrained by the present surface heat flux and mantle viscosity. Internal heat sources produce only about 55% of the Earth model's present surface heat flow. 相似文献
19.
S. M. Molodensky 《Izvestiya Physics of the Solid Earth》2008,44(8):615-621
New, unique information on the inertial and dissipative coupling of the liquid core and the mantle has been retrieved from modern high-precision (radiointerferometer and GPS) data on tidal variations in the rotation velocity and nutation of the Earth. Comparison of theoretical and observed data provided new estimates for the dynamic flattening of the outer liquid and the inner solid cores, mantle quality factor, viscosity of the liquid core, and electromagnetic coupling of the liquid core and the mantle [Molodensky, 2004, 2006]. As was shown in the first part of the paper [Molodensky, 2008] (further referred to as [I]), generation of eddy flows in Proudman-Taylor columns, whose orientation is controlled by the topography of the liquid core-mantle boundary, should be taken into account for correct estimation of the inertial coupling (see formulas (8) and (34) in [I]). The range of periods within which this effect plays a significant role is determined by the decay time of these flows. This time is estimated in the paper for the case where dissipation is related to viscous friction at the core-mantle boundary or with the electromagnetic coupling of the liquid core and the mantle. Because of significant uncertainties in modern data on the viscosity of the liquid core, the magnetic field intensity at the core-mantle boundary, and the electrical conductivity of the lower mantle, the dissipative coupling of the liquid core and the mantle cannot be calculated as yet. However, as shown in the paper, the decay time of eddy flows is connected with the attenuation time of subdiurnal free nutation and with the liquid core viscosity. This enables the estimation of the frequency dependence of the dissipative coupling in a fairly wide range. It is shown that the range of periods for which relations (8) and (34) in [I] are valid encompasses the best-studied length-of-day variations and, therefore, these relations are applicable to analysis of the majority of modern data. 相似文献
20.
Mass heterogeneities and convection in the earth's mantle inferred from gravity and core-mantle boundary irregularities 总被引：1，自引：0，他引：1
Mass heterogeneities in the earth's mantle are retrieved from the gravity data and the topography of the core-mantle boundary as well as the topography of the earth's surface. A mantle circulation induced by the heterogeneities is modelled by solving the Stokes problem for incompressible Newtonian fluid. The derived models of mantle motions correlate well with the plate tectonics and point at a close relation between the surface tectonic activity and the processes in the vicinity of the core-mantle boundary. 相似文献