液核动力学扰动引起的地球形变

讨论了地球固体部分对液核动力学效应引发的核幔边界和内核边界上压力和引力扰动的形变响应．采用弹性-引力形变理论描述地幔和内核的形变，给出了内部负荷Love数的一般表达式．以初始参考地球模型为例，分别计算了在地球表面、核幔边界和内核边界上的内部负荷Love数．探讨了液核边界上压力和引力扰动导致的地球形变场的空间和频率分布特征．本文的结果可以为中短周期液核动力学理论模拟提供必要的边界条件．      

Earth’s deformation due to the dynamical perturbations of the fluid outer core

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).     

SNREI地球对表面负荷和引潮力的形变响应

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．     

液核自由运动的变分方法

从流体静力平衡地球的弹性-引力运动动量方程出发,以角动 量方程控制弹性地幔、液态外核和弹性内核之间的相对转动,在球对称近似下考虑了地幔和 内核对液核边界扰动的形变响应,并以此作为液核边界运动的约束条件．根据地球简正模对 称性的一般特征,建立了自转、非黏性、椭球分层流体外核自由振荡运动的变分原理并给出 了相应的泛函．     

内核地球自转动力学理论的研究进展--Ⅲ液核自转动力学方程

本文是序列文章的第三篇,其内容包括：基于连续介质力学的基本理论,给出了液体外核（FOC）两种形式的角动量方程,对作用在FOC上外力矩进行了详细研究,同时对液核作用在固体内核（SIC）上的压力产生的压力矩进行了讨论,在O(ms)的量级上给出了它们的表达式.本文改正了文献〔1〕在推导过程中的某些错误（例如：（B18）、（B28）、（B29）、（B30）、（B35a）和（B35b）式）.本文是对文献〔1〕有关理论的扩展和改进,对进一步研究内核地球自转的动力学理论是非常重要的.     

Structure of the inner core boundary

Abstract

A model of the inner-core boundary (ICB) is constructed which is consistent with current ideas of the dynamic and thermodynamic state of the core and which is capable of reflecting seismic waves with period of one second. This requires the mass fraction of solid below the ICB to grow to an appreciable fraction in roughly one kilometer. This rapid growth of solid with depth is a result of downward fluid flow from the outer core which is a part of the convective motions which sustain the geodynamo. The solid which crystallizes from this descending fluid after it crosses the ICB continually coats the dendrites which occur there. The gradual cooling of the outer core causes the ICB to advance by growth of dendrites at their tips. The balance of these two effects gives an equilibrium profile for the mass fraction of solid with depth below the ICB which is capable of yielding sharp reflection of seismic waves.     

内核地球的自转运动和地球固定参考系的研究

本文研究了内核地球模型下的地球表面的旋转运动和地球形变场的复数矢量球函数表示,以及外壳固定参考架、地球参考系的理论定义和它们之间等价性的理论证明.同时给出了液体外核（FOC）、固体内核（SIC）和整体地球的转动惯量张量和角动量的具体表达式.在考虑到引潮力位对地球形变场的影响下,研究了地幔相对角动量的具体表述.本文的工作是对前人有关理论的扩展和改进,对进一步研究内核地球自转的动力学理论是非常重要的.     

超导重力技术在探讨核幔边界黏性特征中的初步应用

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.     

The monosulfid solid solution in the FeNiS system: relationship to the earth's core on the basis of experimental high-pressure investigations

Experimental high-pressure results on phase stability, electrical conductivity and compression behavior up to 5 and 21 GPa respectively are used to calculate an isothermal equation of state for a monosulfid solid solution (MSS-composition) in the FeNiS system. The high-pressure relations in the range 1–8 GPa are very complex. A continuous electrical transition, from semiconducting to metallic, takes place at high pressures and temperatures and results in anomalous compression behavior at pressures in this region. No polymorphic transition from the NiAs-structure to another type could be observed; however, density increases by as much as 8.8%. Using compression values for pressure greater than 10 GPa, the bulk modulus, a zero-pressure density and a core density were calculated. Extrapolation for the conditions of the outer core yields a difference in the density of up to 20%, relative to seismological models.In a composition model with (Fe, Ni)+MSS, a MSS-content must be assumed to be in the range of 30–35 wt% at the core-mantle boundary (CMB) and 13–17 wt% at the inner-core boundary (ICB). That corresponds to a sulfur content of 10.8–13.3 wt% (CMB) and 4.9–6.5 wt% (ICB), respectively, the values increasing with increasing Ni content of the MSS-phase.     

Axial and equatorial rotations of the Earth's cores associated with the Quaternary ice age

The differential axial and equatorial rotations of both cores associated with the Quaternary glacial cycles were evaluated based on a realistic earth model in density and elastic structures. The rheological model is composed of compressible Maxwell viscoelastic mantle, inviscid outer core and incompressible Maxwell viscoelastic inner core. The present study is, however, preliminary because I assume a rigid rotation for the fluid outer core. In models with no frictional torques at the boundaries of the outer core, the maximum magnitude of the predicted axial rotations of the outer and inner cores amounts to ∼2° year⁻¹ and ∼1° year⁻¹, respectively, but that for the secular equatorial rotations of both cores is ∼0.0001° at most. However, oscillating parts with a period of ∼225 years are predicted in the equatorial rotations for both cores. Then, I evaluated the differential rotations by adopting a time-dependent electromagnetic (EM) torque as a possible coupling mechanism at the core-mantle boundary (CMB) and inner core boundary (ICB). In a realistic radial magnetic field at the CMB estimated from surface magnetic field, the axial and equatorial rotations couple through frictional torques at the CMB, although these rotations decouple for dipole magnetic field model. The differential rotations were evaluated for conductivity models with a conductance of 10⁸ S of the lowermost mantle inferred from studies of nutation and precession of the Earth and decadal variations of length of day (LOD). The secular parts of equatorial rotations are less sensitive to these parameters, but the magnitude for the axial rotations is much smaller than for frictionless model. These models, however, produce oscillating parts in the equatorial rotations of both cores and also in the axial rotations of the whole Earth and outer and inner cores. These oscillations are sensitive to both the magnitude of radial magnetic field at the CMB and the conductivity structure. No sharp isolated spectral peaks are predicted for models with a thin conductive layer (∼200 m) at the bottom of the mantle. In models with a conductive layer of ∼100 km thickness, however, sharp spectral peaks are predicted at periods of ∼225 and ∼25 years for equatorial and axial rotations, respectively, although these depend on the strength of radial magnetic field at the CMB. While the present study is preliminary in modelling the fluid outer core and coupling mechanism at the CMB, the predicted axial rotations of the whole Earth may be important in explaining the observed LOD through interaction between the equatorial and axial rotations.     

液核地球的周日固体潮响应

本文研究了液核地球对日月引潮力位球谐函数项的变形响应,即周日固体潮。作为数值结果,计算了1066A地球模型的周日潮汐勒夫数。所建立的周日固体潮理论模型改进了Molodensky液核动力学理论模型。为了比较两者之间的差异,还根据Molodensky理论模型计算了1066A地球模型的周日潮汐勒夫数。     

深内部地球结构对内核平动振荡本征周期的影响

地球固态内核的平动振荡是地球的基本简正模之一,又称Slichter模,其本征周期大约为几个小时,与地球内部结构密切相关.为了研究影响内核平动振荡的本征周期与内部结构的依赖关系,本文利用球对称、非自转、弹性和各向同性地球模型（SNREI）,通过自由振荡运动方程的数值积分,以地球模型PREM为基础,理论上系统研究了地球内部介质（包括密度、地震波速等）分布异常对Slichter模本征周期的影响.数值结果表明,Slichter模周期随着内外核边界（ICB）密度差的增加以类似于双曲线的特征显著减小,当ICB密度差从597 kg·m^-3减小到200 kg·m^-3时,周期增大66.44%,当ICB密度差从597 kg·m^-3增大到1000 kg·m^-3时,周期减小21.48%;Slichter模周期随着核幔边界（CMB）密度差的增大而缓慢增大;相对于PREM,地球模型1066A在ICB和CMB的密度差分别相差45.321%和1.132%,内部地震波速度和密度梯度也存在差异,但是,当密度差减小到1066A模型提供的数值时,得到的Slichter模周期与基于1066A获得的结果（4.599 h）非常接近,差异分别只有3.762%和0.037%;表明Slichter模本征周期与地球内部介质的精细结构关系不大,而对ICB的密度差非常敏感.内、外核P波波速分布异常对Slichter模周期的影响基本相当,当内核和外核P波波速均增加5%时,Slichter周期分别减小1.02%和1.69%,P波波速分别减小5%时,Slichter模周期分别增加1.27%和1.847%,内核S波波速分布异常比P波波速分布异常对Slichter模周期的影响小1个量级;与地核相比,地幔中的地震波速异常对Slichter模本征周期的影响小1~2个量级;表明地核中地震波速异常对Slichter模周期的影响很小,目前有关Slichter模周期理论计算的差异主要来自于所采用的地球模型中内核边界的密度差的差异,本文结果可以为Slichter模的研究、探测及其对地球深内部结构的约束提供理论依据.     

Global tidal parameters

Summary Global tidal parameters are shown to have recently increased in accuracy, after more than twenty years of LLR and a decade of superconducting gravimetry, whereas the numerical values for the Earth have not changed substantially. Numerical values of Love numbers for terrestrial planets and the moon are also given for degrees higher than four as load numbers are basically linear combinations of Love numbers, at least for spherical non-rotation approximations. Numerical values for planetary moons, as far as they are known, have also been included in the paper. The static and dynamic behaviour of long-period and pole tide is discussed. Inner solid and outer fluid core effects are critically reviewed, also in view of a century of terrestrial tide observations of the classical type. The separation of long-period tides from secular effects (on a rotating Earth) such as J_n (n<5), is considered.Dedicated to the Memory of M. S. Molodensky     

Another look at the core density deficit of Earth’s outer core

A constraint adopted in several geochemical studies of core composition is that the core density deficit (cdd) is 10%, with the implication that this number is based on robust geophysical evidence. The cdd is the perceived difference between the density of pure iron at core conditions and the seismically-determined density of the outer core. The importance of the cdd is that it limits the concentration of allowable light elements, such as sulfur and silicon, which, when mixed with Fe, or an Fe-Ni alloy, comprise the geochemical model of the inner core.We present evidence that the value of 10% for the cdd of the outer core is too high. Using a thermal-pressure equation-of-state, we find that for assumed melting temperatures of pure iron at the inner-outer core (ICB) pressure of 330 GPa ranging from 7500 to 4800 K, the cdd ranges from 2.9 to 7%, respectively. Reports that the cdd value of the outer core is less than 10% are found in a number of shock-wave studies, but the values reported here are apparently the lowest. Our cdd value for an assumed melting temperature of 6000 K for iron at 330 GPa is 5.4% and is compatible with proposed concentrations of Si and S impurities found from solubility studies at high P and T.     

Numerical simulations of thermal convection in a rapidly rotating spherical shell cooled inhomogeneously from above

Abstract

Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell with and without inhomogeneous temperature anomalies on the top boundary have been carried out using a three-dimensional, time-dependent, spectral-transform code. The spherical shell of Boussinesq fluid has inner and outer radii the same as those of the Earth's liquid outer core. The Taylor number is 10⁷, the Prandtl number is 1, and the Rayleigh number R is 5R_c (R_c is the critical value of R for the onset of convection when the top boundary is isothermal and R is based on the spherically averaged temperature difference across the shell). The shell is heated from below and cooled from above; there is no internal heating. The lower boundary of the shell is isothermal and both boundaries are rigid and impermeable. Three cases are considered. In one, the upper boundary is isothermal while in the others, temperature anomalies with (l,m) = (3,2) and (6,4) are imposed on the top boundary. The spherically averaged temperature difference across the shell is the same in all three cases. The amplitudes of the imposed temperature anomalies are equal to one-half of the spherically averaged temperature difference across the shell. Convective structures are strongly controlled by both rotation and the imposed temperature anomalies suggesting that thermal inhomogeneities imposed by the mantle on the core have a significant influence on the motions inside the core. The imposed temperature anomaly locks the thermal perturbation structure in the outer part of the spherical shell onto the upper boundary and significantly modifies the velocity structure in the same region. However, the radial velocity structure in the outer part of the shell is different from the temperature perturbation structure. The influence of the imposed temperature anomaly decreases with depth in the shell. Thermal structure and velocity structure are similar and convective rolls are more columnar in the inner part of the shell where the effects of rotation are most dominant.     

Dynamos with weakly convecting outer layers: implications for core-mantle boundary interaction

Convection in the Earth's core is driven much harder at the bottom than the top. This is partly because the adiabatic gradient steepens towards the top, partly because the spherical geometry means the area involved increases towards the top, and partly because compositional convection is driven by light material released at the lower boundary and remixed uniformly throughout the outer core, providing a volumetric sink of buoyancy. We have therefore investigated dynamo action of thermal convection in a Boussinesq fluid contained within a rotating spherical shell driven by a combination of bottom and internal heating or cooling. We first apply a homogeneous temperature on the outer boundary in order to explore the effects of heat sinks on dynamo action; we then impose an inhomogeneous temperature proportional to a single spherical harmonic Y ₂² in order to explore core-mantle interactions. With homogeneous boundary conditions and moderate Rayleigh numbers, a heat sink reduces the generated magnetic field appreciably; the magnetic Reynolds number remains high because the dominant toroidal component of flow is not reduced significantly. The dipolar structure of the field becomes more pronounced as found by other authors. Increasing the Rayleigh number yields a regime in which convection inside the tangent cylinder is strongly affected by the magnetic field. With inhomogeneous boundary conditions, a heat sink promotes boundary effects and locking of the magnetic field to boundary anomalies. We show that boundary locking is inhibited by advection of heat in the outer regions. With uniform heating, the boundary effects are only significant at low Rayleigh numbers, when dynamo action is only possible for artificially low magnetic diffusivity. With heat sinks, the boundary effects remain significant at higher Rayleigh numbers provided the convection remains weak or the fluid is stably stratified at the top. Dynamo action is driven by vigorous convection at depth while boundary thermal anomalies dominate in the upper regions. This is a likely regime for the Earth's core.     

利用前临界PcP-PKiKP资料研究中国东部内核边界性质

前临界内核边界反射震相PKiKP与核幔边界反射震相PcP构成组合,能有效压制浅部结构及震源因素的干扰,提供了对内核边界精细结构的直接约束. 本研究从华北克拉通西北部密集流动地震台阵一年观测资料中筛选出8个地震事件,得到共计 73对PcP-PKiKP组合,覆盖了从朝鲜半岛到我国东北及华中地区下方的内核边界. 本文系统分析了走时残差和振幅比数据,结果显示:(1)密集台阵资料有助于前临界PKiKP震相拾取,而浅源地震亦可提供高质量的PcP-PKiKP观测资料.(2)走时残差呈现了自西北向东南从正常到负异常的迅速变化(沿内核边界70 km范围内>0.5 s), 限制了研究区域内核界面不超过3 km的起伏. (3)相对振幅比变化表明了研究区内核边界密度差北西-南东向的系统增加, 揭示了内核结晶环境的小尺度扰动.     

地球外核的电荷密度

为计算地球磁极处的磁感应强度,建立地球的磁场是由带电的地球外核的旋转产生的模型.先根据毕奥-萨伐尔定律计算球形模型绕自转轴旋转时在自转轴直径上产生的磁感应强度;再利用已知的地球外核的内外半径及地球半径和磁极处的磁感应强度值,计算出地球外核的电荷体密度及面密度.结果表明:若外核的电荷呈均匀的体密度分布,则其电荷体密度为3.5507 C/m³;若外核的电荷均匀分布在外核的外表面,则其面密度为2.4581×10⁶ C/m².通过地球表面的磁感应强度信息利用物理规律和地球物理数据推测地球内部难以直接进行探测的相关信息,具有实际意义.根据地震学方法对地球外核厚度、转向等变化的最新研究数据按该文模型可推测地球磁场强度、极性等的变化.而地球磁场的变化对地球上的人类生活颇有影响.     

On the Mechanism of the Secular Tidal Acceleration of the Solid Inner Core and the Viscosity of the Liquid Core

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     

The earth's thermal profile: Is there a mid-mantle thermal boundary layer?

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 T_ICB = (5000 ± 900) K. Adiabatic extrapolation to the core-mantle boundary (CMB) gives T_ICB = (3800 ± 800) K. The temperature increment across the D″ layer is not well constrained, but is estimated to be T_D″ = (800 ± 400) K and a slightly superadiabatic extrapolation to 670 km gives T_{670 +} = (2300 ± 950) K. This is only about 300 K higher than the extrapolation to the same level from the upper mantle, T_670? = (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.