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．      

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．     

10年尺度的日长变化的一种机制

固态地球内核与地幔之间强烈的重力耦合作用提供了液态地球外核和地幔之间角动量交换的一种方式。本文提出的机制涉及液态地球外核的振荡,由于液态地球外核具有很高的电导率,这种振荡可将巨大的电磁扭转力矩施加于固态地球内核之上。固态地球内核并不能自由地对这个扭转力矩做出反应,因为重力迫使地球内核与地幔之间保持一定的相对位形。对这种相对位形的微小偏离引起重力扭矩,从而使角动量由内核传递到地幔。对这一祸合系统的简正振型的计算结果解释了观测得到的周期为数十年的地幔的运动。能量的电阻消耗所导致的振荡阻尼给出品质因子Q值约为20。基于近年来地磁发电机理论的计算结果,提出了维持这种振荡的一种激发机制。     

内核地球自转动力学理论的研究进展(Ⅴ)——地球自转耦合运动方程组

本文是序列文章的第五篇,其内容包括：基于连续介质力学的基本理论,在考虑到地球的自引力、液核对核幔边界的压力和外部引潮力的作用下,严格地给出了地幔的角动量方程.利用前文的有关结论,进而给出了整体地球自转的动力学方程和内核地球模型的地球自转耦合运动学方程组.本文顾及了高阶岁差章动力矩对地球自转的影响,因而在理论上扩展了文献〔1〕给出的理论模型.本文的理论对进一步研究在高阶岁差章动力矩作用下的内核地球章动是非常有意义的.     

地球的差异旋转

对于具有流体对流层的旋转星球 ,由于星球自转对对流的影响 ,必然会在星球对流层内部不同部分间以及星球的不同圈层间产生差异旋转 (differentialrotation) .所谓差异旋转是指旋转角速度随着深度 (星球不同圈层的旋转角速度不同 )以及纬度 (同一圈层内部不同部分间的角速度不同 )具有差异的现象 .地球是一个多圈层的旋转系统 ,主要由大气圈、水圈、岩石圈、地幔、外核以及内核组成 .大气圈和水圈具有明显的流体性质 ,并且在漫长的地质年代中 ,地幔、岩石圈和地幔之间的软流层以及外核均具有流体性质 ,而且在大气压力、热、重力和电磁力等的作用下发生了对流 .这些对流运动一旦受到地球自转的影响 ,就必然会致使地球各圈层间以及对流层内部不同部分间产生差异旋转 .几个重要现象 :基本地磁场的长期西漂、岩石圈的长期西漂、地球自转速率变化 (周日长度波动 )和固体内核各向异性对称轴的移动表明在固体地球内部各圈层—岩石圈、地幔、外核和内核间存在差异旋转 .来自地震学上的数据证明了固体内核与地幔之间存在较明显的差异旋转 ,速率可达 1.1°～ 3.0°/a.这跟其它数据如自由振荡数据以及地磁场长期西漂数据获得的结果具有很大的差异 .导致固体地球内核相对于地幔差异旋转的主要宏观机制为电磁力矩、引     

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.     

利用多种地球物理观测资料直接反演地幔对流模型

假定地幔为一个均匀的、粘滞系数为常数、同时均匀分布放射性热源的流体球层,其内部存在的对流则由流体力学3个基本方程:运动方程、能量方程和连续性方程确定.如果假定地幔处于低瑞利数的状态（临界瑞利数1.5倍左右）,那么上述方程中的非线性项可以忽略不计.作为一类可能的模型,本文计算一组用6个边界条件确定6个未知数的线性方程组.这些条件包括板块绝对运动极型场、地球大地水准面异常和地震层析结果提供的地幔密度分布横向不均匀相应的“刚性地球”水准面异常等.模型计算表明:1.地幔中流体运动格局不仅受地幔热动力学参数（瑞利数）控制,而且强烈地受边界条件的影响.2.若不限定下边界为等温边界,则上、下地幔之间并不呈现出活动性明显差异;但是在模型瑞利数加大到一定值时,核-幔边界附近将出现一些局部的小尺度对流环.3.当模型瑞利数从很小增加时,对流格局将发生变化,这些格局可能反应由地幔热动力学参数决定的地幔固有特性.4.当瑞利数为50000和80000时,核-幔边界形变与PcP波得到的结果吻合较好.     

地球内核的旋转和磁性

地球发电机三维数值模拟说明,地球固内核相对于地幔的超（速）旋转是由内核和液体外核内的东向热风之间的耦合来维持的。这种机制类似于同步电动机的机制,在地球磁场的产生中也起着重要作用。     

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.     

地球内核处于熔融状态

地球的磁场是由液态铁核形成的地磁发电机所产生的,这种液态铁核在上覆层地幔岩石的冷却下导致对流.地核由最里面向外冷却,生成固态的内核和释放轻元素.这些驱动着组分上的对流[1-3].地幔从地核以一定的速率吸收了热量,且吸热速率在空间上存在着很大的横向变化和差异[4].本文利用地磁发电机模拟显示这种横向差异会传递至内核边界,从而足以导致热量流入内核.如果地球内部确实是这样,将导致局部的熔融作用.熔融释放密度较重的液体形成变化的组分层,这一点可由内核上边界向上150 km处的地震波速度异常来解释[5-7].     

Earth tides and polar motion

We establish a general theory that describes the rotational motion of a layered, oblate, elastic Earth under the influence of tidal forces when account is taken of the liquid outer core. We obtain a linearized version of the Navier-Stokes equation; within it not only have we retained the Coriolis and centrifugal acceleration terms, but also have included the nutational terms. We also make use of the Euler equation for angular momentum to analytically relate the nutational motion of the rotational axis with the oscillations of the liquid core and obtain a constraint for the nutational amplitude. Consideration of the Poisson equation for density variation completes our analytical model.We primarily discuss the equations of motion for the liquid core and present the solution as the sum of two terms: one being a component of the spheroidal displacement field, the other of the toroidal field. We also formulate the equations valid for the solid mantle when rotational effects are included, and establish the boundary conditions that must hold at the various interfaces in order that a complete integration of the differential system of equations be accomplished.We assume that the outer core consists of an inviscid fluid and ignore the existence of any boundary layer. We do not impose, however, any restriction on the stratification of the fluid. The dynamical coupling between liquid core and solid mantle is represented by a torque which is generated by the forced oscillations within the liquid core; these oscillations are in turn triggered by the diurnal tides.The expected influence of the liquid core/solid mantle boundary on the nutational motion is discussed in view of Poincare's results concerning a liquid core surrounded by a rigid shell. Comparison is finally made of our model with Molodenskii's 1961 theory for a neutral core and the 1976 Shen-Mansinha nutational theory for an unrestricted core.     

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

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…     

全球流体通道网

新近取得的深反射与全球地震层析成像资料,为地球内部结构和流体通道的研究提供了一些依据．通过研究这些地震资料,可以了解地球内部物质分布状态的几何模式．综合研究表明,地球内存在流体通道网,它连通地球外核、中幔圈、软流圈和岩石圈,是固体地球系统的重要组成部分．这种通道网络象“动脉”那样把地球外核中的流体和热量向外传送,但与热羽说不同的是,不见得有对应的“静脉”存在以保持地幔质量平衡．固体地球作为多层次多要素的巨型复杂系统,其动力学过程要用浑沌理论去解释．研究地球流体活动的轨迹和吸引子,将有助于深入了解地球活动的规律性．     

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).     

On the theory of core-mantle coupling

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.     

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.