Core-mantle coupling and viscoelastic deformations

Writing the angular momentum theorem for the Earth and for its fluid core, we show that there are couplings between the core and the mantle induced by viscomagnetic torque, by external active torque, by topographic torque acting at the core-mantle boundary (CMB) but also by viscoelastic deformations of the CMB which may perturb the axial rotations of the Earth and of the core. We compute these deformations at the CMB induced by the Pleistocenic deglaciation. The time-dependence of inertia tensor perturbations, i.e. the rheology of the mantle, is very important in the calculation of the coupling. Taking into account the passive viscomagnetic torque of tangential traction acting at the CMB, we investigate, for different values and various temporal evolutions of the topographic torque, the perturbations in the rotations of the Earth and of the core induced by the deglaciation, by the constant torque of tidal friction and by the 18.6 year tidal potential. We show that, for these excitation sources, the existence of a constant topographic torque involves the core oscillating with respect to the mantle and thus forbids any large drift of the core with respect to the mantle. However, it seems theoretically possible to have an excitation source with enough energy which involves a shift of the core with respect to the mantle. If the pressure within the fluid core varies with time, the motion of the core with respect to the mantle could be drastically different.     

Torsion design implications from shake‐table responses of an RC low‐rise building model having irregularities at the ground story

A 1:5 scale five‐story RC building model having the irregularities of a soft/weak story and torsion at the ground story was subjected to a series of earthquake simulation tests. The test results reveal the following: The eccentricity varied from zero to infinity with the values of base shear and torque bounded by some limits. As the intensity of table excitations increased, representing earthquakes with return periods from 50 to 2500 years in Korea, the range of eccentricities at the peak values in the time histories of drift and base shear decreased from approximately ±30% to within ±10% of the transverse dimension of the model. The inertial torque was resisted by both longitudinal and transverse frames, in proportion to their instantaneous rigidity. Yielding of the longitudinal frames under severe table excitations caused a substantial loss in their instantaneous torsional resistance and thereby transferred most of the large torque to the transverse frames, resulting in a significantly degraded torsional stiffness with an enlarged torsional deformation despite almost zero eccentricity. From these observations, it is clear that the eccentricity in itself cannot represent the critical torsional behaviors. To overcome this problem, the demand in torque shall be determined in a direct relationship with the base or story shear, given as an ellipse constructed with the maximum points in its principal axes located by the two adjacent torsion‐dominant modal spectral values. This approach provides a simple but transparent design tool by enabling comparison between demand and supply in shear force–torque diagrams. Copyright © 2014 John Wiley & Sons, Ltd.     

Axial poloidal electromagnetic core-mantle coupling torque: A re-examination for different conductivity and satellite supported geomagnetic field models

We investigate the temporal behaviour of the axial component of the electromagnetic core-mantle coupling torque that is associated with the poloidal part of the geomagnetic field observable at the Earth surface. For its computation, we use different models of the geomagnetic field, expanded into spherical harmonics (Wardinski and Holme, 2006; Sabaka et al., 2004), and the mantle conductivity. The geomagnetic field, which we have to know at the core-mantle boundary for the associated computations, will be inferred from the field at the Earth surface by the non-harmonic field continuation through a conducting mantle shell. The aims of this investigation are (i) to check how sensitive is the computation of the torque with respect to the different geomagnetic field models, (ii) to check its dependence on the spherical harmonic degree n, and (iii) to determine the difference between the mechanical torque derived from the observed length-of-day variations (atmospheric influence subtracted) and the poloidal electromagnetic torque in dependence on the assumed conductivity. To use the non-harmonic field continuation for the torque calculation and to obtain an insight into the influence of the different geomagnetic field models on the EM torques are the major aspects of this paper. grm@gfz-potsdam.de     

Second Tesseral Harmonic Torque Due to the DynamicS of the Oceanic Surface Layer as Detected by TOPEX/POSEIDON Altimetry 1993-2000

Estimates of the second tesseral torque due to the variations in the radial space position of the mean ocean surface as monitored by TOPEX/POSEIDON altimeter system are derived. The magnitude of the studied torque may be compared to the tidal torque and to the tesseral torque caused by deformations due to the Earths rotation. However, such torque estimates strongly depend on the thickness of the ocean surface layer adopted in the spherical model of which the dynamics is believed to be responsible for the derived torque. The dependence on the thickness is discussed.     

矩形高层建筑扭转动力风荷载解析模型

本文通过研究不同长宽比、高宽比的矩形棱柱体在边界层风洞中典型攻角下的扭矩，提出了矩形高层建筑扭矩功率谱密度、均方根扭矩系数和Strouhal数的经验公式，并对相干函数作了一定的探讨，建立了完整的扭转动力风荷载解析模型。该模型和试验结果吻合较好，证明它是合理有效的，可在此基础上建立高层建筑扭转动力响应频域计算方法。     

Addressing Hurricane Intensity through Angular Momentum and Scale Energetics Approaches

This paper addresses two avenues for gaining insight into the hurricane intensity issue—the angular momentum approach and the scale interaction approach. In the angular momentum framework, the torques acting on a parcel's angular momentum are considered along an inflowing trajectory in order to construct the angular momentum budget. These torques are separable into three components: The pressure torque, the surface friction torque, and the cloud torque. All torques are found to diminish the angular momentum of an inflowing parcel, with the cloud torques having the most important role. In the scale interaction approach, energy exchanges among different scales within a hurricane are considered as a means of understanding hurricane intensity. It is found that the majority of kinetic energy contribution to the hurricane scales originates from potential-to-kinetic in-scale energy conversions. The contribution of mean-wave interactions in the kinetic energy varies with distance from the center and with the life stage of a storm. In the early stages, as the disorganized convection becomes organized on the hurricane scales, upscale energy transfers (i.e., from small to large scale) are found to take place in the outer radii of the storm. In a mature storm, the kinetic energy transfers are downscale, except for the inner radii.     

The magnetic anisotropy of hematite bearing rocks

Summary The high field torque curves of hematite bearing rocks are not caused by directional differences in the energy of magnetization to saturation, but rather by the couple between the ferromagnetic moment and the applied field. An expression, derived for the high field torque curve of a single crystal of hematite, whose basal plane makes an arbitrary angle with the plane of rotation of the applied field, is found to be in excellent agreement with experiment. Furthermore it is shown that the Fourier spectrum of hematite bearing rocks should in general contain significant higher harmonics and that therefore the high field method is not particularly suitable for determining the preferred crystalline alignment of hematite bearing rocks.     

Understanding the inelastic seismic behaviour of asymmetric-plan buildings

Studied in this paper is the inelastic seismic behaviour of asymmetric-plan buildings using the histories of base shear and torque. The first step in understanding this behaviour is to construct the base shear and torque surface (BST) for the building, which represents all combinations of shear and torque that applied statically lead to collapse of the structure. Several factors controlling the shape of this surface, such as strength eccentricity and bidirectional ground motion, are identified. Also, their effects on the building responses are studied considering several structural configurations. The results obtained show that the BST surface, in conjunction with the base-shear and torque histories, provides a useful conceptual framework for understanding the behaviour of asymmetric systems. Furthermore, using these surfaces, relevant aspects of the behaviour and design of such buildings become apparent even before dynamic analysis of the structure.     

ON THE POSSIBILITY OF SEISMIC EXPLORATION USING SURFACE TORQUE SOURCE AND RELATED TOPICS*

In this study we derive expressions for particle displacement or particle velocity anywhere inside a stratified earth and at its surface due to horizontal torque source located in the top layer. Equivalently, invoking Green's function reciprocity theorem, the solution applies also to the case of a surface or subsurface source when the resulting displacement or velocity is measured within the top layer. In order to evaluate the closed-form analytical solution economically and accurately it is advisable to introduce inelastic attenuation. Causal inelastic attenuation also lends the necessary realism to the computed seismic trace. To provide proof that the analytical solution is indeed correct and applicable to the multilayer case, a thick uniform overburden was assumed to consist of many thin layers. The correctness of the computed particle velocity response can be very simply verified by inspection. The computed response can also serve as a check on other less accurate methods of producing synthetic seismograms, such as the techniques of finite differences, finite elements, and various sophisticated ray-tracing techniques. It is not difficult to construct horizontal surface torque source. It appears that such source is well suited for seismic exploration in areas with a high-velocity surface layer. A realistic source function is analyzed in detail and normalized displacement response evaluated at different incidence angles in the near and the far fields. In an effort to distinguish the features of an SH torque seismogram from a pressure seismogram two models with identical layerings and layer parameters have been set up. As expected the torque seismogram is very different from the compressional seismogram. One desirable feature of a torque seismogram is the fast decay of multiples. Exact synthetic seismograms have many uses; some of them, such as the study of complex interference phenomena, phase change at wide angle reflection, channeling effects, dispersion (geometrical and material), absolute gain, and inelastic attenuation, can be carried out accurately and effortlessly. They can also be used to improve basic processing techniques such as deconvolution and velocity analysis. The numerical evaluation of the analytical solution of the wave equation as described in this paper has a long history. Most of the work leading to this paper was carried out by one of us (M. J. K.) in the years 1957 to 1968 at the Geophysical Research Corporation. However, the full testing of the various computer codes was carried out only very recently at the Phillips Petroleum Company.     

Variability of the topographic core-mantle torque calculated from core surface flow models

With the prospect of studying the relevance of the topographic core-mantle coupling to the variations of the Earth’s rotation and also its applicability to constraining the core surface flow, we investigate the variability of the topographic torque estimated by using core surface flow models accompanied by (a) uncertainty due to the non-uniqueness problem in the flow inversion, and (b) variance originating in that of geomagnetic secular variation models employed in the inversion. Various flow models and their variances are estimated by inverting prescribed geomagnetic models at the epoch 1980. The subsequent topographic torque is then calculated by using a core-mantle boundary topography model obtained by seismic tomography. The calculated axial and equatorial torques are found subject to the variability of order 10¹⁹ and 10²⁰  Nm, respectively, on which (b) is more effective than (a). The variability of the torque is attributed even to (a) and (b) of the large-scale flows (degrees 2 and 3). Yet, it still seems unlikely for the decadal polar motion with the observed amplitude to be excited exclusively by the equatorial topographic torque associated with any of reasonable core surface flow models. It is also confirmed that, with the topography model adopted here, the axial topographic torque on a rigid annulus in the core (coaxial with the Earth’s rotation axis) associated with any of reasonable flow models is larger by two orders of magnitude than the plausible inertial torque on such cylinders. This implies that any core surface flow model consistent with the topographic coupling does not exist, unless the topography model is appropriately modified. Nevertheless, the topographic coupling might provide not only a weak constraint for explaining the decadal LOD variations, but also the possibility to probe the core surface flow and the core dynamics.     

近海复杂环境下的H-M-T受荷桩内力位移分析

为探讨近海复杂恶劣环境（台风超强风力、车辆冲击力或地震产生的复杂力等）下水平力H、弯矩M及扭矩T共同作用时的基桩桩身内力变形特性,基于传统有限杆单元法思想,获得了H-M-T受荷桩的基本单元刚度矩阵。然后,基于m法考虑桩周地基土的侧向约束作用,并计入H-M-T耦合效应,采用凝聚方法导得了具有简洁统一形式的桩身杆单元刚度矩阵,由此建立水平力、弯矩和扭矩组合作用下的桩身内力位移有限杆单元法计算模型,进而采用MATLAB编制出相应的分析计算程序。最后,结合近海工程算例进行了分析。结果表明：1文中提出的改进有限杆单元法能考虑桩周地基土的分层特性、不同边界条件及H-M-T的耦合效应;2相比单一考虑水平受荷,扭矩的存在加大了桩身的位移和内力;3H-M-T复杂受荷模式下,荷载传递存在有效传递深度,当相对深度z/L超过0.5后,桩身弯矩和剪力趋近于零,而扭矩显著减小。     

建筑物偏心结构对其抗震性能的影响

偏心对建筑物的抗震效果有很大的影响。在对三种常见建筑物框架结构在偏心扭矩作用下的受震反应进行数值模拟时,采用6层建筑物模型,通过三维非线性模拟偏心结构对建筑物抗震性能影响的分析,采用最大层间位移作为衡量标准,绘制易损曲线来进行结果分析。结果显示:若忽略意外扭矩的影响,可能会高估钢结构体系的抗震性能,而影响安全评估结果;如果采用全层5%质量偏心来考虑意外偏心扭矩的话,会低估钢结构建筑物的抗震性能。     

正弦行波激励下单层偏心框架结构扭转响应的解析解

文中针对单层偏心框架结构,利用正弦行波激励研究了质量偏心率和激励频率对偏心框架结构行波扭转响应的影响规律.建立了行波激励下单层偏心框架结构的振动方程,采用相对运动法求解给出了正弦行波激励下单层偏心框架结构楼板的质心平动位移和转角位移以及楼板扭矩和柱剪力的解析解.计算了一个钢筋混凝凝土单层偏心框架结构的峰值楼板扭矩和峰值...     

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.     

The magnetic anisotropy of the Yampi Sound hematite ores

Summary The magnetic fabric of the Yampi Sound hematite ore bodies of Cockatoo and Koolan Island in Western Australia has been determined with a low field torque meter in an attempt to investigate the origin of the ores. The ore bodies are conformable with a ferruginous sedimentary sequence, which has been folded into overturned synclines and anticlines. Each ore body shows a consistent distribution of the principal susceptibility axes due to a preferred alignment of the trigonal axes of hematite, but the magnetic fabric is not related to the sedimentary structure of the ores. For the Cockatoo Island ore body the magnetic fabric indicates the presence of an axial plane foliation within the ore, suggesting that the preferred crystalline alignment is caused by arecrystallization of hematite during the folding of the sediments. The magnetic fabric of the ore bodies on Koolan Island is not related to either bedding or axial planes. This can be explained by assuming that the hematite recrystallized during an earlier stage of the folding process and that then the limbs of the fold were rotated into their present position. High field torque measurements on several ore specimens indicate a preferred crystalline alignment of hematite of about 25%. The ferruginous sediments of Cockatoo Island show a composite fabric caused by the superposition of two foliations, one being the bedding plane and the other the axial plane foliation impressed during the folding of the sediments.     

西安黄土新型旋转触探试验研究

对西安理工大学研制的新型旋转触探仪进行调试并进行了5个干密度,4个含水率试样的室内旋转触探试验。通过对实验数据的分析定性得出了:相同含水率条件下稳定锥尖阻力与稳定扭矩随干密度增大而增大;相同干密度条件下稳定锥尖阻力与稳定扭矩随含水率增大而减小。试验结果也为通过旋转触探定量确定岩土物理力学性质参数提供了依据。     

Torsional response of structures to obliquely incident seismic sh waves

A study is made of the torsional response of an elastic structure placed on a rigid circular foundation supported on an elastic half-space and subjected to the action of obliquely incident plane SH waves. The problem is solved by considering first the steady-state response of a massless rigid foundation excited externally by a harmonic torque and through the soil by an obliquely incident plane SH wave. In a second stage the coupling between the structure and the soil is considered to obtain the torsional response at the base and top of the superstructure. The results obtained indicate a range of conditions under which the torsional effects will be most pronounced.     

A simplified model for analysis and design of asymmetric-plan buildings

A new simplified model for analysis and design of multistorey buildings is developed. The model is based on a single super-element per building storey capable of representing the elastic and inelastic properties of the storey. This is done by matching the stiffness matrices and ultimate yield surface of the storey with that of the element; this surface relates storey shear and storey torque. For practical convenience, these surfaces are parametrized in terms of seven important physical parameters controlling the seismic response of asymmetric structures. Several numerical studies showed that the accuracy of the super-element model is satisfactory for most design purposes; the errors in peak responses are expected to be less than 20 per cent for most practical structures. Among the important advantages of this simplified model is that the time required in formulating, analysing and interpreting the structural model and its response is at least an order of magnitude smaller than for any conventional 3-D inelastic model. This enables the engineer to try different structural configurations and, thus, produce designs that have the desired seismic behaviour and are cost-effective. Furthermore, it has been shown through a multistorey building example that the super-element model is a powerful tool for conceptual design of a building. In spite of its simplicity, the model uses an accurate representation of the storey-shear and torque surfaces, which enables it to capture the fundamental features controlling the inelastic behaviour of the building.     

The role of phase difference components of ground motions in the torsional response of asymmetric buildings

It is demonstrated that the difference in phase content between orthogonal, horizontal, accelerograms can directly influence the effective (band‐limited) torque energy applied to a plan asymmetric structure. This is not the case where a plan asymmetric structure is excited solely by a unidirectional, horizontal, accelerogram ground motion. It is shown that this effective torque energy is well correlated with building torsional (response) acceleration energy and element ductility demands for a broad class of multistorey structures. Nonlinear time‐history analyses employing a database of accelerogram abstracted from USGS are used to quantify the influence of the phase difference content on these building responses. Bias in nonlinear time‐history analyses based on a small sample of accelerograms caused by phase difference content is discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

On a certain doubt L. Euler had with respect to determining the rotation of the earth and of celestial bodies

Summary The application of Euler's postulate , which determines rotation (here denotes the derivative of the angular momentum with respect to time, L the resultant torque of exterior forces relative to the centre of inertia), to a celestial body, which is not spherically symmetric, had aroused doubts in Euler himself because of the displacement of the resultant attractive force of other celestial bodies from the said centre. As Minding had noted, it is more logical to compute the resultant torque relative to a point at which the torque has a minimum. This point should be named the attrahentis centrum after Euler. Newton was aware of this displacement of the resultant force and had mentioned it in the Principia. A review of Euler's works connected with this subject is given.