Weakly nonlinear stability to large-scale perturbations in convective magnetohydrodynamic systems without the α-effect

The problem of weakly nonlinear stability with respect to large-scale perturbations in 3-D convective magnetohydrodynamic (MHD) states in which the α-effect is absent or insignificant (e.g., because the system has symmetry relative to a center or a vertical axis) is examined. It is assumed that the MHD state whose stability is studied is free from large spatiotemporal scales and is insensitive to perturbations with the same small spatial scale as in the state under study. The equations for mean perturbation fields derived by asymptotic methods generalize the standard equations of magnetohydrodynamics (the Navier-Stokes and magnetic induction equations). A combined eddy diffusion operator, generally anisotropic and not necessarily negative definite, and additional quadratic terms similar to advective terms arise in the inferred generalized equations.     

A RESPONSE OF A RANDOMLY LAYERED EARTH TO AN ELECTRIC POINT OR DIPOLE SOURCE*

A point source or a dipole source of electric current, placed on a randomly layered semi-infinite medium, produces an inhomogeneous random potential field on the surface. The variance of the random potential, normalized with reference to the normal field (that is, a field due to a point source or a dipole source on a homogeneous medium), falls off inversely as the distance from the source. The conductivity of the layers is assumed to vary randomly about a mean value (unity) such that the variations can be represented by a zero mean homogeneous random function. Further the variations are assumed to be small compared to the mean so that the first order perturbation is adequate. The analysis shows that the dipole field is more sensitive than the single pole field to the conductivity variations.     

Perturbation of eigenfrequencies of a cylinder due to a ridge on the surface

Summary An infinite cylinder is assumed to have a small ridge on the surface. The effect of the ridge on the eigenfrequencies of flute mode of oscillation is obtained in the linear approximation. The usefulness of these results in seismological problems is indicated.     

Electromagnetic response of a buried cylindrical conductor for sheet and line current sources

A major problem in electromagnetic induction studies in regions of localized source fields, such as the auroral and equatorial electrojet regions, is the source effect. Using an analytical model, the electromagnetic response of a buried conducting cylinder to sheet current and line current excitations has been studied for the period rangeT=5 s to 24 h. The validity of the numerical results obtained from the analytical model are compared with the numerical results obtained from a finite difference model. The results show that for periods less than 30 min, there is no significant difference in the response of the cylinder to both source fields. However, significant differences are observed at longer periods. It was also observed that the equivalent height at which a uniform sheet current at 100 km above the earth's surface can be approximated by a line current varies as a function of the source period.     

井间电磁场时域有限差分数值模拟

为进一步了解井间地下介质结构及其电性特征,本文用时域有限差分方法(FDTD),实现了井间电磁场响应的数值模拟.激发源是探测深度相对磁偶极子更大一些的电偶极子,首先选择一个位于井轴上的垂直电偶极子作为场源,并假设参与计算的介质相对于发射井井轴是轴向对称的,这样可将研究区域作为二维问题处理.推导了二维井间电磁波传播时域差分公式.该方法适用于任何方向入射的电偶极子源,尤其善于解决频域差分方法所难以描述的宽频脉冲.给出了井间金属圆柱和矿体圆柱数值模拟2个例子,结果表明,时域有限差分方法能有效的模拟井间地下介质中电磁波的传播,揭示电磁波传播规律.该方法速度快、精度高、结果稳定,适合用于井间电磁场反演成像的正演响应计算.     

Analytical configurations of a force-free magnetic cylinder in the solar wind

The problem of a smooth field configuration, which should be an initial configuration in modeling (using the method of coarse particles) the problem of a stationary solar wind flow around a magnetic cloud in the case of a spatially two-dimensional statement (when a magnetic cloud is considered as a force-free magnetic cylinder with a finite radius) is considered. It has been indicated that such a statement is possible only when the magnetic field in the solar wind is parallel to the cylinder axis. The method for finding the magnetic field of a force-free cylinder with a finite radius, when some field component is specified and another component is determined based on this one (which makes it possible to construct fields with preassigned properties), has been proposed. The variant for constructing the initial field configuration in the transition region around a cylinder has been proposed. This variant makes it possible to gradually pass from homogeneous crossed fields in the solar wind to a force-free magnetic and zero electric fields within a cylinder, an electric field being potential and orthogonal to a magnetic field (in the reference system related to a magnetic cloud).     

Geological setting of hydrothermal activity at 12°50′N on the East Pacific Rise: A submersible study

A detailed submersible investigation of a 20-km segment of the East Pacific Rise near 12°50′N between the Orozco and Clipperton fracture zones has resulted in the localization of 24 active hydrothermal vent fields and over 80 sites of sulfide accumulations. The active vents range from low-temperature vents characterized by exotic benthic communities to high-temperature “black smokers” and the deposition of polymetallic sulfides. The study is based upon a combination of fine scale topography obtained using the SEABEAM sonar system on N/O “Jean Charcot”, camera lowerings along the axis using the RAIE vehicle, and 32 dives by the submersible “Cyana” operating from N/O “Le Suroit”. The observations made between the Orozco and Clipperton fracture zones show topographic highs situated along the strike of the accreting plate segment separated by a small ridge offset at 11°49′N. This offset divides this portion of the ridge into two separate spreading segments each of which has a primary topographic high along strike. Secondary highs are associated with each segment of the ridge separated by either small offsets (or relay zones) or in some cases, zones where spreading centers overlap. Dives made on the tops of both primary highs (12°50′N and 11°30′N) confirm the presence inferred from previous surface work of high-temperature vent fields while one reconnaissance dive (14°20′N) near the Orozco fracture zone/ridge axis intersection reveals the absence of any hydrothermal activity in the present or recent past. The vast majority of vent fields investigated were found at the topographic high near 12°50′N, are associated with the most recent period of volcanism, and are confined to lava ponds situated within the axial graben.     

Serpentinite protrusions in the oceanic crust

Serpentinite may be a significant component of the oceanic crust, not as a continuous layer, but as vertical tectonic protrusions and sills emplaced from the upper mantle into fault zones parallel to the axis of spreading ridges. The diapiric emplacement of serpentinite bodies occurs within 100–200 km of ridge axis, with a rate of ascent on the order of 1 mm/year. Serpentinite protrusions may cause small-scale linear magnetic anomalies parallel to ridge axis. Serpentinites are distributed in the oceanic crust according to an orthogonal pattern, with large serpentinite protrusions aligned along major fracture zones, and smaller serpentinite bodies emplaced in bands parallel to ridge axis.     

横向各向同性地层斜井中正交偶极子激发声场的数值模拟

本文采用三维应力-速度有限差分(SV-FD)方法,数值模拟了横向各向同性(TI)地层对称主轴与井轴斜交情况下正交偶极子声源激发的井孔声场.主要解决了与倾斜角有关的三维空间弹性模量矩阵的推导,柱坐标系下应力-速度有限差分方程组的建立,井轴上场点奇异性与内边界处理等几个关键问题,提高了计算精度.在横向各向同性地层对称主轴与井轴平行的情况下,与实轴积分法所得结果进行了对比,验证了本文方法的正确性.计算了不同倾角情况下xx和yy两分量的弯曲波,并用频域加权相似法提取了弯曲波频散曲线,结果显示了横向各向同性介质中不同方向偏振的弯曲波传播的分裂现象,其频散曲线在低频段分裂,随频率增大而逐渐重合.弯曲波低频截止频率处速度与理论公式得到的横波速度基本符合.     

各向异性双相介质中多极源声波测井理论研究

将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场     

各向异性双相介质中多极源声波测井理论研究

将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场     

各向异性双相介质中多极源声波测井理论研究

将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场     

弹性波逆散射微扰论

本文将普遍声逆散射微扰论应用于弹性波层析成像问题,在Born变换下推出了以旋转角为补偿参数的各阶微扰重建公式,实现了对非均匀各向同性散射体内3个参数（质量密度ρ和两个Lamé系数λ,μ）的同时重建. 对于层析成像问题,在弹性波的传播过程中P波与SV波有耦合,但它们不会和SH波发生耦合,于是可以得到3个形式相对简单的标量方程. 在Born变换下,在散射波中引入微扰参数,将散射体的3个参数分别按该微扰参数展开,然后利用二维自由空间的Green函数分别得到散射的P波、SV波和SH波的积分表示. 最后,经一维傅氏变换后,得到Born变换下散射体3个参数的各阶微扰重建公式.     

Anisotropic tomography of the Atlantic Ocean

We present the first regional three-dimensional model of the Atlantic Ocean with anisotropy. The model, derived from Rayleigh and Love wave phase velocity measurements, is defined from the Moho down to 300 km depth with a lateral resolution of about 500 km and is presented in terms of average isotropic S-wave velocity, azimuthal anisotropy and transverse isotropy.The cratons beneath North America, Brazil and Africa are clearly associated with fast S-wave velocity anomalies. The mid-Atlantic ridge (MAR) is a shallow structure in the north Atlantic corresponding to a negative velocity anomaly down to about 150 km depth. In contrast, the ridge negative signature is visible in the south Atlantic down to the deepest depth inverted, that is 300 km depth. This difference is probably related to the presence of hot-spots along or close to the ridge axis in the south Atlantic and may indicate a different mechanism for the ridge between the north and south Atlantic. Negative velocity anomalies are clearly associated with hot-spots from the surface down to at least 300 km depth, they are much broader than the supposed size of the hot-spots and seem to be connected along a north-south direction.Down to 100 km depth, a fast S-wave velocity anomaly is extenting from Africa into the Atlantic Ocean within the zone defined as the Africa superswell area. This result indicates that the hot material rising from below does not reach the surface in this area but may be pushing the lithosphere upward.In most parts of the Atlantic, the azimuthal anisotropy directions remain stable with increasing depth. Close to the ridge, the fast S-wave velocity direction is roughly parallel to the sea floor spreading direction. The hot-spot anisotropy signature is striking beneath Bermuda, Cape Verde and Fernando Noronha islands where the fast S-wave velocity direction seems to diverge radially from the hot-spots.The Atlantic average radial anisotropy is similar to that of the PREM model, that is positive down to about 220 km, but with slightly smaller amplitude and null deeper. Cratons have a lower than average radial anisotropy. As for the velocities, there is a difference between north and south Atlantic. Most hot-spots and the south-Atlantic ridge are associated with positive radial anisotropy perturbation whereas the north-Atlantic ridge corresponds to negative radial anisotropy perturbation.     

Flow through the annular space between two porous co-axial elliptic cylinders

Summary In this paper slow steady motion of fluid, through the annular space between two porous co-axial elliptic cylinders has been studied. There is a suction or injection perpendicular to the walls of the tube; the amount of suction (or injection) per unit length through the outer wall is equal to the amount of injection (or suction) through the inner wall. The pressure gradient along the length of the cylinder is constant. The cylinders are assumed to be large and the distance between them is small. The amount of injection or suction is assumed to be small. Method of perturbation is applied to obtain the velocity distribution.     

On the computation of the electrical potential inside a horizontally‐layered half‐space

A new formulation is proposed for the electrical potential developed inside a horizontally‐layered half‐space for a direct current point‐source at the surface. The recursion formula for the kernel coefficient in the potential integral is simpler than the generally used two‐coefficient recursion. The numerical difficulties that may occur during the computation of the integrals and near the source axis are examined and solutions are proposed. The set of equations permits a stable and accurate computation of the tabular potential everywhere in the medium.     

Exact solution of the source problem for a finite threedimensional source

Summary In this note the surface displacement for an elastic half-space due to a finite cylindrical source has been calculated in exact terms. The source consists of outward body forces acting on the surface of the right circular cylinder, one end of which is parallel to the free surface of the half-space.     

Three‐dimensional non‐geostrophic disturbances in a baroclinic zonal flow

Abstract

A study is made to determine the stability properties of a baroclinic zonal current on which small amplitude three‐dimensional non‐geostrophic disturbances are superimposed. The flow is assumed to be bounded to the north and south by rigid vertical walls and the Rossby number Ro is taken to be small compared to unity. It is then shown that if the perturbation quantities are expanded in power series in Ro the leading or zero order terms in the series correspond to the quasi‐geostrophic solution obtained by Eady (1949) and that the higher order terms represent the “non‐geostrophic” effects neglected by the latter.

It is shown that to the second order in Ro the non‐geostrophic effects decrease the growth rates of those disturbances which are found to be unstable according to Eady's analysis but do not alter their speed of propagation. The results indicate, on the other hand, that to the same order of approximation the stable waves travel at a speed which is different from that given by Eady's solution. The modification of the perturbation wave structure by the non‐geostrophic effects is also investigated. It is found in particular that to the first order in Ro the latter produce a northward tilt with height in the ridge (or trough) lines of the meridional and vertical particle velocity fields away from the lateral boundaries.     

Bifurcations in Spherical MHD Models

A series of numerical studies on the behaviour of magnetic fields and motions in a spherical body of an electrically conducting incompressible fluid have been carried out. The magnetic field was assumed to be maintained by a given electromotive force inside the body and to continue as a potential field in outer space. In view of the motion an external forcing was taken into account, and boundary conditions were considered which correspond to a stress-free surface. The stability of several steady states has been studied as well as the evolutions starting from unstable states. In this paper a configuration with a poloidal magnetic field and a differential rotation, both symmetric about the same axis, is considered. This configuration is stable only for sufficiently small Hartmann numbers but evolves, if disturbed, in the case of larger Hartmann numbers toward a non-axisymmetric state. In this case the well-known symmetrization effect of differential rotation in magnetic fields is destroyed.     

地震地热说原理与应用

从地震与火山资料出发,定义了地震柱的概念,全球划分24个地震柱并逐个研究.发现了地幔深部能量自下而上逐层驱动的稳定通道,揭示了浅源地震与中深源地震的差异性、壳内地震与火山的同一性、本尼奥夫剖面的独立性、地震柱活动的间歇性、地震柱的衰变性等自然现象,探讨了地震柱的成因,构成了M型的热机带.同时,对全球GPS观测资料与大洋中脊带的继承性运动和脊轴扩张的比较研究,揭示了当前大陆漂移的优势方向,构成了W型的冷机带.两大系统呈倒扣之势并具有相位差异或许由于地球自转角速度的变更所造成,从而构成了当今地球的地貌差异.冷机带造成大陆漂移的渐变而热机带造成壳内强震和火山的灾变,形成地震地热说的两个研究体系.文中给出了地震地热说应用方面的几个例子.