On the possibility of using an electromagnetic ionosphere in global MHD simulations

Global magnetohydrodynamic (MHD) simulations of the Earths magnetosphere must be coupled with a dynamical ionospheric module in order to give realistic results. The usual approach is to compute the Reld-aligned current (FAC) from the magnetospheric MHD variables at the ionospheric boundary. The ionospheric potential is solved from an elliptic equation using the FAC as a source term. The plasma velocity at the boundary is the E × B velocity associated with the ionospheric potential. Contemporary global MHD simulations which include a serious ionospheric model use this method, which we call the electrostatic approach in this paper. We study the possibility of reversing the flow of information through the ionosphere: the magnetosphere gives the electric Reld to the ionosphere. The Reld is not necessarily electrostatic, thus we will call this scheme electromagnetic. The electric Reld determines the horizontal ionospheric current. The divergence of the horizontal current gives the FAC, which is used as a boundary condition for MHD equations. We derive the necessary formulas and discuss the validity of the approximations necessarily involved. It is concluded that the electromagnetic ionosphere-magnetosphere coupling scheme is a serious candidate for future global MHD simulators, although a few problem areas still remain. At minimum, it should be investigated further to discover whether there are any differences in the simulation using the electrostatic or the electromagnetic ionospheric coupling.     

二维频率测深边界单元法正演计算

在二维层状介质中含有横向非均匀体的地电断面情况下，对电偶源的偶极长度作了延长，并选取了适当的基本解及无穷远边界条件，因而将相应的含源谐变电磁场的边值问题转化为较简单的边界积分方程．用边界单元法求出了相应的电磁场分量，进而计算阻抗视电阻率，并对这一算法作了相应的检验．     

二维频率测深边界单元法正演计算

在二维层状介质中含有横向非均匀体的地电断面情况下,对电偶源的偶极长度作了延长,并选取了适当的基本解及无穷远边界条件,因而将相应的含源谐变电磁场的边值问题转化为较简单的边界积分方程．用边界单元法求出了相应的电磁场分量,进而计算阻抗视电阻率,并对这一算法作了相应的检验．     

Range finding of Alfvén oscillations and direction finding of ion-cyclotron waves by using the ground-based ULF finder

A new approach to the problem of direction and distance finding of magnetospheric ULF oscillations is described. It is based on additional information about the structure of geoelectromagnetic field at the Earths surface which is contained in the known relations of the theory of magnetovariation and magnetotelluric sounding. This allows us to widen the range of diagnostic tools by using observations of Alfvén oscillations in the PC 3–5 frequency band and the ion-cyclotron waves in the PC 1 frequency band. Preliminary results of the remote sensing of the magnetosphere at low-latitudes using the MHD ranger technique are presented. The prospects for remote sensing of the plasmapause position are discussed.     

A three-dimensional,iterative mapping procedure for the implementation of an ionosphere-magnetosphere anisotropic Ohm’s law boundary condition in global magnetohydrodynamic simulations

The mathematical formulation of an iterative procedure for the numerical implementation of an ionosphere-magnetosphere (IM) anisotropic Ohm’s law boundary condition is presented. The procedure may be used in global magnetohydrodynamic (MHD) simulations of the magnetosphere. The basic form of the boundary condition is well known, but a well-defined, simple, explicit method for implementing it in an MHD code has not been presented previously. The boundary condition relates the ionospheric electric field to the magnetic field-aligned current density driven through the ionosphere by the magnetospheric convection electric field, which is orthogonal to the magnetic field B, and maps down into the ionosphere along equipotential magnetic field lines. The source of this electric field is the flow of the solar wind orthogonal to B. The electric field and current density in the ionosphere are connected through an anisotropic conductivity tensor which involves the Hall, Pedersen, and parallel conductivities. Only the height-integrated Hall and Pedersen conductivities (conductances) appear in the final form of the boundary condition, and are assumed to be known functions of position on the spherical surface R=R₁ representing the boundary between the ionosphere and magnetosphere. The implementation presented consists of an iterative mapping of the electrostatic potential , the gradient of which gives the electric field, and the field-aligned current density between the IM boundary at R=R₁ and the inner boundary of an MHD code which is taken to be at R₂>R₁. Given the field-aligned current density on R=R₂, as computed by the MHD simulation, it is mapped down to R=R₁ where it is used to compute by solving the equation that is the IM Ohm’s law boundary condition. Then is mapped out to R=R₂, where it is used to update the electric field and the component of velocity perpendicular to B. The updated electric field and perpendicular velocity serve as new boundary conditions for the MHD simulation which is then used to compute a new field-aligned current density. This process is iterated at each time step. The required Hall and Pedersen conductances may be determined by any method of choice, and may be specified anew at each time step. In this sense the coupling between the ionosphere and magnetosphere may be taken into account in a self-consistent manner.     

二维水平电偶极变频测深阻抗视电阻率的有限元正演计算

在二维地电断面情况下,电偶源变频测深阻抗视电阻率的有限元计算,存在着两个困难:一个是对源的处理;另一个是边界条件的确定。本文提出了解决这两个问题的方法,构成了含源波动方程的边值问题,用有限元法求出了相应的电磁场分量,从而计算出二维地电断面的阻抗视电阻率。对各种地电断面计算的结果表明,计算方法是正确的,可对实际地电断面进行有限元模拟,求得其电磁响应。     

二维水平电偶极变频测深阻抗视电阻率的有限元正演计算

在二维地电断面情况下,电偶源变频测深阻抗视电阻率的有限元计算,存在着两个困难:一个是对源的处理;另一个是边界条件的确定。本文提出了解决这两个问题的方法,构成了含源波动方程的边值问题,用有限元法求出了相应的电磁场分量,从而计算出二维地电断面的阻抗视电阻率。对各种地电断面计算的结果表明,计算方法是正确的,可对实际地电断面进行有限元模拟,求得其电磁响应。     

C-RESPONSE OF GEOMAGNETIC DEPTH SOUNDING ON A 1D THIN SHELL MODEL

This paper tries to formulate the C-response of geomagnetic depth sounding(GDS)on an Earth model with finite electrical conductivity. The computation is performed in a spherical coordinate system. The Earth is divided into a series of thin spherical shells. The source is approximated by a single spherical harmonic P₁⁰ due to the spatial structure of electrical currents in the magnetosphere. The whole solution space is separated into inner and external parts by the Earth surface. Omitting displacement current, the magnetic field in the external space obeys Laplacian equation, while in the inner part, due to the finite conductivity, the electromagnetic fields obey Helmholtz equation. To connect the magnetic fields in the inner and external space, the continuity condition of magnetic fields is used on the Earth surface. The external magnetic fields are expressed by the inner and external source coefficients, from which a new parameter called C-response is computed from the inner coefficient divided by the external coefficient, thus normalizing the actual source strength. The inner magnetic fields in each layer can be recursively derived by the continuity boundary condition of both normal and tangential components of the magnetic field from the initial boundary condition at core-mantle-boundary. The consistency of our C-responses with that from a typical 1-D global model validates the accuracy of the proposed algorithm. Numerical results also show that the C-response estimated from the geomagnetic transfer function method will deviate exceeding 5%from the actual response at longer periods than about 10⁶s, which means that ignoring the curvature of the Earth at extreme long periods will make inversion result unreliable. Therefore, an accurate C-response should be computed in order to lay a solid foundation for reliable inversion.     

On the latitudinal structure of the magnetohydrodynamic Alfvén resonances

According to the data of the IMAGE network of magnetometers the latitudinal profile of the amplitude of the Pc5 geomagnetic pulsations is constructed, which are excited in the Earth’s magnetosphere in the form of the resonance Alfvén magnetohydrodynamic pulsations. The approaches to the solution of two problems are studied on a specific example. The first concerns the anharmonicity of Alfvén’s resonances. The displacement of the peak of the resonance curve towards to the north with the reduction of the amplitude of the pulsations is discovered. Based on the results of measurements, the nonlinear distortion coefficient of the latitudinal profile is determined. The second problem is connected with the magnetotelluric sounding. Information about the resonance structure of the Alfvén pulsations is useful for magnetotelluric sounding. This information gives the possibility of evaluating the accuracy of the sounding with the application of the local impedance relationship and of introducing corrections if necessary.     

Asthenospheric parameters of dipping plate regions by magnetotelluric investigations

The multifrequency resolving capability of the electromagnetic surface impedance parameter, employed in magnetotelluric investigations, has been examined for an upper mantle model incorporating (1) a deep-seated lithosphere-asthenosphere boundary and (2) preferred orientations of olivine crystals in the lithosphere, usually associated with the subducting plate boundary zones. Numerical results display the quantitative errors in the resolution of various anisotropic and dipping plate conditions. It is found that (1) conductivity anisotropy, particularly with higher dips, causes a significant dispersion in the impedance values and higher resolving power, and (2) variations in the geometrical/physical parameters are reflected predominantly in the phase component of the surface impedance. The study has relevance to the understanding of the electrical nature of materials, its relationship with physical properties and associated geothermal and seismic activities in the dipping plate regions.     

Direct and inverse problems in electromagnetic sounding of three-dimensional heterogeneous medium

The methods for solving three-dimensional (3D) direct and inverse problems of electromagnetic sounding are considered. It is shown that the method of integral equations is an efficient instrument for mathematical modeling of electromagnetic fields in 3D heterogeneous media. Adaptation of the integral equation technique to the solution of inverse problems is demonstrated.     

A new approach to gradient geomagnetic sounding

A spherical model of the Earth including a heterogeneous upper mantle and excited by the magnetic field of a magnetospheric ring current is constructed. The obtained synthetic data are used for testing a new approach to gradient geomagnetic sounding ensuring the immunity of the sought impedance to distortions caused by lateral heterogeneity of the Earth. It is shown that this approach significantly increases the informativeness of deep electromagnetic sounding.     

Transformation and absorption of magnetosonic waves generated by solar wind in the magnetosphere

Resonant transformation of fast magnetosonic (FMS) wave flux into Alfven and slow magnetosonic (SMS) oscillations is investigated in the one-dimensionally inhomogeneous magnetosphere. Spatial distribution of energy absorption rate of FMS oscillations penetrating into the magnetosphere from the solar wind is studied. The FMS wave energy absorption rate caused by magnetosonic resonance excitation is shown to be several orders of magnitude greater than that caused by Alfven resonance excitation at the same surface. It is connected with the spectrum of incident FMS waves. The Kolmogorov spectrum is used in numerical calculations. Magnitude of the Fourier harmonics exciting resonant Alfven oscillations is much smaller than that of the harmonics driving lower-frequency magnetosonic resonance. It is shown that resonant transformation of FMS waves into SMS oscillations can be an effective mechanism of energy transfer from the solar wind to the magnetosphere.     

A primitive pseudo wave equation formulation for solving the harmonic shallow water equations

A finite element method formulation for solving the harmonic shallow water equations in their primitive or unmodified form is developed and analysed. The scheme, referred to as the Primitive Pseudo Wave Equation Formulation (PPWE), involves developing a weak weighted residual form of the continuity equation and furthermore forming a pseudo wave equation by substituting the discretized form of the momentum equation into the discretized form of the continuity equation. The final set of equations to be solved, the pseudo wave equation and the primitive momentum equations, deceptively resemble the discretized equations of the wave equation formulation of Lynch and Gray. Despite this resemblance, Fourier analysis indicates that the PPWE scheme is still fundamentally primitive.However, application of the PPWE scheme to a set of stringent test problems results in very good solutions with well controlled nodal oscillations. It is shown that this low degree of spurious oscillations is due to the treatment of the boundary conditions such that elevation is taken as an essential condition and normal flux is taken as a natural condition. This particular boundary condition treatment is suggested by the formation of the pseudo wave equation. Furthermore, even though the equation re-arrangement does not in itself effect the solutions, it does make the scheme much more efficient.     

Penetration to the Earth’s surface of standing Alfvén waves excited by external currents in the ionosphere

The problem of boundary conditions for monochromatic Alfvén waves, excited in the magnetosphere by external currents in the ionospheric E-layer, is solved analytically. Waves with large azimuthal wave numbers m≫1 are considered. In our calculations, we used a model for the horizontally homogeneous ionosphere with an arbitrary inclination of geomagnetic field lines and a realistic height disribution of Alfvén velocity and conductivity tensor components. A relationship between such Alfvén waves on the upper ionospheric boundary with electromagnetic oscillations on the ground was detected, and the spatial structure of these oscillations determined.     

The phenomenon of synchronism in the magnetosphere-technosphere-lithosphere dynamical system

Synchronism in geophysical events became the focus of the research in the second half of the last century when the study of this subject was almost simultaneously launched in the former Soviet Union and the United States. Interest in this issue has recently risen after a 20-year hiatus. The impetus was provided by the successful application of the synchronous detection technique to analyzing vast volumes of digital data on the electromagnetic waves in the magnetosphere and on the earthquakes. These studies revealed signs of the strictly periodic synchronous influence of the technosphere on the regime of electromagnetic oscillations in cosmic plasma and on seismic activity. The phenomenon of synchronism between the electromagnetic and seismic events manifests itself in the form of the so-called hour-mark effect and the weekend effect. The hourmark effect shows itself in the 24th, 48th, and 96th harmonics, and the weekend effect, in the 7th subharmonic of the circadian rhythm. The both effects indicate that the technosphere has a nontrivial impact on the magnetosphere and lithosphere. The present review aims to introduce the morphology of the phenomenon and to focus the attention of researchers on the physical interpretation of the effects of synchronism, which is a challenging problem. Both the fundamental and practical value of the problem is analyzed. In particular, it is hypothesized that the study of the anthropogenic modulation of the natural wave processes will promote the development of energy saving technologies.     

Contribution of global Pc5 oscillations to magnetic disturbance during geomagnetic storms

The contribution of global magnetospheric oscillations to magnetic disturbance during magnetospheric storms is studied. The bases of magnetic data from the INTERMAGNET global network in combination with the interplanetary and intramagnetospheric measurements of the magnetic field and plasma and the sets of the Kp, Dst, and AE indices are used for this purpose. The most favorable conditions in the solar wind and magnetosphere for generation of global Pc5 have been revealed. The contribution of these oscillations to the variations in the magnetic disturbance level, characterized by the AE index, has been estimated. The findings confirm that magnetospheric MHD oscillations participate in the processes of energy income from the solar wind and energy dissipation in the magnetosphere.     

中国及邻区大地水准面异常的场源深度探讨

利用中国及邻区地形、地震层析成像、沉积层底面、Moho面及岩石层底面资料,正演计算出中国及邻区岩石圈大地水准面异常;再从全阶大地水准面异常中扣除正演模拟得到的岩石圈大地水准面异常与不同阶次波段的大地水准面进行比较,寻求表示中国及邻区地幔物质不均匀的大地水准面异常的最佳阶次为2-60阶. 结果表明,对应于岩石圈的大地水准面异常的重力位球谐函数阶数为61-20阶;下地幔重力位球谐函数阶数为2-6阶;而-60阶重力位球谐函数则表示中国及邻近区域上地幔大地水准面异常.     

中国及邻区大地水准面异常的场源深度探讨

利用中国及邻区地形、地震层析成像、沉积层底面、Moho面及岩石层底面资料,正演计算出中国及邻区岩石圈大地水准面异常;再从全阶大地水准面异常中扣除正演模拟得到的岩石圈大地水准面异常与不同阶次波段的大地水准面进行比较,寻求表示中国及邻区地幔物质不均匀的大地水准面异常的最佳阶次为2-60阶. 结果表明,对应于岩石圈的大地水准面异常的重力位球谐函数阶数为61-20阶;下地幔重力位球谐函数阶数为2-6阶;而-60阶重力位球谐函数则表示中国及邻近区域上地幔大地水准面异常.