Effect of surface stress on magneto-elastic surface waves in finitely conducting media

This paper deals with the investigation of the effect of surface stress and conductivity on the propagation of surface wave in isotropic, homogeneous, elastic media under the action of a primary magnetic field. Formulation of the general surface wave propagation problem has been made, and the corresponding frequency equation has been derived. Frequency equations for Rayleigh wave, surface shear wave and Stoneley wave have been deduced from that of general surface wave as special cases. The effects of surface stress and magnetic field on the wave velocities and attenuation factors of Rayleigh wave and surface shear wave are shown by numerical calculations and graphs. Some important wave velocity equations, as obtained by other authors, have been deduced as special cases from the wave velocity equation for Stoneley wave. It is found that the combined effect of surface stress and magnetic field modulates the wave velocity ratios and attenuation factors of Rayleigh wave and surface shear wave to a considerable extent.     

Magneto-acoustic-gravity waves in the horizontal magnetic field

Abstract

In this paper we consider the propagation of magneto-acoustic-gravity waves in a compressible, conducting isothermal atmosphere permeated by a uniform horizontal magnetic field. The singular levels, arising in a horizontal magnetic field, are considered in their most general form. Exact analytical solutions for a number of particular cases of wave propagation are obtained. The wave transformation is analyzed for all these cases using the solutions obtained.

Based on the theory of wave propagation across a magnetic field, low-frequency wave trapping in a chromospheric resonator is explained, and some properties of running penumbral waves are discussed.     

Magneto-elastic waves and disturbances in initially stressed conducting media

Summary The object of the present paper is to investigate magneto-elastic waves and disturbances in initially stressed conducting media. Firstly, the theory of magneto-elastic surface waves in a conducting medium under an initial uniaxial tension has been deduced and then it has been employed to investigate the particular cases of surface waves such as Rayleigh, Love and Stoneley waves. Secondly, propagation of waves in an elastic layer has been considered using the fundamental equations of motion for magneto-elastic waves in conductors under an initial uniaxial tension or compression. This is followed by the case of plane Lamb's problem in a magneto-elastic semi-space under the same initial tension. The final results obtained in the above cases are in agreement with the corresponding classical problems when the initial tension is zero and the magnetic field is absent.     

Magneto-elastic plane waves in a cosserat medium

Summary The propagation of plane waves in an electrically conducting cosserat medium placed in a magnetic field is investigated. The constitutive equations of cosserat elasticity developed recently byParia have been combined with the field equations of electromagnetism to obtain the basic equations for the problem. The results obtained in this investigation are in agreement with the corresponding results on magneto-elastic plane waves in Hookean solids when the cosserat constants are supposed to be absent.     

Magneto-elastic shear waves in a conducting,infinite plate in vacuum

Summary The influence of an external magnetic field on the propagation of purely transverse waves polarized parallel to the plane faces in a homogeneous, initially unstressed, infinitely conducting, elastic flat plate extending to infinity has been investigated. We have found that such waves can be propagated only if the field is normal to the direction of polarization.The effects are of three fold depending on the inclination of the field to the direction of propagation. When the field is normal, it is to decrease the range of modes in which a disturbance of given frequency can be propagated; when parallel, it is to increase the velocity of each mode without decreasing the range of modes of propagation. In both these cases, the different modes can be classified into symmetric and anti-symmetric modes. In the general case, not only the phase velocity and the range of modes are affected over those of purely elastic case but the symmetric and anti-symmetric types of motion are coupled in every mode.     

3D modelling of VLF radio wave propagation in terrestrial waveguide allowing for localized large-scale ionosphere perturbation

The problem of radio wave propagation allowing for 3D localized lower ionosphere irregularity appears in accordance with the necessity of the theoretical interpretation of VLF remote sensing data. The various processes in the Earth's crust and in space (earthquakes, magnetic storms, sporadic E-layers, lightning induced electron precipitations, rocket launches, artificial ionosphere heating, nuclear explosions, etc.) may cause different power and size ionospheric disturbances. This paper presents a further development of the numerical–analytical method for 3D problem solving. We consider a vector problem of VLF vertical electric dipole field in a plane Earth-ionosphere waveguide with a localized anisotropic ionosphere irregularity. The possibility of lowering (elevating) of the local region of the upper waveguide wall is taken into account. The field components on the boundary surfaces obey the Leontovich impedance conditions. The problem is reduced to a system of 2D integral equations taking into account the depolarization of the field scattered by the irregularity. Using asymptotic (kr⪢1) integration along the direction perpendicular to the propagation path, we transform this system to a system of 1D integral equations. The system is solved in the diagonal approximation, combining direct inversion of the Volterra integral operator and the subsequent iterations. The proposed method is useful for study of both small-scale and large-scale irregularities. We obtained estimates of the TE field components that originate entirely from field scattering by a 3D irregularity.     

Magnetic fields of 3-D anisotropic bodies: Theory and practice of calculations

The general theory of the distribution of the volume and surface magnetic mass within 3-D anisotropic bodies and solving the forward problem is given in this paper. An algorithm for calculating the magnetic fields of monoclines of complex shape and folded structures with uniform anisotropy is constructed. The algorithm is based on the regularities in the relationship between the magnetic susceptibility of anisotropy, tectonic structure, and the anomalous magnetic field established experimentally by Zavoisky. These regularities not only simplify the solution of the problem, but significantly facilitate the preparation of original field data necessary for solving it. The latter circumstance is of especial importance. The algorithm is designed for wide practical application in the construction of 3-D magnetic models of local and regional geological structures.We draw attention to the fact that the use of a curvilinear coordinate system is reasonable in cases when the distribution of the magnetic mass density in anisotropic geological formations is studied.The features of the relationship between the intensity and induction of a magnetic field in different unit systems are pointed out in their application to magnetology problems.     

磁尾等离子体片中周期性高速流相伴随磁场超低频波

本文利用Cluster卫星2004年11月8日的观测数据,分析了磁尾等离子体片中与地向周期性高速离子流相伴随的ULF波.结果显示周期性高速流的速度波动与磁场和温度中的ULF波同时出现、同时增强、同时消失,而且波动的频率都集中在60~70 mHz.这说明磁场和温度ULF波与周期性高速流密切相关,周期性高速流是ULF波产生的来源.高速流波动的相位与磁场波动的相位大致反相关,与热离子温度波动的相位正相关,同时磁场波动与热离子温度波动呈相位反相关的特性.最小方差法分析的结果显示虽然波传播方向有地向分量,但其主要传播方向是向等离子体片中心传播,并与周期性高速流速度方向垂直.以上观测说明是高速流的周期性变化产生了磁场在Pi1频率范围内的ULF波.     

Shear waves in elastic medium with void pores welded between vertically inhomogeneous and anisotropic magnetoelastic semi-infinite media

The paper intends to study the propagation of horizontally polarized shear waves in an elastic medium with void pores constrained between a vertically inhomogeneous and an anisotropic magnetoelastic semi-infinite media. Elasto-dynamical equations of elastic medium with void pores and magnetoelastic solid have been employed to investigate the shear wave propagation in the proposed three-layered earth model. Method of separation of variables has been incorporated to deduce the dispersion relation. All possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. The role of inhomogeneity parameter, thickness of layer, angle with which the wave crosses the magnetic field and anisotropic magnetoelastic coupling parameter for three different materials has been elucidated and represented by graphs using MATHEMATICA.     

Inertial effects in the Earth’s crust and magnetosphere

A review of studies devoted to the problem of exciting magnetic signals in the crust associated with the formation of the major rupture in an earthquake source and with the propagation of seismic waves was given in [Sgrigna et al., 2004]. However, this review contains incorrect citations from original papers and several erroneous statements concerning inertial and inductive mechanisms of conversion of the energy of rock motion into magnetic field energy. These mistakes are analyzed in the present paper. The formal and physical similarity between seismomagnetic waves in the crust and Alfvén waves in the magnetosphere is used in the analysis. A comparative analysis of the inertial and inductive mechanisms of seismomagnetic field generation is performed. The Cherenkov criterion of Alfvén wave generation due to the ionospheric effect of acoustic waves from earthquakes and explosions is derived. Attention is also given to nonlinear phenomena (nonlinearity of a mechanomagnetic conversion in the crust and anharmonicity and self-focusing of Alfvén waves in the magnetosphere).     

Ground penetrating radar inversion in 1-D: an approach for the estimation of electrical conductivity, dielectric permittivity and magnetic permeability

This paper presents a method for inverting ground penetrating radargrams in terms of one-dimensional profiles. We resort to a special type of linearization of the damped E-field wave equation to solve the inverse problem. The numerical algorithm for the inversion is iterative and requires the solution of several forward problems, which we evaluate using the matrix propagation approach. Analytical expressions for the derivatives with respect to physical properties are obtained using the self-adjoint Green's function method. We consider three physical properties of materials; namely dielectrical permittivity, magnetic permeability and electrical conductivity. The inverse problem is solved minimizing the quadratic norm of the residuals using quadratic programming optimization. In the iterative process to speed up convergence we use the Levenberg–Mardquardt method. The special type of linearization is based on an integral equation that involves derivatives of the electric field with respect to magnetic permeability, electrical conductivity and dielectric permittivity; this equation is the result of analyzing the implication of the scaling properties of the electromagnetic field. The ground is modeled using thin horizontal layers to approximate general variations of the physical properties. We show that standard synthetic radargrams due to dielectric permittivity contrasts can be matched using electrical conductivity or magnetic permeability variations. The results indicate that it is impossible to differentiate one property from the other using GPR data.     

Magnetic field disturbance in magnetoactive plasma with a localized electrostatic field

Charged particle motion in magnetoactive plasma with an axially symmetric electrostatic field has been studied. It has been indicated that a difference between drift velocities of electrons and ions leads to a magnetic field disturbance. The equations for stationary magnetic field disturbances stretched along the magnetic field, which can be magnetic ducts for propagation of whistlers, have been obtained. The possibility of formation of such ducts by electrostatic fields from thunderstorm sources, penetrating into the ionosphere, has been estimated.     

The effect of the electron sound speed on wave propagation in the ionospheric plasma

In this study, the effect of the electron sound speed on the extraordinary wave propagation is calculated without an approximation for either collisional or collisionless cases in the ionospheric plasma by using the real geometry of the Earth’s magnetic field for the Northern Hemisphere. It is observed that there is no remarkable effect on the propagation of the extraordinary wave, especially at reflection altitudes. But it is also observed that the magnitudes of k ² (the square of the wave number) have changed every season, and the phase velocity of wave in warm ionospheric plasma has increased.     

日面方位磁场扰动和行星际磁场螺旋结构

文采用球坐标下2.5维理想MHD模型,对日球子午面内方位磁场扰动的传播进行数值模拟,重点分析它对行星际磁场螺旋角的影响. 本文认为,观测到的行星际磁场螺旋角大于Parker模型的预言值,是太阳表面不断向行星际发出同向方位磁场扰动的结果;太阳较差自转在太阳内部产生的方位磁场为这类扰动提供了源头. 模拟结果表明,采用持续时间等于周期的十分之一、扰动幅度为103nT量级的正向方位磁场扰动,就可使1 AU处行星际磁场的螺旋角增加2°左右,与有关观测结果相符. 模拟结果还表明,上述方位磁场扰动对日球子午面内的太阳风特性和磁场位形的影响基本上可以忽略.     

A note on disturbances in a certain type of visco-elastic solid deformed by a magnetic field

Summary The present note is an attempt to study the propagation of disturbances in a semiinfinite visco-elastic rod which is of three-parameter type, and which is subjected to a static magnetic field.     

Alfven波在低纬电离层中的传播研究

Alfven波在低纬地区电离层的传播有其特殊性,一方面,低纬地区同样存在Alfven速度梯度的巨大变化,导致电离层Alfven谐振器(Ionospheric Alfven resonator, IAR)的形成;另一方面,由于在低纬地区磁倾角很小,所以剪切Alfven波在传播的过程中纬度方向跨度很大,不同纬度电离层参数将共同对其产生影响;并且,由于电离层水平分层,故磁力线与电离层不正交.本文选取双流体力学模型,在忽略场向电场的条件下,利用非正交坐标系,结合IRI07模型与MSISE00模型模拟低纬地区Alfven波的传播,得到其反射及耦合特性.结果表明,低纬地区同样存在电离层Alfven谐振现象,由耦合产生的压缩模有向磁赤道方向传播的趋势,夜间电离层状态相对于白天更适合IAR的形成,谐振频率沿磁力线L值增大单调递增.     

Interaction between the electromagnetic and acoustic fields in the marine environment

The possibility of generation of additional acoustic harmonics in the geomagnetic field after the propagation of an acoustic wave in the conducting medium through the region with a variable magnetic field has been considered. Two possible procedures of such a generation have been analyzed: the parametric procedure and the dynamic procedure related to ponderomotive forces. The expressions have been obtained for three acoustic harmonics generated by an oscillating magnetic field.     

A note on magnetic modelling with remanence

The general problem of magnetic modelling involves accounting for the effect of both remanent magnetization and the application of an external magnetic field. However, as far as the disturbing field of a magnetic body in a magnetic environment is concerned, there is an equivalence between the effects of these two causations that allows the remanence to be represented in terms of an equivalent primary magnetic H field. Moreover, due to the linearity of the magnetic field in terms of its causations, the general modelling problem involving an applied magnetic field in the presence of remanence can be simply and more efficiently dealt with in terms of an equivalent primary field acting in the absence of any remanent magnetization.     

瞬变电磁快速成像解释系统研究

为了提高瞬变电磁测深法对地探测的垂向分辨能力,文中研究了磁偶源瞬变电磁法快速成像的方法.详细讨论了电磁波与地震波在介质中的传播规律,分析了磁偶源瞬变电磁场在远区的响应特性.根据磁偶源瞬变电磁场与反射地震波的传播规律的相似性,提出了TEM资料拟地震快速成像解释的思路.理论模型正、反演计算结果表明方法理论是可行的,野外实测资料处理结果进一步说明了该方法是有效的.     

A New Algorithm for Depth Determination from Total Magnetic Anomalies due to Spheres

We have developed an automatic method to determine the depth of a buried sphere from numerical second horizontal derivative anomalies obtained from total field magnetic data. The method is based on using a relationship between the depth and a combination of observations at symmetric points with respect to the coordinate of the projection of the center of the source in the plane of the measurement points with a free parameter (graticule spacing). The problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of f(z) = 0. Procedures are also formulated to determine the magnetic moment and the effective angle of magnetization. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal. In all cases, the depth solutions are in good agreement with the actual ones.