共查询到20条相似文献，搜索用时 15 毫秒
1.
Peter Furness 《Geophysical Prospecting》1994,42(5):405-416
The superposition integral expressing the field due to a magnetic source body is relatively simple to evaluate in the case of a homogeneous magnetization. In practice this generally requires that any remnant component is uniform and the susceptibility of the body is sufficiently low to permit the assumption of a uniform induced magnetization. Under these conditions the anomalous magnetic field due to a polyhedral body can be represented in an intuitive and physically appealing manner. It is demonstrated that the components of the magnetic field H can be expressed as a simple combination of the potentials due to two elementary source distributions. These are, firstly, a uniform double layer (normally directed dipole moment density) located on the planar polygonal faces of the body and, secondly, a uniform line source located along its edges. In practice both of these potentials (and thus the required magnetic field components) are easily computed. The technique is applicable to polyhedra with arbitrarily shaped faces and the relevant expressions for the magnetic field components are suitable for numerical evaluation everywhere except along the edges of the body where they display a logarithmic singularity. 相似文献
2.
Milan Hvoždara 《Studia Geophysica et Geodaetica》1990,34(1):10-31
Summary Based on the generalized potential of a double layer, integral formulae have been derived for calculating the stationary approximation of the magnetotelluric field in a halfspace divided by a vertical boundary into two quarterspaces, one of which contains a three-dimensional perturbing body. The appropriate boundary integral equation and other surface integrals have been computed for a perturbing body in the shape of the three-dimensional prism located at the vertical boundary, or in contact with the said boundary. The exciting electrical field is assumed to be homogeneous and perpendicular to the vertical boundary. Isoline graphs of the electrical and magnetic fields on the surface of the halfspace have been plotted and their anomalies are discussed. 相似文献
3.
The forward computation of the gravitational and magnetic fields due to a 3D body with an arbitrary boundary and continually varying density or magnetization is an important problem in gravitational and magnetic prospecting. In order to solve the inverse problem for the arbitrary components of the gravitational and magnetic anomalies due to an arbitrary 3D body under complex conditions, including an uneven observation surface, the existence of background anomalies and very little or no a priori information, we used a spherical coordinate system to systematically investigate forward methods for such anomalies and developed a series of universal spherical harmonic expansions of gravitational and magnetic fields. For the case of a 3D body with an arbitrary boundary and continually varying magnetization, we have also given the surface integral expressions for the common spherical harmonic coefficients in the expansion of the magnetic field due to the body, and a very precise numerical integral algorithm to calculate them. Thus a simple and effective method of solving the forward problem for magnetic fields due to 3D bodies of this kind has been found, and in this way a foundation is laid for solving the inverse problem of these magnetic fields. In addition, by replacing the parameters and unit vectors in the spherical harmonic expansion of a magnetic field by gravitational parameters and a downward unit vector, we have also derived a forward method for the gravitational field (similar to that for the magnetic case) of a 3D body with an arbitrary boundary and continually varying density. 相似文献
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YUE-KUEN KWOK 《Geophysical Prospecting》1991,39(3):435-443
Using the conjugate complex variables formulation, closed-form formulae for the gravity gradient tensors of the gravitational potential due to a homogeneous polyhedral body composed of polygonal facets are derived. The treatise considers the cases of the observation point being inside the polyhedron, on the surface of a facet, or outside the polyhedron. 相似文献
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7.
We derive expressions for computing the gravitational field (potential and its radial derivative) generated by an arbitrary
homogeneous or laterally varying density contrast layer with a variable depth and thickness based on methods for a spherical
harmonic analysis and synthesis of gravity field. The newly derived expressions are utilised in the gravimetric forward modelling
of major known density structures within the Earth’s crust (excluding the ocean density contrast) beneath the geoid surface.
The gravitational field quantities due to the sediments and crust components density contrasts, shown in numerical examples,
are computed using the 2 × 2 arc-deg discrete data from the global crustal model CRUST2.0. These density contrasts are defined
relative to the adopted value of the reference crustal density of 2670 kgm−3. All computations are realised globally on a 1 × 1 arc-deg geographical grid at the Earth’s surface. The maxima of the gravitational
signal due to the sediments density contrast are mainly along continental shelf regions with the largest sedimentary deposits.
The corresponding maxima due to the consolidated crust components density contrast are over areas of the largest continental
crustal thickness with variable geological structure. 相似文献
8.
A versatile integral equation technique for magnetic modelling 总被引：1，自引：0，他引：1
Peter Furness 《Journal of Applied Geophysics》1999,41(4):737
A requirement currently exists in both mineral exploration and environmental or engineering geophysics for a technique to model the magnetic fields caused by bodies with large to extreme susceptibilities in which both induced and remanent magnetizations are significant. It is well known that modelling such magnetic fields is not amenable to any known approximation. It is a significantly difficult task that requires the solution of a magnetostatic boundary value problem. Analytical solutions to the problem are extremely useful for providing insight but generally of limited application in practical interpretation due to the geometrical complexity of real situations. Available numerical solutions include both volume and surface integral equation formulations. However neither of these are particularly efficient for the purpose. An alternative surface integral equation formulation is presented here which represents the required magnetic field in terms of a double layer over the surface of the body. The technique accommodates both remanent and induced magnetization and is generally applicable to any 3D body in a magnetic environment for which the Green's function is available. The present technique has significant advantages over other integral equation solutions in the geophysical literature. It is particularly economic in terms of the density of the surface discretization and consequently the computational effort. Moreover, it is extremely robust. It is found to yield accurate solutions for the type of thin bodies that cause numerical instability with other surface integral equation approaches. 相似文献
9.
均匀弹性半空间表面或内部震源产生的地震波场的解析解属于Lamb问题,采用Cagniard-deHoop方法,对与水平面呈任意夹角的表面线源,求解了其作用于弹性半空间时的拉普拉斯-傅里叶双积分变换解.以δ-脉冲函数为例,给出了任意方向作用力下波场的构成,并定量解出了P波、S波、首波和Rayleigh波等各波的位移表达式,分析了不同作用方向下各波位移的相对大小.建立数值模型并进行数值模拟,模拟结果验证了理论研究的正确性.研究成果为近地表地震波场的研究提供了理论依据. 相似文献
10.
We present the theory of electromagnetic induction in spherical cap current sheets of arbitrary angular size, with arbitrary axisymmetric integrated electrical conductivity variations and located at any radial position with respect to the surface of observation. The external time-varying magnetic field may be arbitrarily oriented with respect to the current layer cap and the induced fields are derived for vacuum boundary conditions appropriate to terrestrial induction and plasma confinement boundary conditions relevant to lunar induction in the solar wind or magnetosheath plasmas. Numerical evaluations show the induced magnetic field as a function of position over the current sheet cap, depth to the current layer, size of the cap, integrated electrical conductivity of the current sheet, and frequency of the fluctuating external field. The local vertical magnetic field component and the horizontal field component which is normal to the periphery of the cap exhibit peak inductive responses above the edge of the current sheet for external magnetic fields perpendicular to the axis of the cap. Thus, induced magnetic field fluctuations observed over the edge of a conductivity anomaly may exhibit a highly directional, or polarized behavior. This may provide an explanation for the asymmetric character of induced magnetic field fluctuations observed on the lunar surface. 相似文献
11.
讨论了地幔内部的粘滞度及施加在地表和CMB 的边界条件对地幔对流环型场的激发分析表明,当粘滞度侧向均匀时,环型场与极型场自然解耦,且环型场不影响重力位,当粘滞度侧向不均时,环型场与极型场耦合在一起.两者共同影响重力位.当引入板块运动速度时,边界条件非零,也能激发环型场;对侧向均匀粘滞度地幔,零边界条件不能激发环型场 相似文献
12.
PETER FURNESS 《Geophysical Prospecting》1993,41(6):779-790
Two methods for computing spontaneous mineralization potentials in the region external to the source body are reviewed. The first of these is a long-established technique in which the causation is assumed to be a distribution of simple current source on the boundary of the mineralization. The second is a more recent technique which assumes a surface distribution of current dipole moment (double layer) along the boundary of the source body. The former technique is a special case of a more general spontaneous potential (SP) model in which the source is a density of current dipole moment (current polarization) distributed throughout the mineralization. As far as the potentials in the region external to the source body are concerned this current polarization can be simply related to an equivalent double layer source function, i.e. the potential discontinuity produced over the boundary of the mineralization by an equivalent double layer model. This simple relationship suggests an integral equation technique for the exact numerical solution of boundary value problems appropriate to the polarization model for spontaneous mineralization potentials. The technique is applied to exploring the justification of interpreting mineralization self-potentials by the traditional approach. 相似文献
13.
Summary The paper presents comprehensive theory based on the boundary integral method for calculations of the electric potential,
electric field and corresponding magnetic field due to a pair of D.C. source electrodes near a vertical resistivity contact
in the halfspace, indlucing a 3-D disturbing body in the vicinity of the contact. Special attention is paid to the case when
the disturbing body touches the vertical contact. Results of numerical calculations are presented in the form of sounding
curves and a set of isoline graphs for potential, components of the electric and magnetic field (total and anomalous) on the
surface of the Earth. It is shown that the presence of the disturbing body at the contact is most pronounced in the electrical
characteristics. Anomalies in the magnetic field are small in comparison to the field due to the electric current in the electrode
cable and primary currents flowing from the electrodes. 相似文献
14.
Summary The potential of the electric field of a stationary current in a two-layered Earth is calculated by applying Green's formula in the case where a three-dimensional inhomogeneity of different conductivity is located in the basement of the layer. It is proved that the potential outside and inside the perturbing body can be calculated from the potential of an electric double-layer distributed on the surface of this body. An integral equation of the Fredholm type is derived for the surface density of the double-layer, together with some of its integral properties. A similar procedure can be applied to computing the magnetic anomalies of three-dimensional magnetized bodies, geothermal anomalies due to three-dimensional inhomogeneities of different heat conductivity, as well as to potential problems of theoretical electrical engineering. 相似文献
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16.
A numerical method is given for calculating resistivity and induced polarization anomalies produced by a surface polarization model. Surface polarization is generated when a purely electronic conductor is located in an electrolyte environment. The system that develops on the boundary between the conductor and the electrolyte is described macroscopically by a net surface charge distribution and an electric double layer. An integral equation is derived for the potential by assuming that the electronic conductor forms an equipotential system and that the polarization impedance across the boundary is linear. The integral equation is solved by means of the method of subsections. As an application some numerical modeling results are presented. The surface impedance values used in calculations are based on laboratory measurements that are briefly described. Implications of the results for scale modeling are discussed. 相似文献
17.
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. 相似文献
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19.
M. Ivan 《Geophysical Prospecting》1996,44(2):279-288
An expression which is optimum with respect to the simplicity of the numerical computations is obtained for the magnetic field of a polyhedron with constant magnetization. The high accuracy of the results is illustrated using a realistic numerical model. The existence of the magnetic field at points inside the source and on its boundary is discussed and related to real magnetic data modelling. 相似文献
20.
M. OKABE 《Geophysical Prospecting》1982,30(2):166-187
Complete analytical expressions are developed for the first and second derivatives of the Newtonian gravitational potential in arbitrary directions due to the homogeneous revolutional compartment with a polygonal vertical section by applying the Gaussian divergence theorem in the cylindrical coordinate system. Elementary solutions presented can easily be translated into magnetic anomalies caused by a uniformly magnetized body. The divergence approach in the polar coordinate system is also described, and gravity attractions in the radial direction are presented in closed form associated with a homogeneous cap compartment. The explicit solutions are tested against well-known formulae for a cylinder, cone, infinite plate, and sphere. 相似文献