Electric Dipole Source Research Articles

Controlled electromagnetic sources for measuring electrical conductivity beneath the oceans: 1. Forward problem and model study

Exact closed‐form expressions for the electromagnetic induction fields produced by vertical and horizontal current sources in the conducting ocean overlying a one‐dimensional earth are derived from the Maxwell equations. Numerical methods for the evaluation of the solutions are given, including correction for the finite size of real sources. Simple models of the electrical conductivity structure of the ocean crust and lithosphere are deduced from geologic, petrologic, and laboratory data, and their electromagnetic response is modeled. Horizontal electric dipole sources produce much larger field amplitudes than their vertical counterparts for a given frequency and range, and the horizontal electric field offers superior received signal performance. Reflections of electromagnetic waves from the sea surface and thermocline must be considered for low enough frequencies or long ranges. Estimates of the ambient noise level from natural electromagnetic sources in the frequency range 0.01–10 Hz are presented. The ability of controlled sources to determine features of the conductivity of the ocean crust and upper mantle, especially low conductivity zones, is demonstrated. If the mantle conductivity is low enough, horizontal ranges of 50 km and conductivity estimates to over 20 km depth can be achieved.

A triaxial coil receiver system for the study of subsurface electromagnetic propagation

A triaxial set of underwater receiving coils was developed and tested. The receiving system was used jointly with an underwater, calibrated, horizontal, electric dipole source in studies of extremely low-frequency electromagnetic propagation. This paper discusses the electromechanical design of the receiver and tethering system and addresses system sensitivity and noise levels. The receiving system was used successfully in a series of measurements, in spite of serious motion noise contamination. A stationary system sensitivity of 5 \times 10^{-4} \gamma/\sqrt{Hz} was achieved.

Surface potentials of stratified spheroidal volume conductors excited by an electric dipole source

Abstract An exact solution for the surface potentials produced by a dipole source surrounded by a stratified prolate (or oblate) volume conductor is given. A transmission matrix approach is used which permits the surface potentials to be calculated using a simple iterative method. The computer implementation of the method is discussed

Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles full-wave solutions

Explicit expressions are presented for the radiation fields scattered by rough surfaces. Both electric and magnetic dipole sources are assumed, thus excitations of both vertically and horizontally polarized waves are considered. The solutions are based on a full-wave approach which employs complete field expansions and exact boundary conditions at the irregular boundary. The scattering and depolarization coefficients axe derived for arbitrary incident and scatter angles. When the observation point is at the source these scattering coefficients are related to the backscatter cross section per unit area. Solutions based on the approximate impedance boundary condition are also given, and the suitability of these approximations are examined. The solutions are presented in a form that is suitable for use by engineers who may not be familiar with the analytical techniques and they may be readily compared with earlier solutions to the problem. The full-wave solutions are shown to satisfy the reciprocity relationships in electromagnetic theory, and they can be applied directly to problems of scattering and depolarization by periodic and random rough surfaces.

Coupling between a dipole antenna and an infinite cable over an ideal ground plane

A formulation is given for the fields radiated by an electric or magnetic dipole of arbitrary orientation in the presence of a cable suspended above a flat and perfectly conducting ground. The cable can be a solid conductor, a leaky coaxial cable, a CATV cable, or a surface‐wave transmission line. Illustrative numerical results for both the far‐field radiation pattern and excitation of the modal currents on the cable are given for the case of a vertical electric dipole source. Among other things, we find that the resultant radiation or far fields are not markedly influenced by the presence of the cable unless the dipole source is very near the cable. However, there is a significant cross‐polarized component produced by the presence of cable that could have important consequences in producing bearing errors in low frequency beacon navigation systems.

Transient ULF Electric and magnetic fields of an electrical current source in a medium with continuously varying conductivity

Recent analytical studies of ULF electromagnetic fields in the atmosphere are reviewed. These fields have their origin in the discharge of thunderclouds. The problem for a vertical electrical dipole source played in an atmosphere where the conductivity increases exponentially with altitude is described. The analytical expressions for the electric and magnetic field, which vary in time and space, are approximately obtained by a vector potential. It is seen that the amplitudes of the pulse decrease with both increases of the horizontal distance and the gradient of the conductivity. However, the shapes of the pulse are almost constant.

NUMERICAL SOLUTIONS OF THE RESPONSE OF A TWO‐DIMENSIONAL EARTH TO AN OSCILLATING MAGNETIC DIPOLE SOURCE

A finite difference formulation is developed for computing the frequency domain electromagnetic fields due to a point source in the presence of two‐dimensional conductivity structures. Computing costs are minimized by reducing the full three‐dimensional problem to a series of two‐dimensional problems. This is accomplished by Fourier transforming the problem into the x-wavenumber [Formula: see text] domain; here the x-direction is parallel to the structural strike. In the [Formula: see text] domain, two coupled partial differential equations for [Formula: see text] and [Formula: see text] are obtained. These equations resemble those of two coupled transmission sheets. For a requisite number of [Formula: see text] values these equations are solved by the finite difference method on a rectangular grid on the y-z plane. Application of the inverse Fourier transform to the solutions thus obtained gives the electric and magnetic fields in the space domain. The formulation is general; complex two‐dimensional structures containing either magnetic or electric dipole sources can be modeled. A quantitative test of accuracy is presented which compares the finite difference results to analytic results for a magnetic dipole on a homogeneous half‐space. In addition, the computed results for a two‐dimensional model are qualitatively compared to published results for a three‐dimensional analog model. Synthetic field data for surveys over several different bodies of anomalous conductivity are presented. Two of these demonstrate the nonuniqueness of single frequency data interpretation. Results also show that the characteristic form of the response given by the anomalous body can be heavily dependent upon the structure of the host medium. This is especially true for horizontal magnetic dipole source surveys.

The polarization losses of offset paraboloid antennas

In this paper the electric field in the aperture of offset front-fed paraboloid antennas and open Cassegrainian antennas, excited by an electric dipole or Huygens source in the focus, is compared with the fields of front-fed circularly symmetrical paraboloid reflector antennas and classical Cassegrainian antennas. The aperture field forms the basis of expressions to calculate the polarization efficiency of all four types of antenna. Computed results are given, showing that offset antennas can compete with front-fed paraboloids if they are excited by an electric dipole; the classical Cassegrainian antenna, however, shows better results. If offset antennas are excited by a Huygens source, the result is very unfavorable compared with the symmetrical antennas which show no cross polarization.

Dipole Antenna Radiation in a Compressible, Anisotropic Electron Plasma Overlying an Imperfectly Conducting Half‐Space—Lunar Applications: 1. Formulation of the Solution

The problem of the electromagnetic response of infinitesimal electric and magnetic dipole sources in a compressible, anisotropic electron plasma overlying a lossy dielectric half‐space is solved by integral transform and matrix techniques to assess antenna radiation in the lunar environment. In part 1, the solutions are formulated in terms of Fourier‐Bessel integrals operating on matrix quantities. In particular, the field solutions are shown to linear combinations of classical plane‐wave modes in a compressible, anisotropic plasma. The introduction of a lossy dielectric half‐space yields uncoupled TE and TM modes propagating into the dielectric plus three reflected plasma modes. The modal reflection coefficients represent reflections coupled to all plasma modes.

Numerical Computations of Terrestrial ELF Electromagnetic Wave Fields in the Frequency Domain

The zero‐order term of the residue series has been employed to calculate the variation of field strength with distance over the earth's surface in the frequency band 7.8 Hz to 1 kHz. Spherical symmetry is assumed for the earth and ionosphere. The ionosphere is taken to be isotropic, but radial inhomogeneity is allowed. A vertical electric dipole source and a realistic propagation‐constant model were assumed. The computations indicate the accuracy of the usual approximations to the residue series and enable the magnitude of the standing wave effects in the earth‐ionosphere cavity to be assessed.

Studies of VLF Radiation Patteras of a Dipole Immersed in a Slightly Lossy Magnetoplasma

Power patterns are presented for VLF radiation (500 Hz to 30 kHz) from arbitrarily oriented, point magnetic and electric dipole sources in a two‐component, slightly lossy magnetoplasma. The patterns show that energy tends to be transported primarily along the magnetic axis of a confinement cone for higher VLF frequencies but that the inclusion of ion motion destroys the confinement cone for extremely low frequencies.

Hydromagnetic radiation from electric and magnetic dipoles in the magnetosphere

This paper deals with the radiation characteristics of elementary electric and magnetic dipoles in a homogeneous, anisotropic, cold plasma of infinite extent with a uniform magnetostatic field. The cases treated include the electromagnetic sources taken parallel and perpendicular to the magnetostatic field. In all cases expressions for the field components are obtained which are valid at frequencies well below the ion cyclotron frequency. It is found that electric and magnetic dipole sources when oriented perpendicular to the magnetic field excite both ordinary and extraordinary modes. For the ordinary mode, the waves are guided in both directions within cones of small apex angle aligned with the static field. When the dipole sources are aligned with the magnetic field, it is found that the electric dipole excites only the ordinary mode leading to guided wave propagation, while the magnetic dipole excites only the extraordinary mode. In all cases the waves propagate at Alfvén speed. The radiation characteristics are isotropic for the extraordinary mode excited by the perpendicular electric dipole and are nearly isotropic for the aligned magnetic dipole. For other cases the radiated power is concentrated in opposite directions along the static field.

Distortion of an ELF pulse after propagation through an antipode

We consider propagation of the slow tail portion of atmospheric waveforms. Using an idealized model of the earth-ionosphere cavity, the transient fields are calculated for a pulse-excited electric dipole source. It is shown that the frequency-independent phase shift at the antipode will lead to a pronounced change in the observed shape of the atmospheric waveform.

Excitation of Waves in a Warm Plasma by a Current Source

The general expression for the electromagnetic field due to an arbitrary monochromatic current source in an unbounded, homogeneous, warm, collisionless plasma in the absence of a magnetostatic field is derived. A hydrodynamic description is used in which ion and electron motion is included. The general results are specialized to the case of an electric dipole source. It is found that the field is generally composed of three parts which, in the radiation region, correspond to the well-known transverse, longitudinal electron, and longitudinal ion waves. The power flow in the radiation region is shown to be largest along the axis of the dipole for low frequencies whereas the maximum occurs perpendicular to the dipole at high frequencies.

Radio waves in rock near overburden-rock interface

An account is given of a theoretical investigation of radio wave propagation in a rock medium situated below a highly conducting plane boundary overburden, due to a vertically polarized electric dipole source immersed in the rock near the boundary. Excluded from this discussion are propagation modes in the rock guided between plane boundaries on top and bottom. Just as with dipoles in air above a plane ground, the rock wave can be considered as the result of a "direct wave," a wave "reflected'' from the overburden and an "interface surface wave." Rock with complex phase constant <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k_{1}</tex> replaces air with real phase constant <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\beta_{0}</tex> . Of interest is the variation with depth below the boundary of the fields in the rock, analogous to "height gain" for fields in air. Of importance is the effect of the relative refractive index of overburden-to-rock. A sample calculation is given for a one-mile path assuming typical electrical constants for the rock and overburden media. At the VLF of interest, loss tangents in the media are large. These results may assist in determining whether or not a received signal is due predominantly to a rock propagated wave or to a possible "up-over-and-down" mode.

Propagation of the radiofrequency ground wave transient over a finitely conducting plane earth

The introduction of precision radio navigation systems employing pulse techniques and the ever increasing interest in spherics have stimulated considerable interest in the propagation of the ground wave transient over the surface of the earth. The theory of the propagation of a transient radio frequency ground wave over a finitely conducting plane earth is presented for the particular case of theNorton surface wave by a consideration of a wave, interrupted abruptly at one point in time (t=0), a wave interrupted abruptly at two points in time (t=0,T2) and a wave interrupted at one point in time followed by an exponential decay. The first case is illustrated by several numerical examples of a cosine current wave applied to a vertical electric dipole source. It is apparent that the method of the inverse Ľaplace transform for the particular cases considered yields some simple mathematical formulas.

PROPAGATION OF TRANSIENT ELECTROMAGNETIC WAVES IN A MEDIUM OF FINITE CONDUCTIVITY

Transient electric and magnetic fields have been calculated for ramp function and sawtooth current sources immersed in a semi‐conducting medium. An electric dipole source has been assumed. In the case of ramp function input, it is observed that the peaks of the overshoots in the θ‐component of the electric field decrease in magnitude with the increase in rise time of the input pulse. It has also been shown that the rise time of the current pulses has definite effect upon the rise time and amplitude of the electric fields and that the sawtooth exciting pulses having large values of rise time may be conveniently used to obtain measurable values of the electric and magnetic fields.

CXVIII. The propagation of a radio atmospheric—II

Summary In a previous paper (Budden 1951 a, referred to as Paper I), it was shown that the propagation of an atmospheric could be treated either in terms of the successive reflection of rays at the earth and the ionosphere, or by considering the space between the earth and the ionosphere as a wave-guide, and discussing the properties of the various wave-guide modes. An outline of the theory was given for the case when the top surface of the wave-guide was the boundary of a homogeneous ionized medium, and the earth's magnetic field was neglected. The present paper gives the full mathematical theory , and shows how the characteristics of the wave-guide modes may be determined in the most general case, provided that the reflecting properties of the earth and the ionosphere are known as functions of the angle of incidence which is, in general, complex. It is found that the wave-guide modes are of two types, which are described as ‘quasi-transverse magnetic’ and ‘quasi-transverse electric’. Allowance can be made for the curvature of the earth. A particular case is then discussed, in which the surface of the earth is assumed to be perfectly conducting, and the ionosphere is assumed to be a homogeneous ionized medium, with the steady magnetic field of the earth superimposed. The results of numerical calculations are given, for a few special cases, in the form of curves. These show (i) the attenuation in the various modes as a function of frequency, (ii) the polarization characteristics of the wave in typical modes, and (iii) the amplitudes of the waves which are excited in typical modes by a vertical electric dipole source.