Vertical Electric Dipole Research Articles

Remarks on the comments and reply on "The electromagnetic field of a vertical electric dipole over the Earth or sea"

The author discusses the comments by Yokoyama (see ibid., vol.43, no.5, p.541, 1995) and the reply by King and Sandler (see ibid vol.43, no.5, p.542, 1995) on the definition of the numerical distance and related matters in the Sommerfeld problem of a vertical electric dipole over a dissipative half-space. It appears that the two definitions are equivalent in the sense that the effective field quantities are essentially the same. But a more important point is that possible confusion has been generated on the relationship between K.A. Norton's [1937] original papers and the more recent writings on the subject.

航行用100kHz帯電波に及ぼす巨大架橋の影響について-II : 横方向橋材の効果

We have reported that the main towers of the huge suspension-bridge have been considered macroscopically as a couple of the vertical electric dipoles from analyzing the disturbances of the electric fields caused by Minami-Bisan Seto-Oohashi Bridge. In this paper, in order to study the effect of the reradiation from the structure of the bridge extending in the horizontal direction, the vertical electric field intensities of Decca Waves were measured near Akashi-Kaikyou Oohashi-Bridge. When two main-towers were built, the distur-bances of the field intensities appeared slightly. Secondly, as the hauling ropes were built between two main-towers, the shielding of the electric field was caused under the hauling ropes. Further, the sinusoidal-like variations of the erectric field intensities were also seen clearly on the transmitter side of the bridge. By the theoretical considerations, the static capacitance of the main-tower was about 0.003μF, and it became about 0.37μF after the hauling ropes were built. It will be concluded that the capacitance of the main-tower is increased apparently by the horizontal structure of the bridge such as hauling ropes or main cables, and consequently the main-towers radiate the strong secondary waves.

Comments on "The electromagnetic field of a vertical electric dipole over the Earth or sea" [with reply

The author comments on the solution given by King and Sandler (see vol.42, p.382-89, 1994) of the electromagnetic field of a vertical electric dipole (VED) over Earth or sea and in the presence of a three layered region. For a homogeneous half-space with complex bulk wavenumber k/sub 2/, King and Sandler present expressions for the E and B field components which are claimed to be accurate in all ranges of the radial distance /spl rho/, when |k/sub 2//k/sub 0/|>3-k0 being the wavenumber in air. Wait (see ibid., vol.44, p.271-2, 1996) has questioned the completeness and generality of King's and Sandler's formulas. In particular, two of Wait's comments have attracted this author attention. The first one is related to the usefulness of King's and Sandler's formulas directly above the VED axis (at /spl rho/=0). The second is the usefulness of their formulas in deriving the input impedance of the VED. The authors investigate these two comments by comparing King's and Sandler's formulas to numerical results for E/sub z/ on the VED axis and for the input impedance as affected by the lower King and Sandler reply that the questions raised in the remarks of Mahmoud (see ibid., vol.46, no.12, p.1745-6, 1998) are based on a comparison of their formulas with the exact numerical results for E/sub z/, on the VED axis and for the input impedance as affected by the lower half-space. Evidently, Mahmoud did not review the derivation of the King-Sandler formulas.

Characteristics of a Vertical Wire Antenna Above a Lossy Earth

The electromagnetic field of a vertical electric dipole in air above a lossy earth (represented by a half space) is studied. An approximate expression for the radial electric field in the half space is derived. Its validity is checked for a selected range of parameters with application to air to subsurface communication. An integral equation for the current on a thin vertical wire antenna kept above the earth is presented. Two moment method formulations are used to solve the integral equation. Numerical results for the antenna impedance from the two solutions are compared. Input impedance and far field pattern are calculated for a half wavelength antenna at varying heights from the air-earth interface for different parameters of the earth.

Electromagnetic modelling of buried line conductors using an integral equation

An integral equation is derived to represent the electromagnetic response of line conductors buried below the surface of a horizontally stratified earth. By permitting several finite-length line conductors of arbitrary topology, this representation is free of the limitations imposed by analytic solutions. The integral equation is formulated in terms of excess electric current (scattering current) flowing along the line conductor and is solved numerically by dividing the line conductor into many small segments. In general, the excess electric current is controlled by both the internal and external impedance of the line conductor. The internal impedance is the longitudinal resistance of the line conductor. The external impedance is caused by galvanic and inductive coupling between the line conductor and its local environment. The galvanic resistance to current channelling is spatially variable with a minimum in the centre of a uniform line conductor and is determined by conductor geometry and the host conductivity structure. The inductive external impedance is proportional to frequency and quadrature dominant. It is a function of line-conductor geometry, cross-section and burial environment. The inductive impedance effectively reduces the spatial dependence of the external impedance at high frequency by presenting a large reactance (which is uniform at all points along the conductor) to the exciting electric field. Within the quasi-static limit (i.e. where displacement current can be neglected), electromagnetic excitation by either horizontal electric or vertical magnetic dipoles produces a constant primary electric field at high frequencies (far field). The excess electric current in the line conductor will always be inversely proportional to frequency for these types of sources at sufficiently high frequencies where the inductive external impedance is dominant. Horizontal magnetic dipole and vertical electric dipole sources generate primary electric fields that are proportional to the square root of frequency in the high-frequency limit of the quasi-static domain and the excess electric current excited by such sources will decrease as the inverse of the square root of frequency.

Excitation of a conducting half-space by a toroidal coil

The possibility exists that a non-contacting "vertical-electrical dipole"source could be devised, to excite both horizontal and vertical currents in the subsurface. The scheme is quite simple, but it seems to have been overlooked or, at least, not disclosed, hitherto. The idea is to employ a toroidal coil carrying an alternating current, which is located in or just above the air/earth interface. As shown, when the diameter of the toroid is small compared to the distance to the observer, the effective source is effectively a vertical-electric dipole. This may be obvious to some, but the situation has some interesting complications, because of the presence of the interface. The pertinent analysis is outlined.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Generation Mechanism of Electric Impulses Observed in Explosion Seismic Experiments.

Generation mechanisms of the electric impulses in the underground chemical explosions are described in this paper. The electric impulses just after triggering were commonly observed in three explosion seismic experiments. The common characteristics of the impulses are as follows: 1) The duration time of the impulse train is always less than 10 ms and no impulse is detected after 10 ms. 2) The duration time of each impulse is approximately 1 ms, the time structure is quite different, and the occurrence is intermittent. 3) The electric charge generation process can be modeled by a vertical electric dipole. It is the first time to clearly show that the duration of the impulses is caused by the total length of the dynamite explosion. The characteristics can be explained by two closely coupled generation processes; chemical explosion and excitation of electric charges by a thermo- or mechano-electric process. The primary process is explained by means of the excitation of high-temperature and high-pressure with a dynamite explosion. The secondary process is interpreted as a theme- or mechano-electric conversion process excited either by thermal energy or by mechanical energy in surrounding media consisted of rock and water. Two thermo-electric and four mechano-electric conversion processes are discussed in terms of the time structure, the direction of expected electric dipoles, and the confinement in the vicinity of dynamite. It is concluded that the most probable source of the observed electric impulses is the fractoelectric effect.

Electromagnetic response of a discretely grounded circuit—An integral equation solution

We derive an integral equation to describe the electromagnetic response of a discretely grounded circuit. This investigation is relevant to the study of man‐made structures such as metallic fences, grounded powerlines, and pipelines, all of which may fall into the class of discretely grounded conductors. The solution developed here is an extension to existing circuit theory and takes into account the self and mutual interaction of the circuit elements. It is possible to ignore these interactions at low frequencies where the grounding impedances dominate the effective impedance of the circuit. However, at frequencies where the electromagnetic skin depth is comparable to the length between adjacent grounding points, the effective impedance of the circuit is proportional to frequency, and the inductance of the circuit dominates its electromagnetic response. Within the quasi‐static limit (i.e., where displacement currents can be neglected) electromagnetic excitation by either horizontal electric or vertical magnetic dipoles produces a constant primary electric field at high frequencies (far‐field). Thus, the electric current in the discretely grounded circuit will always be inversely proportional to frequency for these types of sources. Horizontal magnetic dipole or vertical electric dipole sources generate primary electric fields that are proportional to the inverse square root of frequency in the high frequency limit of the quasi‐static domain, and thus the current in a circuit excited by such sources will decrease as the inverse of square root of frequency. The integral equation solution derived here can be used to investigate the influence from cultural conductors on actual electromagnetic surveys and also provides further insights into the current channeling response of surficial conductors.

Resistivity structure of the underconsolidated sediments of the Cascadia Basin

SUMMARY The Cascadia Basin is located on the abyssal plain of the Juan de Fuca Plate, off the west coast of Vancouver Island. The sediments of the Cascadia Basin are very thick, over 2 km, and are underconsolidated because of a high rate of sedimentation. Seismic results suggest that the sediment acoustic velocities are low, and increase slowly and monotonically with depth from the sea-floor. A vertical electric dipole (VED) survey was conducted to obtain the resistivity structure of the upper kilometre of sediments, to determine the physical properties of a thick sequence of abyssal basin sediments, and for comparison with seismic results. While models with multiple layers can be found which fit the data, the‘best-fitting’models share a common feature—decreasing resistivity with depth, which is suggestive of a gradient in the resistivity. The feature is consistent with the results of other geological and geophysical studies. In particular, the seismic results do not indicate any significant contrast in the physical properties, i.e. layering, in the upper 500 m. We extend the VED theory to the case where resistivity varies continuously with depth, and obtain a gradient model that fits the Cascadia Basin data marginally better than simple layered models. The model resistivity is combined with heat-flow measurements for the determination of physical properties versus depth; the physical property models, the porosity, for example, are not consistent with the physical properties derived from seismic survey results. The mismatch is diagnostic of the underconsolidation, and is primarily due to the effects of the high rate of sedimentation on the seismic velocity and on the heat flow, which in turn influence the physical properties.

ELF radio wave propagation in a locally nonuniform Earth‐ionosphere cavity

The vertical electric field component of the ELF radio wave propagating in the spherical Earth‐ionosphere cavity with a localized nonuniformity is studied. The analysis is performed in the framework of Born's approximation of the perturbation theory applied to the Stratton‐Chu integral equation. Both the vertical electric dipole and the horizontal grounded wire antenna are considered as the ELF field sources. It is shown that different effects can arise within the nonuniform waveguide depending on the disturbance position between or beyond the endpoint of the propagation path that are conditioned by the vectorial nature of the radio wave. Backscatter is the prevailing effect in the case of impedance or height disturbances. A localized nonuniformity can bring forth pattern rotation of the horizontal wire antenna and at the same time an amplitude modification of its lobes.

A signal-to-noise model for ELF propagation in subsurface regions

Measurements of the natural extremely low-frequency (ELF) radio noise (known as Schumann resonances) in the period 1988-1989 have enabled average atmospheric noise levels and Schumann resonance parameters to be deduced. At 45 Hz, the average measured electric field was 41.6 dB/spl middot//spl mu/V/m/spl middot//spl radic/(Hz). It is assumed that the Schumann resonance noise field in the air-space in the vicinity of the observation point can be considered to be represented as the sum of four components, one arising from propagation over a short great-circle path, and a second representing a long great-circle path contribution, each of these having an upgoing and a downgoing part. The noise fields can then be estimated at any given depth below the ground (or sea) surface from the measured values in the air. The authors present results showing the computed fields produced in the sea from submerged horizontal electric quadrupole and vertical electric dipole man-made sources, and compare these with the subsurface atmospheric noise fields deduced from the experimental measurements.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The electromagnetic field of a vertical electric dipole over the Earth or sea

The analysis of King (1990) of the electromagnetic field of a vertical electric dipole over an imperfectly conducting half-space is applied to obtain the far field when the dipole is at a specified height d. The contributions by the space wave with its 1/r dependence and the lateral surface wave with its 1/r/sup 2/ dependence are separated and studied in detail when the dipole is over a wide range of media such as sea water, wet and dry Earth, lake water and dry sand. Graphs of the far-field patterns are shown.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Disturbances of decca waves near a huge bridge

A hyperbolic navigation system using a radio wave in the 100-kHz band is installed in the ocean surrounding Japan. This system is used widely by the fishing industry because the reproducibility of the measured location is high. Recently, near the land, several huge structures such as the Seto Bridge have been erected on the water which causes significant error in determining the location of a ship. This paper studies the disturbances of Decca waves of the Kita-Kyushu Decca chain due to the Minami-Bisan Seo-Ohashi Bridge. It was found that, with respect to the disturbance of Decca waves, the two main towers of the suspension bridge could be considered as vertical electric dipoles. In the measurement of the electrical field strength at four frequencies of the Decca station, the standing wave of the electrical field strength appeared more conspicuously with a higher frequency at the locations away from the bridge by more than 0.18 wavelength except near the bridge on the west side. It is assumed that the secondary waves from two main towers considered as vertical electric dipoles are superposed on the primary wave. Then the numerical results are carried out from the theoretical equation of the received electric field, and the measured results are explained. Also, it is found that the static capacitance of the vertical electric dipoles is 0.1 to 0.2 μF. Hence, it was possible to establish a macroscopic model of the bridge for which the main towers are considered as vertical electric dipoles.

Theoretical analysis of VHF-UHF propagation through air-vegetation-ground media

The electromagnetic radiation from a vertical electric dipole in three electrically different layers: air, vegetation and the ground is analysed. Starting with Maxwell&apos;s field equations, a rigorous analysis of the electromagnetic fields is carried out and an integral representation of the field components in the problem with two semi-infinite media is obtained. Using Debye&apos;s steepest descent method for asymptotic expansions of the contour integrals a set of formulas are derived for evaluation of different field components in air, vegetation and ground media.

The electromagnetic field of a vertical electric dipole in the presence of a three‐layered region

The electromagnetic field generated by a vertical electric dipole in the air over the surface of a two‐layered region is determined for continuous‐wave excitation. The region of interest consists of a conductor or dielectric with high permittivity, coated with an electrically thin layer of a dielectric under a half‐space of air. Simple explicit formulas are derived for the field at all points in all three regions including the surface wave. Typical applications are to microstrip circuits and antennas, communication over the earth when this is coated with a layer of asphalt or cement, and communication over the sea or a lake when this is under a layer of ice.

Electromagnetic-wave excitation and diffraction by metal cylinder inside flat waveguide

Electromagnetic-wave excitation by a vertical electric dipole located inside a flat waveguide containing a vertical circular metal cylinder is examined. An exact solution is obtained, and the diffracted field inside the waveguide is analyzed. Algorithms are provided for electromagnetic-field calculation in a Rayleigh approximation and in a short-wave approximation. Results of numerical calculations of fields and directivity characteristics are presented. The effect of the cylinder on the radiation power of the dipole in the waveguide is analyzed.

Application of the contour transformation method to a vertical electric dipole over Earth

A contour transformation method is applied to the computation of the Sommerfeld integral associated with a vertical electric dipole above Earth. In this method the slowly varying part of the transformed Sommerfeld integrand is approximated by a few exponential terms using Prony's method. The resulting integrals are then carried out analytically, thereby, yielding incomplete Lipschitz‐Hankel integrals. Therefore numerical integration of the Sommerfeld integral is unnecessary since the incomplete Lipschitz‐Hankel integrals are computed using efficient Bessel series expansions. This method is compared with a direct numerical integration of the Sommerfeld integral and a contour deformation technique which also utilizes Prony's method. The results demonstrate that the contour transformation method enables the accurate and efficient computation of the Sommerfeld integral for all source and observation locations (i.e., near zone, far zone and even grazing). This technique can also be applied to problems involving multiple layers.

Exact Image Theory for Fields Reflected from Bi-Isotropic Impedance Surfaces

Conditions for replacing a bi-isotropic half-space by an impedance surface are formulated. The most general bi-isotropic surface impedance is a dyadic containing an antisymmetric part, which is non-null for nonreciprocal media. To formulate the general radiation problem in front of the bi-isotropic surface, the exact image theory has been extended. The image theory is verified by known special cases and demonstrated by an example of a vertical electric dipole in front of the surface.

Application of the fast Fourier transform to the computation of the Sommerfeld integral for a vertical electric dipole above a half-space

The fast Fourier transform (FFT) is used in conjunction with analytical techniques to obtain an approximate expression for the Sommerfeld integral associated with a vertical electric dipole above a half-space. The resulting expression, which is an analytic function of the source and observation locations, can be used in lieu of a numerical integration of the Sommerfeld integral. It can be used in either the near zone or the far zone, and it can even be applied for observation angles close to grazing. The accuracy of the expansion directly depends on the number of terms used in the FFT. Results obtained using the expansion are compared with those obtained both from a direct numerical integration of the Sommerfeld integral and the reflection coefficient method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Time-harmonic electromagnetic response of an isotropic chiral halfspace

Radiation by sources wholly confined to a vacuous halfspace bordering an isotropic chiral halfspace has been examined. The relevant Green's functions have been formulated using the Fresnel reflection coefficients. For illustration and understanding, the radiation fields of a vertical electric dipole have been investigated.