Horizontal Electric Dipole Research Articles

A Corrected Physical-Optics Solution to 3-D Wedge Diffraction

A physical-optics (PO) solution to the three-dimensional problem of dipole radiation over an arbitrary-angled wedge is presented. The medium beneath each face of the wedge is nonmagnetic, lossy, and not necessarily the same for both faces. Excitation is provided by an electric dipole that is parallel to the edge of the wedge. The analytical formulation is based on the Stratton-Chu formula. The electromagnetic (EM) field due to a horizontal electric dipole over a lossy half-space is used on the faces and a charge distribution along the edge is introduced to account for the discontinuity of the EM field across the edge. The integral expression for the electric-field intensity far from the edge is evaluated asymptotically, thus resulting in a formula that is uniformly valid. The validity of this edge-corrected PO solution is established through a reciprocity check and comparisons with other solutions.

Response to comments on "An analysis of a staked dipole probe on a lossy earth plane using the finite-difference time-domain method" [and reply

The paper by D.V. Thiel and R. Mittra, IEEE Trans. Geosci. Remote Sensing, vol.35, p.1357-62 (1997) is commented upon. The present author deals with the basis of the expression for the effective complex area of a horizontal electric dipole (HED) over a layered conductive half-space. The second related item deals with a basic flaw in an estimate of the error when the HED is lifted relative to the air/earth interface. The present author provides an additional analysis. In both cases the HED is oriented to have a maximum response.

Electric dipole fields over an anisotropic seafloor: theory and application to the structure of 40Ma Pacific Ocean lithosphere

Seismic anisotropy has been detected in the oceanic crust and upper mantle, and likewise it is geologically reasonable to expect that a certain amount of lateral anisotropy exists in seafloor electrical properties. Anisotropy in Earth properties can often lead to surprising effects on geophysical responses that are not anticipated from simple isotropic theories. Here, we investigate the effects of lateral anisotropy on the frequency-domain, controlled-source electromagnetic (CSEM) response of a uniaxially conducting, non-magnetic seafloor excited by a horizontal electric dipole whose moment is oriented obliquely with respect to the electrical strike direction. A ‘paradox of anisotropy’ is observed, in which the seafloor electric field strength is enhanced in the most conductive direction of the seafloor. This enhancement is opposite to what one would expect based on naive isotropic theory. We also show that it is possible in certain circumstances to extract the along-strike electrical conductivity from marine controlled-source electromagnetic data using only isotropic modelling. The extraction of across-strike conductivity, however, requires full anisotropic modelling. The physical insight into electromagnetic induction in uniaxial media that is presented here should greatly assist the geological interpretation of marine CSEM experimental data. Applying our algorithm to the PEGASUS data set (CSEM data collected over 40Ma Pacific Ocean lithosphere) produces a model with conductivity in the fossil spreading direction that is seven × greater than the conductivity perpendicular to spreading. Strain-aligned mineralogical fabric, as predicted by tectonic modelling, would explain our result, with enhanced conductivities caused by hydrogen conduction along the olivine a-axis or connected accumulations of trace conductors such as graphite or magnetite.

The RAMESSES experiment-III. Controlled-source electromagnetic sounding of the Reykjanes Ridge at 57°45′N

SUMMARY A controlled-source electromagnetic sounding survey centred on an axial volcanic ridge (AVR) segment of the Reykjanes Ridge at 57°45aeN was performed as part of the RAMESSES experiment. Low-frequency (0.35‐11 Hz) electromagnetic signals were transmitted through the crust to an array of horizontal electric field recorders at the seafloor to ranges of 15 km from the source, which was a 100 m long horizontal electric dipole towed at heights of 50‐80 m from the seafloor. Coincident seismic and magnetotelluric studies were conducted during the rest of the RAMESSES experiment. Data were interpreted using a combination of 1-D forward modelling and inversion, and iterative forward modelling in two dimensions. On the axis of the AVR, the resistivity at the seafloor is 1 V m. There is a steep resistivity gradient in the upper few hundred metres of the crust, with the resistivity reaching approximately 10 V ma t a depth of 500 m. In order to explain the low resistivities, the upper layer of the crust must be heavily fractured and saturated with sea water. The resistivity increases with distance from the axis as the porosity decreases with increasing crustal age. The most intriguing feature in the data is the large diVerence in amplitude between fields transmitted along and across the AVR axis. A significant zone of low-resistivity material is required at approximately 2 km depth beneath the ridge crest in order to explain this diVerence. It is coincident with the low-velocity zone required by the seismic data, and has a total electrical conductance in excellent agreement with the results of the magnetotelluric study. The low-resistivity zone can be explained by the presence of a body of partially molten basalt in the crust. Taken together, these results provide the first clear evidence for a crustal magma chamber at a slow spreading mid-ocean ridge. The data constrain the melt fraction within the body to be at least 20 per cent, with a melt volume suYcient to feed crustal accretion at this segment of the ridge for of the order of 20 000 years. Since this body would freeze in the order of 1500 years, this finding lends support to the hypothesis that, at slow spreading rates, crustal accretion is a cyclic process, accompanying periodic influxes of melt from the mantle to a crustal melt reservoir.

Transient fields of a horizontal electric dipole on a multilayered dielectric medium

The transient electric fields of a horizontal electric dipole excited by a short pulse current and located on a layered dielectric medium were analyzed using the Cagniard-de-Hoop method. The fields are expressed as the convolution of the exciting current with the layered medium response. The layered medium response is obtained directly from the integral representation for the electric fields in the frequency domain and is expressed as a finite integral. In contrast to the conventional frequency synthesis approach, the Cagniard-de-Hoop (1960) method proves to be computationally more efficient and numerically more stable. Compared with the asymptotic approach, the solution involves no approximation. The nature of the various waves, reflected waves (guided wave and leaky wave), and lateral waves can be easily recognized on the Cagniard integral path. Numerical results are obtained to provide a rigorous forward modeling for the geo-radar operating on layered media.

The DC field components of horizontal and vertical electric dipole sources immersed in three-layered stratified media

Abstract. Formulas for computing the Cartesian components of the static (DC) fields of horizontal electric dipoles ( HEDs) and vertical electric dipoles ( VEDs) located in the central zone of a three-layer horizontally stratified medium are derived and presented in a summary form suitable for immediate computation. Formulas are given for the electric and magnetic field components in the upper and central regions. In the general case the computation involves the summation of a convergent infinite series. For the particular case of an infinitely thick central region (corresponding to the two-layer problem), the analysis produces relatively simple closed-form equations for the field components which are suitable for a 'hand calculation'. Specimen calculations for dipoles in seawaters are included and the derived results are compared with computations made using an ac model.

The DC field components of horizontal and vertical electric dipole sources immersed in three-layered stratified media

Formulas for computing the Cartesian components of the static (DC) fields of horizontal electric dipoles ( HEDs) and vertical electric dipoles ( VEDs) located in the central zone of a three-layer horizontally stratified medium are derived and presented in a summary form suitable for immediate computation. Formulas are given for the electric and magnetic field components in the upper and central regions. In the general case the computation involves the summation of a convergent infinite series. For the particular case of an infinitely thick central region (corresponding to the two-layer problem), the analysis produces relatively simple closed-form equations for the field components which are suitable for a 'hand calculation'. Specimen calculations for dipoles in seawaters are included and the derived results are compared with computations made using an ac model.

On-Land Detecting a Motionally Induced Electric Field: Test Measurements in Northern Finland

Test measurements of the electric voltage in Kilpisjarvi, northern Finland during September 9-October 12, 1995 were made with the aim of studying the possibility of detecting a motionally induced electric field by means of a horizontal electric dipole 3800 meters in length located at a distance of about 50 km from the nearest fjord of the Norwegian Sea. In addition to the electric voltage we measured at Kilpisjarvi, the water level, magnetic field and meteorological data from Tromso, Norway, the meteorological data from Kilpisjarvi and the magnetic field data from Sodankyla, Finland were used in analysis. Raw data were preprocessed to eliminate non-stationarities (remove outliers) and to remove solar daily variations, and were then smoothed. No significant influence of the local temperature, humidity and rainfall on the smoothed voltages was found. Probably due to a source effect the voltage was not coherent with the magnetic field from Tromso and Sodankyla. The long-period anomaly with the period of about 16 days was observed in the smoothed voltage, water level and air pressure. More data are necessary to derive a definite conclusion about the nature of the observed phenomenon, which is probably associated with direct atmospheric forcing on the coastal zone of the Norwegian Sea.

Two-dimensional theory of elf electromagnetic wave propagation in the earth-ionosphere waveguide channel

We present a surface theory of the 2-D telegraph equation and describe the methods for obtaining parameters L and C of this theory from the electromagnetic field of the dominant normal wave and its propagation constant together with the first two azimuthal derivatives. To excite the waveguide by vertical and horizontal electric dipoles, we determine the external sources of the 2-D telegraph equation, which are the 2-D point external voltage and the oriented point external specific voltage, respectively. The relation between the effective and physical sources is practically independent of the ionospheric conditions. The effective source of the horizontal dipole is proportional to the earth 's surface impedance at the source location.

Grounded-source transientE-field modeling of a shallow resistive layer with 3-D inhomogeneity

There is growing interest in the use of transient electromagnetic (TEM) sounding for shallow geotechnical, environmental and groundwater investigations. Two commonly used transmitterreceiver configurations for TEM sounding are 1) loop-loop or its variation, in-loop configuration and 2) wire-loop configuration. The less common configuration of a horizontal electric dipole (HED) transmitter and receiver is treated in this study and called wire-wire configuration.

Diffraction at the edge of a truncated grounded dielectric slab

A uniform high-frequency solution is presented for the diffraction of a horizontal electric dipole located upon a truncated, semi-infinite grounded dielectric slab. This solution is achieved by an asymptotic evaluation of a diffraction Sommerfeld-type integral, which is derived by using a physical optics formulation. The final uniform result is given in terms of a geometrical optics contribution and ray-diffracted contributions from space waves, surface waves, and leaky waves. Although this asymptotic expression is derived by assuming a large distance between the source and the edge, comparisons with a numerical integration have shown very good accuracy also for a distance about 0.2 wavelength. This solution provides physical insight into the diffraction phenomenon and an effective tool for predicting the effects of finite substrates in patch antennas. Indeed, within the expected limitations of the PO approximation, the present formulation is applicable to most of the substrate thicknesses and dielectric constants of practical interest in patch antennas.

A new method to define the full-zone resistivity in horizontal electric dipole frequency soundings on a layered Earth (in Chinese): Tang Jing-Tian & He Ji-Shan, Acta Geophysica Sinica, 37(4), 1994, pp 543–552

A new method to define the full-zone resistivity in horizontal electric dipole frequency soundings on a layered Earth (in Chinese): Tang Jing-Tian & He Ji-Shan, Acta Geophysica Sinica, 37(4), 1994, pp 543–552

Electric Dipole Excitation of a Long Conductor in a Lossy Medium

ABSTRACT Excitation of currents on an Infinitely long conductor Is analyzed for horizontal electric dipole or line sources and for a plane-wave, far-field source. Any of these sources can excite strong currents which produce strong scattered fields for detection. Numerical results for these sources Indicate that long conductors produce a strong anomaly over a broad frequency range. The conductor can be either insulated or bare, Co model either ungrounded or grounded conductors.

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.

A New-Type Source of Power Line Harmonic Radiation Possibly Located on the Kola Peninsula.

A new-type source of power line harmonic radiation (PLHR) is described in this paper to point out its significance to the magnetospheric emissions. Characteristic electromagnetic fields were observed over the Kola Peninsula, northern Russia, during the flight of the balloon B15-2N in 1982. The source is characterized by (a) the fundamental frequency of 24.4 Hz, (b) the harmonic spectrum continuously extending up to VLF, and (c) the isolation from commercial power lines. These characteristics are different from the previously reported PLHR sources that could trigger the magnetospheric emissions. Based on the low impedance field and the amplitude variation along the balloon trajectory, the source can be modeled by a horizontal electric dipole or a horizontal magnetic dipole, and then the source distance is estimated within the induction area of a few hundred kilometers. The most probable source is an electric railroad or a single-phase power line, driven by an isolated power generator, and located on the Kola Peninsula. Estimating the radiation power through the ionosphere, it is shown that enough power to trigger magnetospheric emissions may be radiated into the magnetosphere from the source. Therefore, it is suggested that the source can be recognized as a new-type PLHR source possibly related to magnetospheric emissions.

A higher‐order surface boundary condition for a dielectric substrate backed by a nonperfect conductor

AbstractA higher‐order surface impedance boundary condition (HOIBC) for a dielectric substrate backed by a nonperfect conductor is presented. The boundary condition is derived first in the spectral two‐dimensional Fourier domain, and later in the space domain. It is shown that in the space domain such a condition is expressed by a dyadic operator acting on the tangential components of the magnetic field. Finally, in order to demonstrate the qualities of the proposed HOIBC, a comparison of the field radiated by a horizontal electric dipole (HED) placed on the considered structure, computed using the exact and the approximated (higher‐order) impedance boundary condition (IBC), has been presented.

Numerical studies of the radiation patterns of resistively loaded dipoles

The far field radiation patterns of finite-size resistively loaded horizontal electric dipoles lying on a low-loss dielectric half-space are computed. The patterns are a superposition of the solutions for transient infinitesimal dipole elements, where the transient waveform for each element is synthesized from the exact steady-state solution. The current excitation for each dipole element is a half cycle of a sine squared waveform that propagates along the line of elements at a speed that can be varied. No reflections from the antenna ends are assumed. The time duration of the current half cycle governs the full period of the dominant part of the transient radiated waveform. The amplitude of the dipole excitation current is determined by a cosine distribution that accurately simulates the resistive loading. The transient radiation patterns differ from those of a steady-state dipole mainly by being more narrow in the E-plane, as is true for a finite-size steady-state dipole radiating in air. In addition, the far field waveforms are slightly distorted in directions off vertical in the E-plane. Two-way power radiation patterns are presented for both conductive and non-conductive dielectric media in a footprint mode, i.e. the power response to an isotropic point scatterer on a subsurface flat plane. The radar footprint in a conductive dielectric shows very narrow beamwidth due to the added conductive attenuation along the longer paths off the vertical direction. Field tests in water and glacial ice and laboratory observations show good agreement with the E-plane model results but suggest that the H-plane directivity is strongly affected by the separation between transmit and receive antennas and by the range.

Electromagnetic field generated in model of human head by simplified telephone transceiver

Possible adverse effects of electromagnetic fields on the human body and especially on the nervous system and the brain are of increasing concern, particularly with reference to cellular telephone transceivers held close to the head. An essential step in the study of this problem is the accurate determination of the complete electromagnetic field penetrating through the skull into the brain. Simple analytical formulas are derived from the theory of the horizontal electric dipole over a layered region. These give the components of the electric and magnetic fields on the air‐head surface, in the skin‐skull layer, and throughout the brain in terms of a planar model with the dimensions and average electrical properties of the human head. The specific absorption rate (SAR) is also determined.

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.

Radiation from a horizontal electric dipole in the presence of a lossy ground

The radiation field of a horizontal electric dipole located above a lossy ground is formulated as a boundary-value problem employing dyadic Green's functions. The resulting field vectors are then split into the primary and secondary components. The primary components represent those that would exist in the absence of the ground, leaving the secondary components to represent the contribution of the ground. For different frequencies and various ground conductivities, the secondary components are determined and compared with the primary ones. The results indicate that in the vicinity of the air–ground interface the effect of the ground on the electric-field components is significant when the field point is inside the ground region while it becomes less significant as the field point moves in the air region away from the interface and toward the source location. On the other hand, the contribution of the ground to the magnetic-field components becomes appreciable only at high frequencies or when the ground conductivity becomes excessively large.