ELECTROMAGNETIC FIELDS OF A VERTICAL MAGNETIC DIPOLE PLACED ABOVE THE EARTH’S SURFACE

Geophysics ◽  
1963 ◽  
Vol 28 (3) ◽  
pp. 408-425 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Electromagnetic Fields ◽  
Current Source ◽  
Step Function ◽  
Impedance Function ◽  
Low Frequencies ◽  
Primary Loop ◽  
Mutual Impedance ◽  
The Earth ◽  
Receiving Antenna ◽  
Rate Of Decay

Electromagnetic fields due to a small loop antenna placed above the surface of a homogeneous and isotropic earth have been calculated. The effect of both the conduction and displacement currents are taken into account. Because of the complexity of the functions defining the fields, expressions valid separately for high and low frequencies are developed for the electric and magnetic field components. These expressions are then utilized to determine, for a step‐function current source, (a) the mutual impedance function [Formula: see text] between the primary loop and a small length of wire and (b) the voltage v(t) induced in a secondary loop. Two parameters are used to fix the locations of the primary loop and the receiving antenna with respect to the earth. A number of curves are plotted showing the mutual impedance function and the voltage function against time for different values of the parameters and the conductivity and the permittivity of the earth. With increase in either the conductivity or the permittivity, the amplitude and the rate of decay of the two functions decrease appreciably. However, the amplitudes of both [Formula: see text] and v(t) become smaller and the rate of decay higher as the receiving antenna is gradually lifted vertically from the ground. For all values of permittivity, the amplitude of the mutual impedance rises to a maximum with the horizontal separation between the two antennas before beginning to decrease, but at the same time the rate of decay of the transient becomes faster. With increase in the horizontal separation, the amplitude of the voltage function decreases inversely as the fifth power of the distance between the image of the transmitting dipole and the receiving antenna, but the rate of decay increases markedly.

ELECTROMAGNETIC FIELDS OF A SMALL LOOP ANTENNA ON THE SURFACE OF A POLARIZABLE MEDIUM

Geophysics ◽  
1964 ◽  
Vol 29 (5) ◽  
pp. 814-831 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Electromagnetic Fields ◽  
Current Source ◽  
Approximate Expression ◽  
Characteristic Parameter ◽  
Step Function ◽  
Loop Antenna ◽  
Electrode Polarization ◽  
Polarizable Medium ◽  
Small Loop ◽  
Rate Of Decay

Studies are made in this paper on the characteristics of the electromagnetic fields produced by a small loop antenna placed on the surface of a medium which exhibits induced‐polarization effects. An approximate expression for the effective impedance of a polarizable medium is used for this purpose. Both the real and imaginary parts of the impedance are appreciably frequency‐dependent. Different expressions suitable for specific ranges of time and specific values of the characteristic parameter of the medium are obtained for the fields when the antenna is excited by a step‐function current source. The step‐function responses show marked differences in characteristics as the parameter of the medium is increased from very small values, typical of membrane polarization, to very large values corresponding to electrode polarization. The rate at which the magnitude of the transients decays with time is highly dependent on this parameter. The rate of decay in the initial small part of the transient curve increases, whereas in the remaining major part the rate decreases with rise in the value of the parameter.

ELECTROMAGNETIC FIELDS OF A TRANSIENT MAGNETIC DIPOLE ON THE EARTH’S SURFACE

Geophysics ◽  
1959 ◽  
Vol 24 (1) ◽  
pp. 89-108 ◽  
Author(s):  
Bimal Krishna Bhattacharyya
Keyword(s):  
Magnetic Fields ◽  
Step Function ◽  
Displacement Current ◽  
Time Interval ◽  
Initial Amplitude ◽  
Impedance Function ◽  
Circular Loop ◽  
Mutual Impedance ◽  
The Earth ◽  
Electric And Magnetic Fields

Transient electric and magnetic fields close to the surface of the earth, as developed by a step‐function current flowing in a circular loop of wire, have been determined. The effect of the insulating air region is fully taken into account. It is observed that the air region has an appreciable influence on the fields over the surface of the earth. The effect of displacement current within the earth has also been considered. Expressions of electric and magnetic fields have been utilized to determine (a) the mutual impedance function between the primary loop and a small length of wire and (b) the voltage induced in a secondary loop. Both these functions are found to have appreciable magnitudes only during the time interval between the arrival of the wave travelling through air and that of the wave via the conducting medium. From a study of this duration and the initial amplitude of either of the two functions, it is possible to obtain values of conductivity and permittivity of the earth. Curves have been plotted to depict the nature of variation of these functions with time for different values of the electric constants of the earth.

HIGH‐FREQUENCY ELECTROMAGNETIC COUPLING BETWEEN SMALL COPLANAR LOOPS OVER AN INHOMOGENEOUS GROUND

Geophysics ◽  
1972 ◽  
Vol 37 (6) ◽  
pp. 997-1004 ◽  
Author(s):  
James A. Fuller ◽  
James R. Wait
Keyword(s):  
Half Space ◽  
High Frequency ◽  
Electromagnetic Coupling ◽  
Current Source ◽  
Vertical Axis ◽  
Loop Current ◽  
Mutual Impedance ◽  
Multiplicative Factor ◽  
The Earth ◽  
Horizontal Electric Dipole

An integral formulation is given for the fields of a loop current source which is located over a horizontally stratified half‐space and has a vertical axis. The electrical properties of the half‐space vary exponentially with the depth into the earth. An asymptotic solution is developed for the case of source and observer on the interface but separated by a large numerical distance. The approximate solution is then used to determine the mutual impedance between two small loops and between the loop and a horizontal electric dipole, when the antennas are on the interface. It is found that the effect of stratification on the mutual impedance is represented approximately by a single multiplicative factor.

Efficient evaluation of the earth return mutual impedance of overhead conductors over a horizontally multilayered soil

2014 ◽  
Vol 33 (4) ◽  
pp. 1379-1395 ◽  
Author(s):  
Jae-bok Lee ◽  
Jun Zou ◽  
Benliang Li ◽  
Munno Ju
Keyword(s):  
Unit Length ◽  
Oscillatory Integral ◽  
Electromagnetic Transients ◽  
Closed Form Expression ◽  
Computational Time ◽  
Horizontal Distance ◽  
Content Type ◽  
Mutual Impedance ◽  
The Earth ◽  
Highly Oscillatory

Purpose – The per-unit-length earth return mutual impedance of the overhead conductors plays an important role for analyzing electromagnetic transients or couplings of multi-conductor systems. It is impossible to have a closed-form expression to evaluate this kind of impedance. The purpose of this paper is to propose an efficient numerical approach to evaluate the earth return mutual impedance of the overhead conductors above horizontally multi-layered soils. Design/methodology/approach – The expression of the earth return mutual impedance, which contains a complex highly oscillatory semi-infinite integral, is divided into two parts intentionally, i.e. the definite and the tail integral, respectively. The definite integral is calculated using the proposed moment functions after fitting the integrand into the piecewise cubic spline functions, and the tail integral is replaced by exponential integrals with newly developed asymptotic integrands. Findings – The numerical examples show the proposed approach has a satisfactory accuracy for different parameter combinations. Compared to the direct quadrature approach, the computational time of the proposed approach is very competitive, especially, for the large horizontal distance and the low height of the conductors. Originality/value – The advantage of the proposed approach is that the calculation of the highly oscillatory integral is completely avoided due to the fact that the moment function can be evaluated analytically. The contribution of the tail integral is well included by means of the exponential integral, though in an asymptotic way. The proposed approach is completely general, and can be applied to calculate the earth return mutual impedance of overhead conductors above a soil structure with an arbitrary number of horizontal layers.

Fast and high-precision calculation of earth return mutual impedance between conductors over a multilayered soil

2018 ◽  
Vol 37 (3) ◽  
pp. 1214-1227 ◽  
Author(s):  
Junjie Ma
Keyword(s):  
Quadrature Rule ◽  
Content Type ◽  
Mutual Impedance ◽  
Numerical Tests ◽  
Sommerfeld Integral ◽  
The Earth ◽  
Finite Integral ◽  
Infinite Integral ◽  
Improper Integrals ◽  
Differential Matrix

Purpose Solutions for the earth return mutual impedance play an important role in analyzing couplings of multi-conductor systems. Generally, the mutual impedance is approximated by Pollaczek integrals. The purpose of this paper is devising fast algorithms for calculation of this kind of improper integrals and its applications. Design/methodology/approach According to singular points, the Pollaczek integral is divided into two parts: the finite integral and the infinite integral. The finite part is computed by combining an efficient Levin method, which is implemented with a Chebyshev differential matrix. By transforming the integration path, the tail integral is calculated with help of a transformed Clenshaw–Curtis quadrature rule. Findings Numerical tests show that this new method is robust to high oscillation and nearly singularities. Thus, it is suitable for evaluating Pollaczek integrals. Furthermore, compared with existing method, the presented algorithm gives high-order approaches for the earth return mutual impedance between conductors over a multilayered soil with wide ranges of parameters. Originality/value An efficient truncation strategy is proposed to accelerate numerical calculation of Pollaczek integral. Compared with existing algorithms, this method is easier to be applied to computation of similar improper integrals, such as Sommerfeld integral.

On modeling a well casing for resistivity and induced polarization

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 2061-2063 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Electrical Properties ◽  
Electric Dipole ◽  
Free Space ◽  
Eddy Currents ◽  
Interfacial Polarization ◽  
Induced Polarization ◽  
Mutual Impedance ◽  
The Earth ◽  
Horizontal Electric Dipole ◽  
Displacement Currents

In a previous communication I proposed an analytical model to simulate the electromagnetic (EM) and induced polarization (IP) response of a metal well casing (Wait, 1983). To facilitate the analysis, the earth was idealized as a homogeneous conducting half‐space of electrical properties (σ, ε, μ). The well casing was represented as a filamental vertical conductor of semiinfinite length that was characterized by a series axial impedance to account for eddy currents and interfacial polarization. A further basic simplification was to neglect displacement currents in the air; this was justified when all significant distances were small compared with the free‐space wavelength. Initially, the source was taken to be a horizontal electric dipole or current element I ds on the air‐earth interface. By integration of the results, the mutual impedance between two grounded circuits could be ascertained. In the absence of the vertical conductor (i.e., the well casing) the results reduced to those given by Sunde (1968) and Ward (1967).

scholarly journals Investigation of Changes in Groundwater Affected by the Electromagnetic Fields of the Earth to Predict Earthquake

2015 ◽  
Vol 9 (3) ◽  
pp. 2961-2982
Author(s):  
Maryam Rezaei ◽  
N. Hasani ◽  
A. Khorsandi ◽  
A. Rezaei ◽  
◽  
...  
Keyword(s):  
Electromagnetic Fields ◽  
The Earth

Localizing the Source of Type II Emission Around a CME with the Sun Radio Interferometer Space Experiment (SunRISE) and MHD Simulations

2021 ◽  
Author(s):  
Alexander Hegedus ◽  
Ward Manchester ◽  
Justin Kasper ◽  
Joseph Lazio ◽  
Andrew Romero-Wolf
Keyword(s):  
Data Processing ◽  
Low Frequency ◽  
Solar Energetic Particle ◽  
Radio Interferometer ◽  
Valuable Insight ◽  
Type Ii ◽  
Plasma Parameters ◽  
Low Frequencies ◽  
The Earth ◽  
Type Ii Bursts

<p>The Earth’s Ionosphere limits radio measurements on its surface, blocking out any radiation below 10 MHz. Valuable insight into many astrophysical processes could be gained by having a radio interferometer in space to image the low frequency window, which has never been achieved. One application for such a system is observing type II bursts that track solar energetic particle acceleration occurring at Coronal Mass Ejection (CME)-driven shocks. This is one of the primary science targets for SunRISE, a 6 CubeSat interferometer to circle the Earth in a GEO graveyard orbit. SunRISE is a NASA Heliophysics Mission of Opportunity that began Phase B (Formulation) in June 2020, and plans to launch for a 12-month mission in mid-2023. In this work we present an update to the data processing and science analysis pipeline for SunRISE and evaluate its performance in localizing type II bursts around a simulated CME.</p><p>To create realistic virtual type II input data, we employ a 2-temperature MHD simulation of the May 13th 2005 CME event, and superimpose realistic radio emission models on the CME-driven shock front, and propagate the signal through the simulated array. Data cuts based on different plasma parameter thresholds (e.g. de Hoffman-Teller velocity and angle between shock normal and the upstream magnetic field) are tested to get the best match to the true recorded emission.  This model type II emission is then fed to the SunRISE data processing pipeline to ensure that the array can localize the emission. We include realistic thermal noise dominated by the galactic background at these low frequencies, as well as new sources of phase noise from positional uncertainty of each spacecraft. We test simulated trajectories of SunRISE and image what the array recovers, comparing it to the virtual input, finding that SunRISE can resolve the source of type II emission to within its prescribed goal of 1/3 the CME width. This shows that SunRISE will significantly advance the scientific community’s understanding of type II burst generation, and consequently, acceleration of solar energetic particles at CMEs.  This unique combination of SunRISE observations and MHD recreations of space weather events will allow an unprecedented look into the plasma parameters important for these processes. </p>

Integral Equation Formulations and Related Numerical Solution Methods in Some Biomedical Applications of Electromagnetic Fields

2020 ◽  
pp. 249-267
Author(s):  
Dragan Poljak ◽  
Mario Cvetković ◽  
Vicko Dorić ◽  
Ivana Zulim ◽  
Zoran Đogaš ◽  
...  
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Nerve Fiber ◽  
Electromagnetic Fields ◽  
Biomedical Applications ◽  
Current Source ◽  
Myelinated Nerve Fiber ◽  
Surface Integral ◽  
Myelinated Nerve ◽  
Solution Methods

The paper reviews certain integral equation approaches and related numerical methods used in studies of biomedical applications of electromagnetic fields pertaining to transcranial magnetic stimulation (TMS) and nerve fiber stimulation. TMS is analyzed by solving the set of coupled surface integral equations (SIEs), while the numerical solution of governing equations is carried out via Method of Moments (MoM) scheme. A myelinated nerve fiber, stimulated by a current source, is represented by a straight thin wire antenna. The model is based on the corresponding homogeneous Pocklington integro-differential equation solved by means of the Galerkin Bubnov Indirect Boundary Element Method (GB-IBEM). Some illustrative numerical results for the TMS induced fields and intracellular current distribution along the myelinated nerve fiber (active and passive), respectively, are presented in the paper.

Sign in / Sign up

Export Citation Format

Share Document