Transient electromagnetic fields of a buried horizontal magnetic dipole

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. E481-E491 ◽  
Author(s):  
Andrei Swidinsky ◽  
Misac Nabighian
Keyword(s):  
Electric Field ◽  
Magnetic Dipole ◽  
Time Domain ◽  
Major Axis ◽  
Secondary Response ◽  
Burial Depth ◽  
Transient Electromagnetic ◽  
The Earth ◽  
Smoke Ring ◽  
Electromagnetic Surveys

Electromagnetic surveys using a vertical transmitter loop are common in land, marine, and airborne geophysical exploration. Most of these horizontal magnetic dipole (HMD) systems operate in the frequency domain, measuring the time derivative of the induced magnetic fields, and therefore a majority of studies have focused on this subset of field measurements. We examine the time-domain electromagnetic response of a HMD including the electric fields and corresponding smoke rings produced in a conductive half-space. Cases of a dipole at the surface and buried within the earth are considered. Results indicate that when the current in the transmitter is rapidly switched off, a single smoke ring is produced within the plane of the vertical transmitter loop, which is then distorted by the air-earth interface. In this situation, the circular smoke ring, which would normally diffuse symmetrically away from the source in a whole space, is approximately transformed into an ellipse, with a vertical major axis at an early time and a horizontal major axis at a late time. As measured from the location of the transmitter, the depth of investigation and lateral footprint of such a system increases with burial depth. It is also observed that the electric field measured in the direction of the magnetic dipole only contains a secondary response related to the charge accumulation on any horizontal conductivity boundaries because the primary field is always absent. This field component can be expressed analytically in terms of a static and time-varying field, the latter term adding spatial complexity to the total horizontal electric field at the earth surface at early times. Applications of this theoretical study include the design of time-domain induction-logging tools, crossborehole electromagnetic surveys, underground mine expansion work, mine rescue procedures, and novel marine electromagnetic experiments.

scholarly journals Ηλεκτρομαγνητική μελέτη υπόγειων αγωγών

2013 ◽  
Author(s):  
Κωνσταντίνος Ράλλης
Keyword(s):  
Electromagnetic Field ◽  
Electric Field ◽  
Finite Length ◽  
Current Distribution ◽  
Time Domain ◽  
Electronic Devices ◽  
Lightning Stroke ◽  
Mutual Impedance ◽  
The Earth ◽  
Improper Integrals

The aim of this doctoral thesis is to study electromagnetic compatibility problems dealing with field couplings to underground transmission lines, communication systems or electronic devices. As an overview: (i) we develop expressions for the accurate computation of mutual impedances between two underground conductors of finite length, (ii) we use a modern technique to solve the well-known Pollaczek and Carson formulas for the evaluation of the earth-return impedance for underground and overground conductors, (iii) we present a method for calculating the electromagnetic field generated by a lightning stroke for studying the problem of induced over-voltage on lines and electronic devices both in power and telecommunication systems, (iv) we deal with the computation of the current distribution along a vertical grounding rod. In all cases, our approach is purely electromagnetic with the use of the elementary electric dipoles technique. More specifically: In the first chapter we provide the expressions for the field generated by a vertical or horizontal elementary electric dipole placed in air or in ground. We form the boundary problem of the system dipole and air-ground interface for the calculation of the Hertz vector components generated by the dipole and the calculation of the electromagnetic field. We also provide tables with the cylindrical components of the produced field. In the second chapter we study the problem of the mutual impedance between two underground conductors of finite length and arbitrary position. With the use of the elementary dipoles technique we derive expressions for the accurate calculation of the mutual impedance that have the form of double infinite improper integrals and we evaluate them by using advanced integration algorithms. We then follow an alternative approach which involves the computation of the equivalent Sommerfeld type integrals by using the Discrete Complex Image Method (DCIM). This method allows the transformation of the Sommerfeld integrals to semi-infinite integrals with known analytical solutions. This is possible by approximating the integrand by a sum of complex exponentials. We finally give results of the mutual impedance and carry out comparisons in order to validate our expressions. In the third chapter we deal with the computation of the current distribution along a vertical grounding rod. We derive the mathematical model by applying the elementary dipoles technique and then we use the Method of Moments for solving the electric field integral equation. For the validation of the developed model, we solve the problem with the FEM method by using the software package COMSOL. In the fourth chapter we evaluate the well-known Pollaczek and Carson formulas for the earth-return impedance for underground and overground conductors. The integrals are solved by using again the DCIM method. For the approximation of the integrand with a sum of exponentials we use the Generalized Pencil of Function (GPOF) method (one and two level). The results of the impedance are compared with results derived with numerical integration of the Pollaczek integral and the analytical solution of Carson’s integral. In chapter five we evaluate the electromagnetic field generated by the lightning stroke in an observation point above and underground. The knowledge of the field is very important when we study couplings with power lines or telecommunication conductors. The expressions for the lightning field have the form of semi-infinite improper integrals in frequency domain, and their numerical computation poses a computational challenge. The problem is more demanding in the case of time domain response, were a large number of computations for a frequency range is required, in order to carry out the required inverse Fourier transform. We propose an efficient method for calculating the lightning integrals, based on their numerical calculation along a deformed path of integration. The method is combined with an interpolation technique in order to reduce the number of frequencies required in the Fourier synthesis of the time domain electric field. The result is a very fast and straightforward tool for the calculation of the underground and overground lightning field, without the use of specially developed numerical algorithms or analytical approximations.

The effect of local distortions on time‐domain electromagnetic measurements

Geophysics ◽  
2004 ◽  
Vol 69 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Andreas Hördt ◽  
Carsten Scholl
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Time Domain ◽  
Step Response ◽  
Model Parameters ◽  
Difficult Case ◽  
Storage Site ◽  
Transient Electromagnetic ◽  
Electromagnetic Measurements ◽  
Distortion Tensor

Based on the time‐domain integral equation, we derive expressions for the effect of an anomalous body close to the receiver or close to the transmitter on transient electromagnetic measurements. Similar to magnetotellurics, the distortion of electric fields at late times can be described by a constant distortion tensor relating the secondary electric field to the primary field components that would be obtained in the absence of the body. The distortion of a single electric field transient is a static shift only for particular configurations over a layered half‐space. In the general case, the perturbation is time dependent because the direction of the total electric field vector varies with time. The theory nicely explains spatial variations in electric field transients measured during a high‐redundancy long‐offset transient electromagnetics (LOTEM) survey over an underground gas storage site. An inversion example with synthetic data illustrates how distortion can be corrected. The elements of the distortion tensor are determined simultaneously with the model parameters. Ambiguity is reduced by a regularization of the distortion parameters. In the example, the background model is recovered well, even for the difficult case where only one transmitter is used. The distortion of the magnetic field time derivatives caused by bodies close to the receiver is proportional to the time derivative of the primary electric step response. The distortion is generally not limited to early times and cannot be neglected in general. Transmitter overprint effects resulting in static shifts of vertical magnetic field time derivatives may also be understood from the theory.

3D time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. F115-F126 ◽  
Author(s):  
Evan Schankee Um ◽  
Jerry M. Harris ◽  
David L. Alumbaugh
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Electric Field ◽  
Time Domain ◽  
Dirichlet Boundary Conditions ◽  
Earth Model ◽  
Time Step ◽  
Transient Electromagnetic ◽  
Backward Euler ◽  
Diffusion Phenomena

We present a finite-element time-domain (FETD) approach for the simulation of 3D electromagnetic (EM) diffusion phenomena. The finite-element algorithm efficiently simulates transient electric fields and the time derivatives of magnetic fields in general anisotropic earth media excited by multiple arbitrarily configured electric dipoles with various signal waveforms. To compute transient electromagnetic fields, the electric field diffusion equation is transformed into a system of differential equations via Galerkin’s method with homogeneous Dirichlet boundary conditions. To ensure numerical stability and an efficient time step, the system of the differential equations is discretized in time using an implicit backward Euler scheme. The resultant FETD matrix-vector equation is solved using a sparse direct solver along with a fill-in reduced ordering technique. When advancing the solution in time, the FETD algorithm adjusts the time step by examining whether or not the current step size can be doubled without unacceptably affecting the accuracy of the solution. To simulate a step-off source waveform, the 3D FETD algorithm also incorporates a 3D finite-element direct current (FEDC) algorithm that solves Poisson’s equation using a secondary potential method for a general anisotropic earth model. Examples of controlled-source FETD simulations are compared with analytic and/or 3D finite-difference time-domain solutions and are used to confirm the accuracy and efficiency of the 3D FETD algorithm.

scholarly journals Numerical Modelling of TEM Fields by the Edge-Based Finite Element Method Using Tetrahedral Element for Central Rectangular Loops

2021 ◽  
Vol 34 (04) ◽  
pp. 1180-1199
Author(s):  
Hossein Shahnazari- Aval ◽  
Mirsattar Meshinchi-Asl ◽  
Mahmoud Mehramuz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Solution ◽  
Electric Field ◽  
Time Domain ◽  
Tetrahedral Mesh ◽  
Computational Time ◽  
Transient Electromagnetic ◽  
Edge Based ◽  
Element Method

In this study, we have implemented an edge-based finite element method for the numerical modeling of the transient electromagnetic method. We took the Helmholtz equation of the electric field as the governing equation for the edge-based finite element analysis. The modeling domain was discretized using linear tetrahedral mesh supported by Whitney-type vector basis functions. We inferred the equations by applying the Galerkin method. The system of equation was solved using a corrected version of the Bi Conjugate Gradient Stabilized Method (BiCGStab) algorithm to reduce the computational time. We obtained numerical solution for electric field in the Laplace domain; then the field was transformed into the time domain using the Gaver-Stehfest algorithm. Following this, the impulse response of the magnetic field was obtained through the Faraday law of electromagnetic induction as it is considerably more stable and computationally more efficient than inversion using the Fourier Transform. 3D geoelectric models were used to investigate the convergence of the edge-based finite element method with the analytic solution. The results are in good agreement with the analytical solution value for two resistivity contrasts in the 3D geoelectric brick model. We also compared the results of tetrahedral elements with the brick element in the 3D horizontal sheet and 3D conductive brick model. The results indicated that these two elements show very similar errors, but tetrahedral reflects fewer relative errors. For the low resistivity geoelectric model, numerical checks against the analytical solution, integral-equation method, and finite-difference time-domain solutions showed that the solutions would provide accurate results.

Comments on the electromagnetic “smoke ring” concept

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 1908-1913 ◽  
Author(s):  
James E. Reid ◽  
James C. Macnae
Keyword(s):  
Electric Field ◽  
Half Space ◽  
Time Domain ◽  
Current System ◽  
One Dimensional ◽  
Homogeneous Half Space ◽  
Conductivity Structure ◽  
The Time Domain ◽  
Smoke Ring ◽  
Number Of Authors

The electromagnetic (EM) fields in a one‐dimensional (1-D) earth due to a dipole or loop transmitter have been studied by a number of authors, including Lewis and Lee (1978), Pridmore (1978), Nabighian (1979), and Hoversten and Morrison (1982). Nabighian (1979) aptly described the time‐domain‐induced current system in a homogeneous half‐space as resembling a “smoke ring” blown by the transmitter, which moves outwards and downwards and diminishes in amplitude with increasing time after the transmitter is turned off. In a homogeneous half‐space, the physical electric field maximum moves outward from the transmitter loop edge at an angle of approximately 30° with the surface. Hoversten and Morrison (1982) show how the direction of propagation of the time‐domain electric field maximum is affected by conductivity structure. In the case of a highly conductive overburden over a resistive basement, the electric field maximum travels essentially horizontally away from the transmitter, and is effectively trapped in the upper layer.

scholarly journals Calibration of Radiocarbon Dates for the Late Pleistocene Using U/Th Dates on Stalagmites

Radiocarbon ◽  
1997 ◽  
Vol 39 (1) ◽  
pp. 27-32 ◽  
Author(s):  
John C. Vogel ◽  
Joel Kronfeld
Keyword(s):  
South Africa ◽  
Magnetic Dipole ◽  
Satisfactory Agreement ◽  
Late Pleistocene ◽  
Calibration Curve ◽  
Dipole Field ◽  
Radiocarbon Dates ◽  
The Past ◽  
The Earth ◽  
Magnetic Dipole Field

Twenty paired 14C and U/Th dates covering most of the past 50,000 yr have been obtained on a stalagmite from the Cango Caves in South Africa as well as some additional age-pairs on two stalagmites from Tasmania that partially fill a gap between 7 ka and 17 ka ago. After allowance is made for the initial apparent 14C ages, the age-pairs between 7 ka and 20 ka show satisfactory agreement with the coral data of Bard et al. (1990, 1993). The results for the Cango stalagmite between 25 ka and 50 ka show the 14C dates to be substantially younger than the U/Th dates except at 49 ka and 29 ka, where near correspondence occurs. The discrepancies may be explained by variations in 14C production caused by changes in the magnetic dipole field of the Earth. A tentative calibration curve for this period is offered.

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