Crone pulse electromagnetic response of a conducting thin horizontal sheet—Theory and field application

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1350-1354 ◽  
Author(s):  
S. S. Rai
Keyword(s):  
Thin Sheet ◽  
Horizontal Layer ◽  
Field Application ◽  
Step Response ◽  
Electromagnetic Response ◽  
Attractive Feature ◽  
Time Domain Response ◽  
The Time Domain ◽  
Interpretation Model ◽  
Response Formula

The horizontal, conducting thin‐sheet model represents a special interest in interpretation of electromagnetic field data since it is a suitable interpretation model for the surficial conductive layer, a common occurrence in many terrains. For small thicknesses of overburden layers [Formula: see text]separation) the resolution of layer thickness and conductivity is not possible and interpretation needs to be carried out in terms of the layer conductance. An attractive feature of the thin‐sheet model is the simplicity with which the time‐domain response [Formula: see text] can be calculated. The step response of an infinitely thin layer was derived by Maxwell (1891). In this paper I derive the Crone pulse electromagnetic (PEM) response of a conducting infinitely thin horizontal layer. Applicability of the study is demonstrated by means of a field example.

On: “Crone pulse electromagnetic response of a conducting thin horizontal sheet—Theory and application,” by S. S. Rai (GEOPHYSICS, 50, 1350–1354, August 1985).

Geophysics ◽  
1987 ◽  
Vol 52 (3) ◽  
pp. 373-374
Author(s):  
David C. Bartel
Keyword(s):  
Time Domain ◽  
Simple Formula ◽  
Thin Sheet ◽  
Step Response ◽  
Electromagnetic Response ◽  
The Subject ◽  
The Time Domain ◽  
Airborne Em

Rai uses a simple formula for the step response of a conducting, horizontal thin sheet in the time domain and applies it to the Crone pulse electromagnetic (PEM) system. He also uses this formulation to interpret some field results. The idea of an infinite, horizontal, conductive thin sheet is valid in some cases for both ground and airborne EM systems. However, I disagree with some of the derivations of the thin‐sheet equation as presented in the subject paper. The applicability of the study is not questioned; but the interpretation of the field example may be different.

The electromagnetic response of thin sheets buried in a uniformly conducting half‐space

Geophysics ◽  
1987 ◽  
Vol 52 (1) ◽  
pp. 108-117 ◽  
Author(s):  
R. Clark Robertson
Keyword(s):  
Thin Layer ◽  
Half Space ◽  
Thin Sheet ◽  
Three Dimensional ◽  
Horizontal Layer ◽  
Thin Layers ◽  
Electromagnetic Response ◽  
Thin Sheets ◽  
Magnetotelluric Data ◽  
The Earth

The interpretation of magnetotelluric data is hampered by the effect of three‐dimensional (3-D) conductivity variations within the earth. In particular, the effects of deep structures are masked by heterogeneities near the surface. In order to understand the effects of 3-D anomalies on magnetotelluric investigations, the electromagnetic response of 3-D models of the earth must be investigated. One technique used to model a 3-D earth is the thin‐sheet approximation. This technique confines all lateral changes in conductivity to a horizontal layer in a laterally homogeneous earth; however, the thin‐sheet technique can be applied only to anomalies that are electrically thin at the frequency of investigation. The thin‐sheet technique can be extended to include a greater variety of models by stacking heterogeneous thin layers. As a first step, the thin‐sheet technique is extended to model a buried, heterogeneous thin layer. Extension of the method to account for buried thin sheets is theoretically and computationally more involved than for a surface thin sheet, but the buried thin sheet still has computational advantages over other 3-D models.

On closed-form expressions for the approximate electromagnetic response of a sphere interacting with a thin sheet — Part 1: Theory in the frequency and time domain

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. E189-E198 ◽  
Author(s):  
Jacques K. Desmarais
Keyword(s):  
Closed Form ◽  
Time Domain ◽  
Mineral Exploration ◽  
Thin Sheet ◽  
Electromagnetic Response ◽  
Uniform Field ◽  
Electromagnetic Modeling ◽  
The Time Domain ◽  
Glacial Clays ◽  
Metamorphic Terranes

In mineral exploration and geologic mapping of igneous and metamorphic terranes, the background is often dominantly resistive. The most important electromagnetic interaction is between a discrete conductor and an overlying sheet of conductive overburden (e.g., glacial clays or weathering products of the basement rocks). To enable the electromagnetic modeling of these common situations, here I provide closed-form expressions for the approximate electromagnetic response of a sphere embedded in highly resistive rocks and interacting with an overlying thin sheet. The sphere is assumed to be dipolar and excited by a locally uniform field. The expressions in the time and frequency domains are represented as sums of complete and incomplete cylindrical functions. New asymptotic approximations are provided for the efficient evaluation of the required incomplete cylindrical functions. The frequency-domain formulas are validated by numerical transformation to the time domain and comparison to the time-domain solution.

scholarly journals Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Anis Allagui ◽  
Todd J. Freeborn ◽  
Ahmed S. Elwakil ◽  
Brent J. Maundy
Keyword(s):  
Cyclic Voltammetry ◽  
Double Layer ◽  
Time Domain ◽  
Electric Double Layer ◽  
Constant Current ◽  
Step Response ◽  
Current Voltage ◽  
The Time Domain ◽  
Double Layer Capacitors ◽  
Electric Double Layer Capacitors

Abstract The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal S s C behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance R s in series with a constant phase element (CPE(Q, α), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived (R s , Q, α)-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α, which is not possible with the classical R s C model. We validate our formulae with the experimental measurements of different EDLCs.

Improving the time domain response of fractional order digital differentiators by windowing

2015 ◽  
Vol 107 ◽  
pp. 282-289 ◽  
Author(s):  
Chengyan Peng ◽  
Xiaochuan Ma ◽  
Geping Lin ◽  
Min Wang
Keyword(s):  
Fractional Order ◽  
Time Domain ◽  
Time Domain Response ◽  
The Time Domain

A finite‐element solution for the transient electromagnetic response of an arbitrary two‐dimensional resistivity distribution

Geophysics ◽  
1986 ◽  
Vol 51 (7) ◽  
pp. 1450-1461 ◽  
Author(s):  
Y. Goldman ◽  
C. Hubans ◽  
S. Nicoletis ◽  
S. Spitz
Keyword(s):  
Finite Element ◽  
Sparse Matrix ◽  
Equation System ◽  
Electromagnetic Response ◽  
Implicit Time ◽  
Two Dimensional ◽  
Time Step ◽  
Transient Electromagnetic ◽  
Exact Boundary ◽  
The Time Domain

We present a numerical method for solving Maxwell’s equations in the case of an arbitrary two‐dimensional resistivity distribution excited by an infinite current line. The electric field is computed directly in the time domain. The computations are carried out in the lower half‐space only because exact boundary conditions are used on the free surface. The algorithm follows the finite‐element approach, which leads (after space discretization) to an equation system with a sparse matrix. Time stepping is done with an implicit time scheme. At each time step, the solution of the equation system is provided by the fast system ICCG(0). The resulting algorithm produces good results even when large resistivity contrasts are involved. We present a test of the algorithm’s performance in the case of a homogeneous earth. With a reasonable grid, the relative error with respect to the analytical solution does not exceed 1 percent, even 2 s after the source is turned off.

Computation of the time‐domain response of a polarizable ground

Geophysics ◽  
1982 ◽  
Vol 47 (11) ◽  
pp. 1574-1576 ◽  
Author(s):  
D. Guptasarma
Keyword(s):  
Time Domain ◽  
Complex Impedance ◽  
Fractional Power ◽  
Domain Model ◽  
Frequency Function ◽  
Step Response ◽  
Linear Filter ◽  
Complex Frequency ◽  
Time Domain Response ◽  
Impedance Functions

Computation of the theoretical time‐domain response of a polarizable ground on the basis of a frequency‐domain model of relaxation, e.g., a Cole‐Cole or any other model that involves a fractional power of the complex frequency variable, runs into difficulties either because the Laplace transform can only be written as a very slowly converging summation or because it cannot be written in closed computable form. A clear way around this is to use a digital linear filter. A filter is presented in this paper that has been designed specifically to work well with complex impedance functions that tend asymptotically to real values at both extremes of the frequency variable, the magnitude descending monotonically from the low‐frequency asymptote to the high frequency asymptote. This filter produces the step response from the real part of the impedance‐versus‐frequency function with reasonable accuracy for all impedance functions that one may like to represent by models of electrical relaxation for a polarizable ground, but it does not work for functions containing sharp resonances or discontinuities.

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