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.

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 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.

On closed-form expressions for the approximate electromagnetic response of a sphere interacting with a thin sheet — Part 2: Theory in the moment domain, validation, and examples

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. E199-E207 ◽  
Author(s):  
Jacques K. Desmarais
Keyword(s):  
Time Domain ◽  
Thin Sheet ◽  
Test Site ◽  
Electromagnetic Response ◽  
Asymptotic Formulas ◽  
Attractive Alternative ◽  
Northern Ontario ◽  
Synthetic Test ◽  
The Moment ◽  
Analytical Time

Fully analytical formulas are derived for the approximate electromagnetic response of a sphere interacting with a thin sheet in the moment domain. The moment-domain expressions are found to be expressed as simple polynomials of hyperbolic functions. These are significantly simpler to evaluate than the frequency- and time-domain expressions and therefore provide an attractive alternative for modeling. An efficient procedure is outlined for generalizing the moment-domain expression to bipolar-repetitive waveforms. This procedure is validated on a synthetic test example and field data from the Reid-Mahaffy test site, in northern Ontario. Here, results are found in agreement with the work of previous studies. The analytical time-domain procedure is validated through synthetic test examples. The asymptotic formulas for the time-domain expressions are found to significantly reduce the number of required function evaluations, especially for models in which the sphere is not too shallow or not too big or conductive. For example, for a sphere (and overburden) of conductivity (and conductance) of [Formula: see text] (and [Formula: see text]), if the sphere radius is three times smaller than the depth to the top, the amount of required function evaluations is halved; when the ratio is two or less, the asymptotic formulas do not reduce the amount of function evaluations, for the tolerances chosen here. Less-strict tolerances will lead to a further reduction of the required function evaluations.

The realizable resistive limit: A new concept for mapping geological features spanning a broad range of conductances

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1124-1127 ◽  
Author(s):  
Richard S. Smith
Keyword(s):  
Real Time ◽  
Time Domain ◽  
Thin Sheet ◽  
Structural Features ◽  
Secondary Response ◽  
Step Response ◽  
Nonlinear Inversion ◽  
Time Data ◽  
Off Time ◽  
The Ideal

The integral of the step response from zero time to infinite time (the ideal resistive limit) can be used to determine the conductance of the ground, in theory, because the former is directly proportional to the latter. However, in a real time‐domain airborne electromagnetic (AEM) system, it is impossible to measure the step response, or the ideal resistive limit. This is because (1) the off time is finite, being interrupted by the next transmitter pulse; (2) the total effect of all previous transmitter pulses is to reduce the measured response; and (3) the process of removing the primary field during the on time removes a component of the secondary response that has the same shape as the primary response. With a real time‐domain AEM system, it is possible to estimate what is defined as the realizable resistive limit (RRL). The RRL can also be calculated theoretically for a horizontal thin sheet of known conductance. Hence, the measured data can be input into a nonlinear inversion scheme and used to estimate an apparent conductance. RRL is calculated using on‐time data, which is above the noise level between 0.001 S and 100 000 S, so it is possible to map conductances in this eight‐decade range. Traditional methods for deriving conductance use off‐time data only and are restricted to a much smaller range of values (i.e., about two decades). A field example illustrates that, within the resistive areas, the RRL map shows many structural features and lithologies that are not evident on the map of conductance derived using off‐time data. Within the conductive areas, the RRL image shows greater variation; a number of geologically meaningful features are also apparent. Another advantage of RRL images is that artifacts associated with current migration near the edge of conductive features are not as evident as they are in the off‐time‐derived conductance images.

scholarly journals Introduction to Communication Systems

2021 ◽  
pp. 1-17
Author(s):  
Stevan Berber
Keyword(s):  
Theoretical Analysis ◽  
Time Domain ◽  
Communication Systems ◽  
Theoretical Concepts ◽  
Analysis And Design ◽  
The Subject ◽  
Definition Of ◽  
The Time Domain ◽  
Analogue To Digital ◽  
Power And Energy

This chapter introduces the subject of the book, defines the main terms in communication systems that will be used in the book, and presents the objectives of the book. It also presents classifications of signals and systems, and theoretical concepts related to the signal conversions in the time domain that will be used in subsequent chapters. The signals are classified using various criteria, including periodicity and symmetry, continuity and discreteness, power and energy properties, randomness, and physical realizability of signals. Analogue-to digital and digital-to-analogue conversions and their places and importance in the processing of signals in relation to their application in communication systems are briefly explained. The final section returns back to the definition of the signals related to the continuity and discreteness in time and their values, due to the importance of distinguishing them in the theoretical analysis and design of digital and discrete communication systems.

The time-domain electromagnetic response of wedge-like structures

2004 ◽  
Vol 2004 (1) ◽  
pp. 1-4
Author(s):  
David Annetts ◽  
Art Raiche ◽  
Fred Sugeng
Keyword(s):  
Time Domain ◽  
Electromagnetic Response ◽  
Time Domain Electromagnetic ◽  
The Time Domain
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