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.

Approximate semianalytical solutions for the electromagnetic response of a dipping-sphere interacting with conductive overburden

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. E265-E277 ◽  
Author(s):  
Jacques K. Desmarais ◽  
Richard S. Smith
Keyword(s):  
Mineral Exploration ◽  
Thin Sheet ◽  
Electromagnetic Response ◽  
Uniform Field ◽  
Geologic Mapping ◽  
Sphere Model ◽  
Northern Ontario ◽  
Simple Method ◽  
Convolution Integrals ◽  
Metamorphic Terranes

Electromagnetic exploration methods have important applications for geologic mapping and mineral exploration in igneous and metamorphic terranes. In such cases, the earth is often largely resistive and the most important interaction is between a conductor of interest and a shallow, thin, horizontal sheet representing glacial tills and clays or the conductive weathering products of the basement rocks (both of which are here termed the “conductive overburden”). To this end, we have developed a theory from which the step and impulse responses of a sphere interacting with conductive overburden can be quickly and efficiently approximated. The sphere model can also be extended to restrict the currents to flow in a specific orientation (termed the dipping-sphere model). The resulting expressions are called semianalytical because all relevant relations are developed analytically, with the exception of the time-convolution integrals. The overburden is assumed to not be touching the sphere, so there is no galvanic interactions between the bodies. We make use of the dipole sphere in a uniform field and thin sheet approximations; however, expressions could be obtained for a sphere in a dipolar (or nondipolar) field using a similar methodology. We have found that there is no term related to the first zero of the relevant Bessel function in the response of the sphere alone. However, there are terms for all other zeros. A test on a synthetic model shows that the combined sphere-overburden response can be reasonably approximated using the first-order perturbation of the overburden field. Minor discrepancies between the approximate and more elaborate numerical responses are believed to be the result of numerical errors. This means that in practice, the proposed approach consists of evaluating one convolution integral over a sum of exponentials multiplied by a polynomial function. This results in an extremely simple algorithmic implementation that is simple to program and easy to run. The proposed approach also provides a simple method that can be used to validate more complex algorithms. A test on field data obtained at the Reid Mahaffy site in Northern Ontario shows that our approximate method is useful for interpreting electromagnetic data even when the background is thick. We use our approach to obtain a better estimate of the geometry and physical properties of the conductor and evaluate the conductance of the overburden.

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.

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 Radiation risk factors in incidence anortality among exposed individuals of East Kazakhstand m

2014 ◽  
Vol 2 ◽  
Author(s):  
Kazbek Apsalikov ◽  
Talgat Muldagaliev ◽  
Rustem Apsalikov ◽  
Shinar Serikkankyzy ◽  
Zaure Zholambaeva
Keyword(s):  
Risk Factors ◽  
Radiation Dose ◽  
Radiation Risk ◽  
Test Site ◽  
Epidemiological Studies ◽  
Long Term Effects ◽  
Respiratory Problems ◽  
East Kazakhstan ◽  
Effects Of Radiation ◽  
The Moment

Introduction: Lengthy clinical and epidemiological studies at the Research Institute of Radiation Medicine and Ecology have discovered basic patterns of long-term effects from ionizing radiation in population groups exposed to radiation risk. Methodology for calculating injury from radiation risk factors has been developed and implemented to minimize the effects of the Semipalatinsk nuclear test site (SNTS).Material and methods: We analyzed materials from the database of the Scientific Medical Register that were exposed to radiation as a result of SNTS. We analyzed both male and female populations of the Abay, Beskaragai and Zhanasemei, Kokpekti (control) areas of East-Kazakhstan region (EKR) from 2008-2012. These populations were split into three groups allocated by the generation. The first group represented persons born from the period of 01/01/1930 -08/01/1949 and their children born from the period of 10/09/1949-12/31/1962. The second group were persons born after 01/01/1963. The third group served as the control and were persons who immigrated to these areas after 1990.Results: There was an increased incidence of cancer (21.5%, p < 0.000734), cardiovascular diseases (10.2%); respiratory problems (9.6%), gastrointestinal issues (9.1%, p < 0.00371-0.00679) in the first group. The effect of the radiation dose has not been fully stuided among the subjects in the second group.The major causes of excess mortality in the first group were neoplams (30.6%), hypertension (23.8%), and myocardial infarction (22.6%). The effects of radiation influenced mortality in the second group were 2-2.5 times lower than the first group.Conclusion: There is a correlation between the size of the radiation dose, the risk profile, and age at the moment of radiation exposure with trends of morbidity and mortality in the radiation exposed areas.

scholarly journals Railway Ballast Monitoring by Gpr: A Test Site Investigation

2019 ◽  
Vol 11 (20) ◽  
pp. 2381 ◽  
Author(s):  
Bianchini Ciampoli ◽  
Calvi ◽  
D’Amico
Keyword(s):  
Asset Management ◽  
Construction Materials ◽  
Site Investigation ◽  
Horn Antenna ◽  
Test Site ◽  
Electromagnetic Response ◽  
Actual Condition ◽  
Railway Ballast ◽  
Set Up ◽  
Ground Penetrating

Effective maintenance of railways requires a comprehensive assessment of the actual condition of the construction materials involved. In this regard, Ground-Penetrating Radar (GPR) stands as a viable alternative to the invasive and time-consuming traditional techniques for the inspection of these infrastructures. This work reports the experimental activities carried out on a test-site area within a railway depot in Rome, Italy. To this purpose, a 30 m-long railway section was divided into 10 sub-sections reproducing different various physical and structural conditions of the track-bed. In more detail, combinations of varying scenarios of fragmentation and fouling of the ballast were reproduced. The set-up was then investigated using different multi-frequency GPR horn antenna systems. The effects of the different physical conditions of ballast on the electromagnetic response of the material were analysed for each scenario using time- and frequency-domain signal processing techniques. Parallel to this, modelling was provided to estimate fouling content. Interpretation of results has proven the viability of the GPR method in detecting signs of decay at the network level, thereby proving this technique to be worthy of implementation in asset management systems.

Imaging depth, structure, and susceptibility from magnetic data: The advanced source-parameter imaging method

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. L31-L38 ◽  
Author(s):  
Richard S. Smith ◽  
Ahmed Salem
Keyword(s):  
Source Parameters ◽  
Thin Sheet ◽  
Signal Amplitude ◽  
Horizontal Cylinder ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Imaging Method ◽  
Structural Index ◽  
Synthetic Test ◽  
Vertical Contact

An important problem in the interpretation of magnetic data is quantifying the source parameters that describe the anomalous structure. We present a new method that uses various combinations of the local wavenumbers for estimating the depth and shape (structural index) of the structure. Because the estimates are derived from third derivatives of the magnetic data, they are noisy. However, there are multiple ways of calculating the depth and index, and these solutions can be averaged to give a stable estimate. Even so, a synthetic test shows that the results are erratic away from the locations where the analytic-signal amplitude is large. Hence, when we generate images of the depth and structural index, we make the results most visible where the analytic-signal amplitude is large and less visible where the signal is small. The advantage of the method is that estimates can be obtained at all locations on a profile and used to generate continuous profiles or images of the source parameters. This can be used to help identify the locations where interference might be corrupting the results. The structural index image can be used to determine the most appropriate type of model for an area. Assuming this model, it is possible to calculate the depth that would be consistent with the model and the data. Knowing both the depth and model, the analytic-signal amplitude can be converted to apparent susceptibility. If a vertical-contact model is assumed, the susceptibility contrast across the contact can be imaged. For the thin-sheet and horizontal-cylinder models, we can image the susceptibility-thickness and susceptibility-area products, respectively.

TIME‐DEPENDENT ELECTROMAGNETIC FIELDS OF AN INFINITE, CONDUCTING CYLINDER EXCITED BY A LONG CURRENT‐CARRYING CABLE

Geophysics ◽  
1973 ◽  
Vol 38 (2) ◽  
pp. 369-379 ◽  
Author(s):  
Saurabh K. Verma
Keyword(s):  
Time Domain ◽  
Horizontal Cylinder ◽  
The Body ◽  
Time Dependent ◽  
Electromagnetic Response ◽  
Secondary Field ◽  
Function Type ◽  
Ore Body ◽  
Induced Field ◽  
Time Domain Electromagnetic

Theoretical and numerical computations have been made for the quasi‐static, time‐domain electromagnetic response of an infinite, conducting horizontal cylinder stimulated by long cable‐carrying step and ramp‐function type pulses. The effect of higher‐order induced multipoles on the secondary electric and magnetic field components is analyzed in detail, and the “threshold distances” at which individual multipoles become effective (contributing more than 5 percent of the secondary field) are presented. Also, the field fall‐off directly above the body and the variations in different induced‐field components along a traverse perpendicular to the strike of the ore body are examined.

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