scholarly journals THE ELECTROMAGNETIC RESPONSE OF A CONDUCTIVE INHOMOGENEITY IN A LAYERED EARTH

Geophysics ◽  
1976 ◽  
Vol 41 (6) ◽  
pp. 1133-1156 ◽  
Author(s):  
J. J. Lajoie ◽  
G. F. West

A numerical model has been constructed to determine the three‐dimensional electromagnetic fields in the vicinity of a finite, thin, conductive plate buried in a horizontally stratified, conductive environment. The EM source is a rectangular loop. The problem is formulated as an integral equation for the electric field in the plate. However, to avoid certain numerical difficulties, the actual working variables are a pair of scalar potentials which represent divergence‐free and curl‐free current flows in the plate, and whose values are known at the nodes of a rectangular grid. The basic integral equation is then reduced to a set of linear equations which can be solved numerically. The cases modeled are a simulation of the Turam method. The models were a shallow plate and a deep plate in a conductive half‐space, a deep plate in an insulating host rock under a conductive layer, and a deep plate in a conductive host rock under a conductive layer. In all cases, the top of the plate was separated from the overburden, and the conductivities of the plate, layer, and host rock were varied widely. It was found that a conductive overburden layer alone causes a phase rotation and an attenuation of the local anomaly, while a conductive host medium causes, mainly, the addition of a “current gathering” component to the anomaly. The importance of the current gathering effect may vary from negligible to enormous as its amplitude and phase depend strongly on the conductivity of the host rock. When a conductive overburden and a moderately conducting host rock are present, both effects may arise. Anomaly enhancement by a conductive host rock is not likely to be advantageous in most prospecting situations, for while the detectability of a target bedrock conductor goes up, the ability to distinguish its anomaly from other weaker conductors is markedly decreased.

Geophysics ◽  
1987 ◽  
Vol 52 (3) ◽  
pp. 301-306 ◽  
Author(s):  
P. K. Gupta ◽  
L. A. Bennett ◽  
A. P. Raiche

The hybrid method for computing the electromagnetic response of a three‐dimensional conductor in a layered, conducting half‐space consists of solving a finite‐element problem in a localized region containing the conductor, and using integral‐equation methods to obtain the fields outside that region. The original scheme obtains the boundary values by iterating between the integral‐equation solution and the finite‐element solution, after making an initial guess based on primary values from the field. A two‐dimensional interpolation scheme is then used to speed the evaluation of the [Formula: see text] to [Formula: see text] Green’s function convolution integrals required by most problems. The two algorithms presented are modifications of the original scheme. Both contain a search routine to identify a set of unique points where the convolution integral evaluations are required. By replacing the two‐dimensional interpolation with a one‐dimensional interpolation and reading the convolution integrals from a reference table, computation time was reduced by up to 70 percent and accuracy was improved. The first algorithm retains the iterative technique for enforcing consistency between the integral‐equation and finite‐element solutions on the boundary of the region. The second algorithm solves the coupled integral‐equation/finite‐element system directly. For some models, the direct method has reduced the computation time to 10 percent of that required by the original scheme. In practice the direct scheme is also more stable.


2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.


2013 ◽  
Vol 391 ◽  
pp. 232-236
Author(s):  
Wen Huan Yang ◽  
Hai Xu Chen ◽  
Shuang Xie ◽  
Chun Ren Fang

A new Multi-degree of freedom motor and its establishing of teeth layer parameters have been introduced in the paper, also including application method of database, namely using Quasi-Newton methods to solve the non-linear equations of the new motors magnetic circuit net, formed a refined method for designing and analyzing of motor. The establishment of 3d tooth layer parameters database, is provided for the calculation in the design of the new type motor conveniently.


1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.


2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Nik Mohd Asri Nik Long ◽  
Lee Feng Koo ◽  
Zainidin K. Eshkuvatov

This paper deals with a nearly circular crack, in the plane elasticity. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over a considered domain, and it is then transformed into a similar equation over a circular region, , using conformal mapping. Appropriate collocation points are chosen on the region to reduce the hypersingular integral equation into a system of linear equations with unknown coefficients, which will later be used in the determination of energy release rate. Numerical results for energy release rate are compared with the existing asymptotic solution and are displayed graphically.


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