scholarly journals A wide‐band integral equation solution for EM scattering by thin sheets

1998 ◽  
Author(s):  
Yoonho Song ◽  
Ki Ha Lee
Keyword(s):  
Integral Equation ◽  
Wide Band ◽  
Thin Sheets ◽  
Em Scattering ◽  
Equation Solution

A robust integral equation solution for electromagnetic scattering by a thin plate in conductive media

Geophysics ◽  
1991 ◽  
Vol 56 (8) ◽  
pp. 1140-1152 ◽  
Author(s):  
P. W. Walker ◽  
G. F. West
Keyword(s):  
Magnetic Field ◽  
Integral Equation ◽  
Electric Field ◽  
Thin Plate ◽  
Current Density ◽  
Scalar Potential ◽  
The Other ◽  
Em Scattering ◽  
Equation Solution ◽  
Host Medium

An integral equation solution for electromagnetic (EM) scattering by a thin plate robustly models scattering in either perfectly resistive, very resistive, or conducting host media. Because the solution is not restricted to modeling certain ranges of host conductivity, it can be used to model scattering over the large ranges in conductivity encountered in geophysics. The solution is developed around a pair of coupled integral equations for the scattering distributions on the plate. In one equation, the scattering distribution is the scalar potential set up by the scattered charge distribution. In the other, it is the component of the scattered magnetic field perpendicular to the plate. The equations are solved numerically using the Galerkin method with simple polynomial basis functions. To find the fields scattered by the conductor, the scattered current density is first calculated from the scalar potential and the magnetic field. The scattered fields can then be found by integrating over the scattered current density. To test the solution, we model horizontal loop EM responses with our solution and compare the results with those from two established integral equation solutions. One of these solutions models pure induction and is used to test our solution when the host is perfectly resistive. Agreement with this solution is very good. Comparisons with the other solution, an electric field integral equation, tests our solution when the host medium is conductive. Agreement with the latter solution is good where induction is not too strong: i.e., where the electric‐field solution is known to work well. Our solution therefore can accurately model EM scattering by a plate in a host medium with any conductivity.

An Efficient Surface Integral Equation Solution to EM Scattering by Chiral Objects Above a Lossy Half Space

2009 ◽  
Vol 57 (11) ◽  
pp. 3586-3593 ◽  
Author(s):  
Ru Shan Chen ◽  
Yun Qin Hu ◽  
Zheng Hong Fan ◽  
Da Zhi Ding ◽  
Dao Xiang Wang ◽  
...  
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Surface Integral ◽  
Em Scattering ◽  
Equation Solution ◽  
Surface Integral Equation

An integral equation representation of wide‐band electromagnetic scattering by thin sheets

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 746-754 ◽  
Author(s):  
Yoonho Song ◽  
Hee Joon Kim ◽  
Ki Ha Lee
Keyword(s):  
Integral Equation ◽  
Frequency Band ◽  
Electromagnetic Scattering ◽  
High Frequency ◽  
Thin Sheet ◽  
Wide Band ◽  
Impedance Method ◽  
Thin Sheets ◽  
Wave Source ◽  
Band Frequency

An efficient, accurate numerical modeling scheme has been developed, based on the integral equation solution to compute electromagnetic (EM) responses of thin sheets over a wide frequency band. The thin‐sheet approach is useful for simulating the EM response of a fracture system in the earth. The focus of this development has been the accuracy of the numerical solution over a wide‐band frequency range of up to 100 MHz. The effect of displacement currents is included to correctly evaluate high‐frequency EM scattering. Currently, EM responses of two thin sheets with different geometrical and electrical properties embedded in a three‐layer earth can be modeled over a frequency band of 10−3 to 108 Hz. The layered earth and the sheets can be electrically dispersive, an important feature that allows analysis of frequency‐dependent characteristics of the model under investigation. The source field can be generated by a remote or local electric or magnetic dipole located on the surface or in a borehole. A plane‐wave source can also be used, and numerical analyses have been made for magnetotellurics and the high‐frequency impedance method.

scholarly journals Integral Equation Solution for Biopotentials of Single Cells

1972 ◽  
Vol 12 (12) ◽  
pp. 1676-1685 ◽  
Author(s):  
Maurice Klee ◽  
Robert Plonsey
Keyword(s):  
Integral Equation ◽  
Single Cells ◽  
Equation Solution
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