Computation of Electromagnetic Fields Induced by a Point Source in A Multicylindrically
Layered Medium
Xiangrong Yang
Master of Science, September 1997
ABSTRACT
In this paper, we present an algorithm to compute the electric and magnetic
fields induced by an arbitrary point source in a borehole region of a multicylindrically
layered medium. This algorithm can be easily extended to related structures
and has potential applications in the areas of optics, defense, and geophysical
exploration. It also corresponds to finding the Green;s functions to the multicylindrically
layered geometry. It is implemented and tested for any number of layers. The
formalism can be extended easily to the case in which the source location is
in any of the layers.
The approach we take is the following: (I) First, we study the standard results
of closed representations and spectral representation of fields due to a point
source in a homogeneous medium. (II) Then we study reflection and transmission
of waves at a cylindrical interface, a simple recursive algorithm can be obtained
to compute the global reflection and transmission coefficients in all layers.
The electric and magnetic fields in all the regions are determined. (III) We
combine the results from the above two parts to obtain the spectral representations
of all fields due to a point source in a multicylindrically layered medium.
(IV) Finally we apply a numerical strategy to compute all the fields and test
our code over several cases to check the correctness of our implementation.
The ideas employed in this paper are well-known. However, it is the first
time that a complete version of the response due to a point source in multicylindrically
layered medium has bee worked out, moreover, the numerical strategy to compute
the integrals is elegant and new.
Research supported by the Minnesota Center for Industrial
Mathematics (MCIM)
