Open AccessElectromagnetic fields in a halfspace scattered by a buried sphere by the method of transformation of local elements
Author(s) -
Thio YongChia,
Gleeson Leo John
Publication year - 1979
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1979.tb06784.x
Subject(s) - electromagnetic field , transformation (genetics) , spherical harmonics , coaxial , fourier transform , electric field , mathematical analysis , loop (graph theory) , inversion (geology) , physics , field (mathematics) , geometry , classical mechanics , geophysics , geology , mathematics , engineering , mechanical engineering , paleontology , biochemistry , chemistry , quantum mechanics , structural basin , gene , combinatorics , pure mathematics
Summary. A problem in modelling electromagnetic fields used in exploration geophysics is treated mathematically. Analytical expressions are obtained for the electric field due to a harmonic current in a horizontal loop on or above a conducting ground in which is buried a conductive and permeable sphere (ore body). The loop is coaxial with the sphere. For a general time‐varying current in the loop, the analysis is carried to the stage where a Fourier inversion can be used to obtain readily the electric field in the time‐domain. A new relationship between spherical and cylindrical wave functions is obtained as a transformation of local elements. Solution of this problem has not been presented before in this form. Lee's solution of 1975 which uses an integral‐equation formulation treats a similar problem without taking account of differences in magnetic permeability. The effects of magnetic permeability may have important and useful implications for geophysical explorations.