Open AccessSolution of the H ‐polarization induction problem by a wavenumber integral equation approach
Author(s) -
Sørensen K.,
Pedersen L. Børsting
Publication year - 1977
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.1977.tb03685.x
Subject(s) - wavenumber , integral equation , mathematical analysis , polarization (electrochemistry) , mathematics , transformation (genetics) , tensor (intrinsic definition) , physics , geometry , optics , chemistry , biochemistry , gene
Summary. The H ‐polarization induction problem is solved in terms of an integral equation, which in the horizontal direction is transformed into the wavenumber domain. By this transformation the usual complicated integral expressions for the Green's tensor elements are removed. By extracting asymptotic features from the system of linear equations, we reduce the number of equations considerably independent of whether the horizontal variation in the conductivity is continuous or discontinuous. Likewise we reformulate the problem so that arbitrary conductivity contrasts may be studied. The method is finally tested by comparing with analytic solutions, and good agreement is achieved. Furthermore the numerical results indicate that a small amount of wavenumbers is required.