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Conductivity and resistivity tensor rotation for surface impedance modeling of an anisotropic half‐space
Author(s) -
Wilson Glenn A.,
Thiel David V.
Publication year - 2002
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/2001rs002535
Subject(s) - anisotropy , tensor (intrinsic definition) , isotropy , electrical resistivity and conductivity , rotation (mathematics) , conductivity , condensed matter physics , geometry , electrical impedance , materials science , physics , optics , mathematics , quantum mechanics
The electromagnetic surface impedance of a half‐space with inclined conductivity anisotropy can be derived from the isotropic half‐space solution provided the conductivity term used in the expressions is the effective horizontal conductivity. For a TM‐mode plane wave incidence, the effective horizontal conductivity must be derived from the tensor rotation of the resistivity tensor and not from the tensor rotation of the conductivity tensor. For a TE‐mode incident with the same geometry as the TM‐mode, the surface impedance is independent upon the inclined anisotropy. This same formulation can then be extended to a multiple layered half‐space where each layer has an inclined anisotropy. For an anisotropic half‐space with coefficient of anisotropy of 4, with a horizontal conductivity of 0.001 S/m inclined at 45° with respect to the horizontal plane, the magnitude of the surface impedance calculated using the resistivity tensor rotation is approximately 53% larger than the magnitude of the surface impedance calculated using the conductivity tensor rotation.