The electromagnetic fields of a horizontal dipole over a vertically inhomogeneous and anisotropic earth

Abstract

Electromagnetic (EM) field components are expressed as a set of improper integrals, the integrands of which depend upon two impedance functions that satisfy nonlinear differential equations. The components are normalized with factors representing the solution for a homogeneous half‐space having the same conductivity characteristics as the first layer. The normalized components of the magnetic field depend only upon the longitudinal conductivity [Formula: see text]. Their variation with normalized distance [Formula: see text] (actual distance divided by first‐layer skin depth computed using [Formula: see text]) reflects the change of resistivity with depth. The normalized components of the electrical field depend upon both [Formula: see text] and transversal conductivity [Formula: see text] and thus reflect changes with depth of both [Formula: see text] and [Formula: see text]. The examples considered show that anisotropy is felt for small normalized distances. Transition layers result in moderate variation of the field components with [Formula: see text] as compared to stacks of homogeneous layers presenting abrupt changes in electrical properties of the structure.