Magnetic field calculation of time varying vertical and horizontal electric current dipoles in a conducting half space via the T -Ω method

The solution of eddy current field problems in geometries with unbounded surfaces is generally quite difficult. Any discretization of volume space as suggested in a finite element or finite difference technique is ruled out as numerically unrealizable. Integral techniques allow an equivalent discretization of a surface with the added advantage of reducing the number of unknowns from N³to N². Representation of the magnetic field intensity as a vector plus the gradient of a scalar (T-Ω representation) lends itself to the integral formulation and to the matching of boundary conditions. The application of the T-Ω method to the problem of time varying vertical and horizontal dipoles imbedded in a conducting infinite half space is discussed. The theoretical formulation is laid out and the numerical results are compared to known exact solutions via Sommerfeld integral equations. Also the accuracy of the integral technique at high frequencies is investigated with the results compared to analytical surface wave expressions.