General Formulation of the Induction Logging Problem for Concentric Layers about the Borehole

The electromagnetic theory of induction sounding in boreholes is developed for the general case where the formation adjacent to the hole is concentrically stratified with any number of layers. The final solution of the boundary value problem is expressed in the form of an equivalent nonuniform transmission line. Any one or more of the sections can have a radial variation of the electrical properties that is continuous. Previous formulations in the literature are recovered as special cases. We pay special attention to the classic and pioneering work of Doll who developed the geometrical factor concept which is limited to low frequencies and/or small coil spacings.