#### Abstract

A problem of current interest is the inductive coupling between an ocean, a solid earth conductor and a conductosphere. The anomaly of this configuration is modelled by (i) the inductive response of a system consisting of two thin half planes and an underlying thin whole plane and (ii) the superposition of the responses of two related systems, each consisting of only one of the two half plane and the whole plane. The configuration is two-dimensional, and the planes are perfectly conducting. These two assumptions allow the derivation of rigorous solutions for the induced magnetic fields by conformal mapping methods. A comparison between the anomalies (i) and (ii) permits the determination of the degree of inductive coupling between the idealized conductors. This establishes a reference for estimating the inductive coupling between more realistic conductors and may therefore assist in the interpretation of complicated magnetic variation anomalies in coastal regions. Our substitute configurations can also be used directly for the rapid modelling of the inductive response of the earth in the vicinity of coastlines. This is demonstrated by analyzing some field data from the recent literature.