Low Frequency, Motionally-induced Electromagnetic Fields in the Ocean, Part 1: Theory.

The theory of electromagnetic induction by motional sources in the ocean is examined from a first principles of view. The electromagnetic field is expanded in poloidal and toroidal magnetic modes based on the Helmholtz decomposition. After deriving a set of Green functions for the modes in an ocean of constant depth and conductivity underlain by an arbitrary one-dimensional conducting earth, a set of exact integral equations are obtained which describe the induction process in an ocean of vertically-varying conductivity. Approximate solutions are constructed for the low frequency (subinertial) limit where the horizontal length scale of the flow is large compared to the water depth, the effect of self induction is small, and the vertical velocity is negligible, explicitly yielding complex relationships between the vertically-integrated, conductivity- weighted horizontal water velocity and the horizontal electric and magnetic fields and accounting for interactions with the conductive earth.