On the theory of electromagnetic induction in the Earth by ocean currents

Abstract

The theory of electromagnetic induction is extended to the case where the driving electric currents must be considered explicitly. Differential equations for independent poloidal magnetic (PM) and toroidal magnetic (TM) modes are derived directly from the governing quasistatic form of the Maxwell equations. They are applied to induction by motional source fields in the ocean by deriving Green functions for the two modes in a constant depth ocean. PM and TM modes are shown to behave in very different ways as a function both of the ocean velocity field dynamics and of the electrical conductivity structure of the earth. TM modes are closely associated with the Coriolis force deflection of water currents and with coastline effects that limit the source currents to the ocean basin. PM modes are induced by nondivergent electric currents that are fully contained within the ocean. Surface gravity waves and a Kelvin wave are examined in detail. The Kelvin wave result of Larsen (1968) is reevaluated, and because the upper lithosphere was modeled as an insulator, significant errors in his magnetic induction values, caused by neglect of the TM mode, are revealed. The sensitivity of the TM mode magnetic field to lithospheric electrical conductivity suggests the use of tidal induced electromagnetic fields to probe the earth's conductivity structure.