The field induced in a two-layer conductor by a magnetic dipole

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Abstract
The integral solutions giving the electromagnetic field induced within the upper layer of a two-layer conductor by a vertical magnetic dipole are evaluated using an asymptotic expansion suggested by Wait. The method is shown to be applicable when the height of the dipole is a large number of "upper-layer skin depths" above the surface of the conductor, and an expression is derived which gives an estimate of the error involved in retaining only the first term of the expansion. The results are presented in a dimensionless form which depends only on the ratio of the conductivities in the layers. Graphs depicting the variation of the field components within the upper layer of the conductor are plotted for the special case of seawater over dry rock, a situation of practical importance when submerged recording instruments are used to measure geomagnetic field variations at sea. The curves show that a layer of seawater has a strong screening effect on the horizontal magnetic component, but that the vertical magnetic and electric components undergo only a slight attenuation beneath the sea.

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