Electromagnetic induction in the earth by an aperiodic non-uniform current source.

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Abstract
Electromagnetic induction in a two-dimensional earth by a non-uniform, spatially varying, aperiodic current source is considered. The two-dimensional diffusion equation (for the E-polarization case) is solved by a separation of variables and is related to the current source by a Fourier integral which synthesizes the actual fields from elementary fields with time dependence exp (iωt) over a horizontally stratified earth. An aperiodic source is obtained by summing the single frequency solutions in a Fourier transformation. The spatial variation is achieved by superimposing the electromagnetic fields of separate aperiodic, non-uniform current sources which vary independently with time. Variations of the magnetic field components with time at the surface of the earth are studied.

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