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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.

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