The nature and accuracy of the deductions that can be drawn about the distribution of conductivity within the earth from surface measurements of natural magnetic variations and earth currents are considered. Both the magnetic variations method and the magnetotelluric method are based essentially on calculating the currents induced in some model distribution by a given inducing field, and adjusting the parameters of the model to make the calculated results agree with observations. But up to now only a few relatively simple problems in electromagnetic induction have been satisfactorily solved, and interpretations of observed values have sometimes been based on the solution of problems which do not adequately represent important features of the physical situation.Global problems and local problems are distinguished and the different types of mathematical problems that arise in the two cases are considered.Magnetotelluric profiling has been largely based on a simple theoretical model which treats the electromagnetic field as uniform over any horizontal plane and therefore ignores the nature and dimensions of the ionospheric inducing field. This is not justifiable and leads in some physically probable situations to serious overestimates of the conductivity.
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A. T. Price (1964) studied this question.