Singular solutions to Maxwell's equations and their significance for geomagnetic induction

Abstract

In conclusion we may state that the correctness of Summers' (1982) response curves must be questioned. The main reason for this is that a dramatic increase of the anomalous field for decreasing frequency, i.e. towards the resistive limit is required. Intuitively, such response characteristics appear highly unusual. As demonstrated by the present discussion, its theoretical justification is likewise difficult. It is therefore suggested that Summers' numerical results be checked against analytical solutions. Kertz's (1960) cylindrical body seems very appropriate for this and also resembles the configuration discussed by Summers (1982) very closely. As the cylinder is embedded into a non-conducting medium, spurious channelling effects are excluded and induction is strictly local. Consequently, Kertz's response curves are as expected, i.e. frequency independence is confined to the high-frequency limit. An easy test of the accuracy of Summers' numerical code is therefore possible, and the character and frequency range of the discrepancies between the two solutions can be determined.