Regional induction in Scotland: an example of three-dimensional numerical modelling using the thin sheet approximation

Abstract

A new algorithm recently devised for the solution of three-dimensional problems of electromagnetic induction by a uniform source in a non-uniform thin sheet at the surface of a conducting half-space is used in a numerical study of regional induction in Scotland. Limitations imposed by grid size and the conductivity of the lower crust restrict the investigation to short periods and for comparison with the published results from a recent magneto-telluric survey of Scotland, a period of 25 s is chosen here. The variations of the field components along parallel traverses across Scotland are plotted for two perpendicular polarizations of the inducing field. The coastlines and other conductivity structures included in the model, notably the Great Glen fault, are clearly revealed by these plots and the importance of vertical as well as horizontal deflections of the induced currents at a conductivity discontinuity is demonstrated. Real induction vectors are drawn at a number of grid points whose positions correspond approximately to the sites of actual field stations. Agreement with the corresponding induction vectors given by the field data is quite good at the coastal stations and near the Great Glen fault, but otherwise the calculated vectors at inland stations are much shorter than those obtained from field data. Apparent resistivities, phases and the azimuth of the major principal axis of impedence are also calculated for each site but there is poor agreement with measured values which show a greater degree of anisotropy. It seems that for many sites the numerical grid is too coarse to model the surface conductivity distribution in sufficient detail to provide realistic estimates of these parameters.