A comparison of analytic and numerical results for a two-dimensional control model in electromagnetic induction – I. B-polarization calculations

Summary. A conducting slab of finite thickness divided into three segments of different conductivities and overlying a perfect conductor is proposed as a suitable two-dimensional 'control' model for testing the accuracy of the various numerical modelling programs that are available for calculating the fields induced in the Earth by an external, time-varying magnetic source. An analytic solution is obtained for this control model for the case of the magnetic field everywhere parallel to the conductivity boundaries ( B -polarization). Values of the field given by this solution for a particular set of model parameters are calculated at selected points on the surface and on a horizontal plane inside the conductor, and are tabulated to three figure accuracy for reference. They are used to check the accuracy of the results given by the finite difference program of Brewitt-Taylor & Weaver and the finite element program of Kisak & Silvester for the same model. Improved formulae for calculating the derived electric field components in B -polarization are first developed for incorporation in the finite difference program, and these give surface electric fields within 1 per cent of the analytic values, while all three field components inside the conductor are calculated to better than 96 per cent accuracy by the finite difference program. The results given by the finite element program are not quite so satisfactory. Errors somewhat greater than 10 per cent are present and although the program requires much less disk space it takes rather more CPU time to complete the calculations.