Electromagnetic Induction in Thin Finite Sheets Having Conductivity Decreasing to Zero at the Edge, with Geomagnetic Applications--II

Electromagnetic induction in a perfectly conducting spherical shell covered by a concentric non-uniformly conducting hemispherical shell by an external magnetic field is considered. The two conductors represent the Earth's conductivity and a large ocean respectively. The integrated conductivity of the outer shell is axisymmetric and reaches a maximum before tending to zero at the edge, hence it is continuous there. The parameters of the problem allow for the consideration of the effects of different periods of variation, different depths of the conducting core and different locations of the edge of the continental shelf. Spherical harmonics are used and the properties of certain vector functions involving Legendre functions are given. The problem is then reduced to the solution of an infinite system of linear equations. The effects of a uniform inducing field are considered in the two cases when its direction is either parallel or normal to the axis of symmetry. The results indicate that the components of the observed field are enhanced in sea and land in the vicinity of the coastline. This enhancement is more pronounced if the continental shelf is near the coastline and for the shorter periods of variations. The effect of taking the Earth's conductivity into account is to reduce the enhancement of the field near the coast. The analysis and the computer program can both be adapted to allow for the estimation of the modification to the external field at any particular station with no conductivity anomaly in the vicinity.