ELECTROMAGNETIC INDUCTION IN THIN SHEETS - INTEGRAL-EQUATIONS AND MODEL STUDIES IN 2-DIMENSIONS

The model consists of a thin sheet of variable conductance in one hori zontal direction above a conducting substructure of lateral uniformity . Transition anomalies are permitted, i.e. the anomalous range of vary ing conductance may be bounded by uniform half sheets of different con ductances. For E-polarization the inducing external source field may b e non-uniform. Two complementary integral equations are derived in the frequency-distance domain, to find the anomalous electric field or al ternatively to find the anomalous sheet current density for each polar ization. The equations involve two sets of response functions for the normal structure outside the anomalous range. A first set generates fo r a given source field at ground level the internal magnetic field by induction and the normal electric field which serves as an input funct ion for the derivation of the anomalous field. A second set accounts f or the inductive coupling of the anomalous fields in sheet and substru cture. Various tests are performed: for the compatibility of complemen tary solutions, for the correct asymptotic behaviour at infinity in th e horizontal direction, and for the accuracy of numerical integrations as controlled by the grid-point spacing. The numerical solutions are also tested against analytical solutions and against numerical solutio ns by other methods, in particular with regard to the validity of the thin-sheet approximation. A comparison with results from integral equa tions, which involve conventional Green's functions, reveals in the ca se of B-polarization complications where a strong influx of currents e xists from the substructure into the thin sheet. A source transfer fun ction is introduced which allows the extension of the response functio n concept to induction by non-uniform sources. Two types are studied: a stationary jet field source and a travelling Sq source above a sedim entary basin and a coastline. Resulting magnetotelluric and geomagneti c deep sounding responses are compared with the respective responses, when the inducing field is quasi-uniform.