Modelling of electromagnetic fields in thin heterogeneous layers with application to field generation by volcanoes - theory and example

When interpreting electromagnetic fields observed at the Earth's surface in a realistic geophysical environment it is often necessary to pay special a ttention to the effects caused by inhomogeneities of the subsurface sedimen tary and/or water layer and by inhomogeneities of the Earth's crust, The in homogeneities of the Earth's crust are expected to be especially important when the electromagnetic field is generated by a source located in a magma chamber of a volcano, The simulation of such effects can be carried out usi ng generalized thin-sheet models, which were independently introduced by Dm itriev (1969) and Ranganayaki & Madden (1980), In the first part of the pap er a system of integral equations is derived for the horizontal current tha t flows in the subsurface inhomogeneous conductive layer and for the vertic al current crossing the inhomogeneous resistive layer representing the Eart h's mantle. The terms relating to the finite thickness of the laterally inh omogeneous part of the model are retained in the equations. This only margi nally complicates the equations, whilst allowing for a significant expansio n of the approximation limits. The system of integral equations is solved using the iterative dissipative method developed by the authors in the period from 1978 to 1988, The method can be applied to the simulation of the electromagnetic field in an arbitr ary inhomogeneous medium that dissipates the electromagnetic energy. When c onsidered on a finite numerical grid, the integral equations are reduced to a system of linear equations that possess the same contraction properties as the original equations. As a result, the rate at which the iterative-per turbation sequence converges to the solution remains independent of the num erical grid used for the calculations. In contrast to previous publications on the method, aspects of the algorithm implementation that guarantee its effectiveness and robustness are discussed here.