SCAIM Seminar: Christoph Schwarzbach

Abstract:

High contrast in electrical conductivity motivates the investigation of electromagnetic methods in geophysics, for instance, for hydrocarbon and mineral exploration. A straightforward approach to modelling the spatial distribution of this parameter within the earth is the assumption of piecewise constant values, defined on a moderately fine tessellation of the volume under investigation by hexahedra or tetrahedra. We study here the solution of the 3-D forward problem for time-harmonic electromagnetic fields using finite elements, based on the above mentioned tessellation. Furthermore, we seek to reconstruct the spatial distribution of conductivity of an overparameterized model by a regularised output least squares approach. Our model assumption, a piecewise constant coefficient, allows for simplifications of the forward solver which eventually lead to an overall faster imaging algorithm. The model assumption also requires special care when the regularisation operator is derived for unstructured meshes within the finite element framework.