Group theoretic reduction of the electromagnetic impedance matrix for large-contrast symmetric prisms in a layered earth

Calculation using integral equations of the electromagnetic response of a geologic body which is much more conductive than the surrounding media requires the use of both current pulse and current tube basis functions. The impedance matrices for such cases can be large and expensive to form, factor, and solve. However, if the surrounding media is layered and the scatterer is symmetric under symmetry operations which preserve the depth of transformed points, then we can apply group representation theory to drastically reduce storage and computation requirements. I discuss this application of group representation theory in detail, using the symmetry groupC₂ for purposes of illustration. In a sample calculation for a body which is invariant under the symmetry operations of the groupC₂, storage was reduced by a factor of 4, matrix formation time was reduced by a factor of 2, and the sum of matrix factorization and solution times was reduced by a factor of 10.