Induced-polarization modelling using complex electrical conductivities

A numerical technique for induced-polarization (IP) modelling of arbitrary 2-D or 3-D distributions of electrical conductivity is developed. This technique is based on the premise that, due to polarization effects, the conductivity is complex. Complex finite-difference equations are obtained for the complex potential by an elemental volume discretization. The accuracy of the discretization is improved by the application of asymptotic boundary conditions and singularity removal. The resulting linear set of complex equations is symmetric. It is solved by a generalized conjugate gradient method which is speeded up by pre-conditioning techniques. A compact storage scheme fully utilizes the sparsity and the symmetry of the matrix. The complex arithmetic ensures that the resulting values of amplitude and phase angle of apparent resistivity can be directly compared with the measured quantities of a spectral IP survey. Models of a layered half-space and of a buried cube are chosen to demonstrate the good agreement of the apparent resistivity curves with the results from other numerical techniques.