S U M M A R YA 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 finitedifference 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.
Complex electrical conductivity tomography has been applied to monitor hydraulic experiments in a research facility for in-situ remediation of contaminated soils and aquifers. Arrays of electrodes were installed in a flume where infiltration experiments with non-aqueous phase liquids (NAPL) were performed. Data sets of about 500 configurations have been acquired with a computer-controlled equipment for spectral induced polarization. The tomographic algorithm used for interpretation is based on the simultaneous iterative reconstruction technique (SIRT). As in other inversion techniques, the Jacobian or sensitivity matrix has to be known. The three-dimensional forward modelling is performed by the ftite difference method using complex values of conductivity and potential. The resulting tomographic images show the distribution of complex conductivity inside the tanks. They reflect both the spatial variability of soil and aquifer properties and changes between different stages of the experiments. These images were successfully used to determine the state of the multiphase system consisting of silicate matrix, water, NAPL and air. 745 Downloaded 06/21/16 to 128.210.126.199. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/ 746 Downloaded 06/21/16 to 128.210.126.199. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.