Effective electromagnetic properties of microheterogeneous materials with surface phenomena

In this paper, we present an approach to calculate the complex dielectric permittivity of a micro-heterogeneous medium composed of non-conductive solid inclusions embedded into the conductive liquid continuous host. To take into account the surface effects, we approximate the inclusion by a layered ellipsoid consisting of a dielectric core and an infinitesimally thin outer shell corresponding to an electrical double layer (EDL). To predict the effective complex dielectric permittivity of materials with a high concentration of inclusions, we have modified the Effective Field Method (EFM) for the layered ellipsoidal particles with complex electrical properties. We present the results of complex permittivity calculations for the composites with randomly and parallel oriented ellipsoidal inclusions. To analyze the influence of surface polarization, we have accomplished modeling in a wide frequency range for different existing physic-chemical models of double electrical layer. The results obtained show that the tensor of effective complex permittivity of a micro-heterogeneous medium with surface effects has complicate dependences on the component electrical properties, spatial material texture, and the inclusion shape (ellipsoid aspect ratio) and size. The dispersion of dielectric permittivity corresponds to the frequency dependence for individual inclusion of given size, and does not depend on the inclusion concentration

Improvement to resistivity pseudosection modelling by removal of near-surface inhomogeneity effects : application to a soil system in South Cameroon

Near-surface inhomogeneities (NSIs) can lead to severe problems in the interpretation of apparent resistivity pseudosections because their effects significantly complicate the image aspect. In order to carry out a more efficient and reliable interpretation process, these problematic features should be removed from fied data. We describe a filtering scheme using two-sided half-Schlumberger array data. The scheme was tested on synthetic data, generated from a simple 2D resistivity model contaminated by NSIs, and is shown to be suitable for eliminating such contaminations from apparent resistivity data. Furthermore, the original model without NSIs can be recovered satisfactorily from the inversion of filtered apparent resistivity data. The algorithm is also applied efficiently to a real data set collected at Nsimi, in Southern Cameroon, along a 200-m shallow depth profile crossing a complex transitional zone. For this case, the filtering scheme provides accurate structural and behavioural interpretations of both the geometry of the major soil constituents and the groundwater partitioning. (Résumé d'auteur

2.5-D/3-D resistivity modelling in anisotropic media using Gaussian quadrature grids

We present a new numerical scheme for 2.5-D/3-D direct current resistivity modelling in heterogeneous, anisotropic media. This method, named the 'Gaussian quadrature grid' (GQG) method, cooperatively combines the solution of the Variational Principle of the partial differential equation, Gaussian quadrature abscissae and local cardinal functions so that it has the main advantages of the spectral element method. The formulation shows that the GQG method is a modification of the spectral element method but does not employ the constant elements or require the mesh generator to match the Earth's surface. This makes it much easier to deal with geological models having a 2-D/3-D complex topography than using traditional numerical methods. The GQG technique can achieve a similar convergence rate to the spectral element method. We show it transforms the 2.5-D/3-D resistivity modelling problem into a sparse and symmetric linear equation system that can be solved by an iterative or matrix inversion method. Comparison with analytic solutions for homogeneous isotropic and anisotropic models shows that the error depends on the Gaussian quadrature order (abscissa number) and the subdomain size. The higher the order or the smaller the subdomain size that is employed, the more accurate are the results obtained. Several other synthetic examples, both homogeneous and inhomogeneous, incorporating sloping, undulating and severe topography, are presented and found to yield results comparable to finite element solutions involving a dense mesh.Bing Zhou, Mark Greenhalgh and S. A. Greenhalg

Effective electromagnetic properties of microheterogeneous materials with surface phenomena

In this paper, we present an approach to calculate the complex dielectric permittivity of a micro-heterogeneous medium composed of non-conductive solid inclusions embedded into the conductive liquid continuous host. To take into account the surface effects, we approximate the inclusion by a layered ellipsoid consisting of a dielectric core and an infinitesimally thin outer shell corresponding to an electrical double layer (EDL). To predict the effective complex dielectric permittivity of materials with a high concentration of inclusions, we have modified the Effective Field Method (EFM) for the layered ellipsoidal particles with complex electrical properties. We present the results of complex permittivity calculations for the composites with randomly and parallel oriented ellipsoidal inclusions. To analyze the influence of surface polarization, we have accomplished modeling in a wide frequency range for different existing physic-chemical models of double electrical layer. The results obtained show that the tensor of effective complex permittivity of a micro-heterogeneous medium with surface effects has complicate dependences on the component electrical properties, spatial material texture, and the inclusion shape (ellipsoid aspect ratio) and size. The dispersion of dielectric permittivity corresponds to the frequency dependence for individual inclusion of given size, and does not depend on the inclusion concentration