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 field 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.

The firsi aim of resistivitv survey is a study of any inhomogeneities. Frequently in practice the effect of anisotropy is displayed together with that of layenng or inhomogeneities. It coinplicates data mterpretation witlun the frainework of anisotropic models, and distorts resuits of interpretation in the framework of layered or inliomogeneous media. Ignoring of anisotropy resuits in wrong data interpretation. At the saine time anisotropy studying can give valuable geological information. That means that anisotropy itself and the mutual infinence of anisotropy and inhomogeneities needs to be studied. We have developed the efi'ective spectraJ algorithni for azimuthal resistivity survey (ARS) modeling over two-layercd (and multilayered) media witli the amsotropic basement. Its advantage is in the fact, that the most tabor-consuming part of the decision is carried Out in speetral domain, and then transformation of the decision info real doniain is fuifliled easily and fast for any azimuths. For two-layered model that approach gives the decision as series, when calculation goes fast and with controllable accuracy The spectral approach heips to fulliti more deep and full analysis of the decision. The ARS diagram is a periodic function, and has a discrete spectrum. With the help of ARS spectra the important fact was established: for any array above the anisotropic halfspace or horizontaily layered medium the odd harmonics are absent in the spectrum. These appear only when the current source is lowered on a depth or the array is placed near some inhomogeneities.The spectral approach has atlowed to explain many facts, established earlier for anisotropic media 1 2

In this article, we propose an approach to obtain the equivalent permeability of the fluid-filled inclusions embedded into a porous host in which a fluid flow obeys Darcy's law. The approach consists in the comparison of the solutions for one-particle problem describing the flow inside the inclusion, firstly, by the Stokes equations and then by using Darcy's law. The results obtained for spheres (3D) and circles (2D) demonstrate that the inclusion equivalent permeability is a function of its radius and, additionally, depends on the host permeability. Based on this definition of inclusion permeability and using effective medium method, we have calculated the effective permeability of the double-porosity medium composed of the permeable matrix (with small scale pores) and large scale secondary spherical pores.

The media with joint influence of anisotropy and inhomogeneity have large practical interest. The difficulty of practical anisotropy studying with collinear arrays results from the fact, that anisotropy exhibits itself weaker, than inhomogeneity at equal resistivity contrasts. The relative anisotropy and inhomogeneity influence is considered with the help of mathematical modeling for gentle dipping interface with anisotropic basement. The algorithm is based on the integral equations' method for 3D models with anisotropy. This model is considered for three different directions of strike of dipping interface and strike of anisotropic basement, in comparison with isotropic model of dipping interface and horizontally-layered model with the anisotropic basement. The modeling data are submitted as azimuthal diagrams and results of their spectral analysis. Spectral analysis helps to receive some diagnostic parameters for anisotropic-inhomogeneous media. All resistivity arrays on sensitivity to anisotropy are divided into two groups: collinear arrays (Schlumberger, pole-pole, pole-dipole, dipole axial) with the axes ratio equal λ, and non-collinear arrays (dipole equatorial, T-array, etc.) with sensitivity up to λ 5. Most sensitive to inclined contact is dipole axial array, and it is the least sensitive to anisotropy. The inhomogeneity influence is displayed in the first harmonic of azimuthal diagrams's spectrum, and anisotropy-in the second harmonic. The inhomogeneity also influences on the second harmonic. The absence of the first harmonic (and following odd ones) testifies to absence of inhomogeneity influence. For comparison of relative influence of anisotropy and inhomogeneity, it is necessary to consider the ratio of the sum odd to the sum of even harmonics. When O/E ratio is >1, the inhomogeneity influence prevails, and when <1-the anisotropy influence prevails. At joint influence of basement anisotropy (λ = 2) and dipping interface (dip is 5°), the anisotropy influence prevails only for non-collinear arrays.

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