Joint Influence of Resistivity Anisotropy and Inhomogeneity for a Single Dipping Interface Between Isotropic Overburden and Anisotropic Basement

Abstract

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.

A comparative evaluation of vertical fractures using different azimuthal electrical resistivity survey arrays

“…Thus, the high sensitivity of this array to identify resistivity anisotropy (Pergavo et al . ) is attested. The results that can be considered valid are those corresponding to model A2, with a = 2 and 3 cm, and to model A5, with a = 4 cm, which yielded Ze / h ≥ 1 (Table ).…”

“…The EDD array recorded the highest apparent resistivity and anisotropy coefficient values, confirming its good sensitivity to detect vertical discontinuities, as observed by other authors (Pergavo et al . ). The square array yields great depths of investigation, making the identification of discontinuities possible with array lengths ( L ) shorter than those obtained with traditional collinear arrays, such as Wenner.…”

“…For the EDD array, the values of λ are higher, between 1.10 and 1.56, suggesting higher sensitivity for detection of vertical resistivity anisotropy, as already observed by other authors (Pergavo et al . ; Chandra ). As expected, the experiments with thinner covers, such as A2, yielded better anisotropy responses.…”

“…This behaviour, known as the paradox of anisotropy (Keller and Frischknecht ; Luling ), has been reported exclusively regarding azimuthal collinear configurations (Pergavo et al . ). However, Watson and Barker () demonstrated that the paradox of anisotropy does not take place in the Wenner array when the thickness of the isotropic cover material ( h ) that overlies the anisotropic fractured rock mass is significant.…”

Electric field modeling in arbitrary anisotropic layered media using the set of Fast Hankel Transformations of integer orders

“…Such a solution corresponds to the angular harmonic decomposition of the azimuthal resistivity diagrams. The analysis of the harmonic coefficients allow separating the heterogeneity and anisotropy effects and estimating the sensitivity to anisotropy of electrical surface arrays and well logging sondes (Bolshakov et al, 1997, Pervago et al, 2001. In this paper we consider the technique for calculating the electric potential in an arbitrary anisotropic multi layered media using the solution expressed by the set of Hankel Transformations of integer orders.…”