Resistivity inversion in 2-D anisotropic media: numerical experiments

Abstract

Many rocks and layered/fractured sequences have a clearly expressed electrical anisotropy although it is rare in practice to incorporate anisotropy into resistivity inversion. In this contribution, we present a series of 2.5-D synthetic inversion experiments for various electrode configurations and 2-D anisotropic models. We examine and compare the image reconstructions obtained using the correct anisotropic inversion code with those obtained using the false but widely used isotropic assumption. Superior reconstruction in terms of reduced data misfit, true anomaly shape and position, and anisotropic background parameters were obtained when the correct anisotropic assumption was employed for medium to high coefficients of anisotropy. However, for low coefficient values the isotropic assumption produced better-quality results. When an erroneous isotropic inversion is performed on medium to high level anisotropic data, the images are dominated by patterns of banded artefacts and high data misfits. Various polepole, pole-dipole and dipole-dipole data sets were investigated and evaluated for the accuracy of the inversion result. The eigenvalue spectra of the pseudo-Hessian matrix and the formal resolution matrix were also computed to determine the information content and goodness of the results. We also present a data selection strategy based on high sensitivity measurements which drastically reduces the number of data to be inverted but still produces comparable results to that of the comprehensive data set. Inversion was carried out using transversely isotropic model parameters described in two different co-ordinate frames for the conductivity tensor, namely Cartesian versus natural or eigenframe. The Cartesian frame provided a more stable inversion product. This can be simply explained from inspection of the eigenspectra of the pseudo-Hessian matrix for the two model descriptions.

Resistivity inversion of transversely isotropic media

“…Estimation of subsurface conductivity distribution from measurement requires inversion. There are many algorithms and methods available in the literature for this purpose (e.g., Pain et al, 2003;Herwanger et al, 2004;LaBrecque et al, 2004;Kim et al, 2006;Greenhalgh et al, 2009b;Wiese et al, 2015). The forward 2D DC FD method can be formulated as the following matrix notation: d=G(m) (11) where G is a nonlinear forward operator, m is a parameter vector, and d is an observation vector (Meju, 1994).…”

“…Anisotropic inversion is not new in resistivity methods: Pain et al (2003), Herwanger et al (2004), LaBrecque et al (2004), Kim et al (2006), and Wiese et al (2015) have studied the inversion method within electrically anisotropic media for different types of applications. LaBrecque et al (2004) studied 3D resistivity inversion using surface DC data.…”

Ultraviolet laser-induced voltage in anisotropic shale

“…Various studies of anisotropic formations and rocks have been taken in the laboratory to provide a basis to interpret the EM logging data [10,11]. However, for DC resistivity methods, anisotropy is seldom incorporated into practical investigations owing to various reasons such as problems of electrical equivalence, the limitation in resolution capability of the geoelectric field, and the increase of parameters to be recovered from the data [12]. Moreover, due to the insulation characteristics caused by pores, cracks as well as the complex composition, it is difficult to measure the anisotropic electrical properties of shales directly by using a conventional DC power in the laboratory.…”

Interpretation of deep directional resistivity measurements acquired in high-angle and horizontal wells using 3-D inversion

“…The size of these problems has often been considered excessively large to be solved in real time for practical applications, thereby preventing the widespread use of full 3D methods for the interpretation of borehole induction measurements. Many of the published borehole induction modelling methods take advantage of the axial symmetry of formation geometry and employ 2D or 2.5D modelling and inversion algorithms (Pardo et al 2006;Abubakar et al 2008;Wang et al 2009;Pardo et al 2013;Wiese et al 2015). Other approximations have been employed as well to limit the large number of model parameters and to mitigate the computational cost of inversion.…”