ASPECTS OF CHARGE ACCUMULATION IN d. c. RESISTIVITY EXPERIMENTS¹

Abstract

LI, Y. and OLDENBURG, D.W. 1991. Aspects of charge accumulation in d.c. resistivity experiments. Geophysical Prospecting 39, 803-826. When an electric current is introduced to the earth, it sets up a distribution of charges both on and beneath the earth's surface. These charges give rise to the anomalous potential measured in the d.c. resistivity experiment. We investigate different aspects of charge accumulation and its fundamental role in d.c. experiments. The basic equations and boundary conditions for the d.c. problem are first presented with emphasis on the terms involving accumulated charges which occur wherever there is a non-zero component of electric field parallel to the gradient of conductivity. In the case of a polarizable medium, the polarization charges are also present due to the applied electric field, yet they do not change the final field distribution. We investigate the precise role of the permittivity of the medium. The charge buildup alters the electric fields and causes the refraction of current lines; this results in the well-known phenomenon of current channelling. We demonstrate this by using charge density to derive the refraction formula at a boundary. An integral equation for charge density is presented for whole-space models where the upper half-space is treated as an inhomogeneity with zero conductivity. The integral equation provides a tool with which the charge accumulation can be examined quantitatively and employed in the practical forward modelling. With the aid of this equation, we investigate the effect of accumulated charges on the earth's surface and show the equivalence between the half-space and whole-space formulations of the problem. Two analytic examples are presented to illustrate the charge accumulation and its role in the d.c. problem. We investigate the relationship between the solution for the potential via the image method and via the charge density. We show that the essence of the image method solution to the potential problem is to derive a set of fictitious sources which produce the same potential as does the true charge distribution. It follows that the image method is viable only when the conductivity structure is such that the effect of the accumulated charge can be represented by a set of point images. As numerical examples, we evaluate quantitatively the charge density on the earth's surface that arises because of topography and the charge density on a buried conductive prism. By these means, we demonstrate the use of the boundary element technique and charge density in d.c. forward modelling problems.

Parameter sensitivity maps of surface geoelectric arrays I. Linear arrays

“…Since the surface change density τ on a resistivity interface k = − 1 + 1 is τ = 2ε 0 kE b (where ε 0 is the dielectric constant, E b is the normal component of the electric field in absence of the interface, as it was shown by Li and Oldenburg 1991), the components i (i = x, y, z) of the dipole moment p, corresponding to the cube, are as follows:…”

Sensitivity of electrical resistivity tomography data to electrode position errors

“…To evaluate the derivative on the delta function, we expand to Poisson's equation and apply the wholespace Green's function for the Laplacian to obtain the integral solution for the sensitivity of wholespace potential φ 0 to the source position: This equation is a scattering‐type equation with a homogeneous primary term and a secondary integral scattering term. Not only does the sensitivity depend on the source‐receiver separation, but it also depends on the location and magnitude of contrasts in electrical conductivity due to the phenomenon of charge accumulation (Li & Oldenburg 1991).…”

Apparent formation factor for leachate-saturated waste and sediments: Examples from the USA and China

“…Bernstone et al (2000) noted that even in MSW landfills containing significant metal and clay content, moisture dominates electrical conductivity. Based on the model of Li and Oldenburg (1991), they suggested that the moisture in the waste results in "currents being channeled into regions of high conductivity and deflected away from resistive regions. This deflection means that the electric current in the waste will be not only strongly controlled by the amount of salinity and the pore electrolytes but also on the tortuosity of the pore space and the proportion of dispersed conducting waste".…”