Robert Eso

Application of 3D electrical resistivity imaging in an underground potash mine

The potential for water infiltration is a geotechnical hazard in underground mining environments. The electrical conductivity contrast between dry and wet salt make it possible to explore for water infiltrated areas in underground salt mines using electrical resistivity imaging. We present a case history on the application of 3D ERI in an underground potash mine in Saskatchewan, Canada to delineate a water inflow to guide mitigation efforts.

Iterative Reconstruction Algorithm For Non-linear Operators

the goal of geophysical inversion is to recover a model (or suite of models) from some set of observations d. It is often the case that the inverse problem of equation 1 is ill-posed, and solutions must be regularized. Additionally, the data image d is usually contaminated by noise. To overcome these difficulties, the inverse problem is formulated as an optimization problem in which an estimate mrec of the true model m is obtained by minimizing the penalty function

Efficient 2.5D Resistivity Modelling Using a Quadtree Discretization

We explore methods for improving the numerical efficiency to solutions of the 2.5D resistivity forward problem. By employing a quadtree structured mesh discretization, fewer model cells are required in the solution and the volume of interest is easily extended so that zero-flux boundary conditions are satisfied. When these alterations are combined with matrix factorization methods we generate a computationally expedient solution to the 2.5D DC resistivity forward problem. A fast and accurate forward modelling forms the foundation of an inversion. Here we illustrate this by carrying out an inversion on a simulated data set. Introduction DC resistivity is a widely used and important technique in applied geophysics, with applications in mineral exploration (Oldenburg et al. 1997), archaeological investigations (Mauriello et al. 1998) and environmental surveys (LaBrecque and Yang 2001). In a typical experiment, a DC electrical current is injected into the earth, either on the surface or underground, and the resulting potentials are measured at receiver locations. Today most DC experiments are collected with multi-channel receivers which can deploy numerous electrodes and allow the simultaneous measurement of several potentials for a given source location. These systems can result in large data sets. Typically, DC resistivity experiments are interpreted using inversion algorithms, in which a minimum-norm solution is sought, that both matches the observed measurements and satisfies some criterion on its size. Although 3D inversion methodologies have been developed (Li and Oldenburg 2000, Loke and Barker 1996 ), 2D interpretation is still an important and commonly used interpretation technique, allowing a rapid and inexpensive reconnaissance of the subsurface. Also, the 2D formulation serves as a test bed for development of 3D algorithms. The successful application of inversion algorithms hinges on an efficient and accurate solution to the forward problem, in which the potential distribution is calculated given a known distribution of the electrical resistivity. In this paper we describe the solution of the 2.5D DC resistivity equations using a quadtree discretization. This discretization scheme has the potential to greatly reduce the number of cells required in a solution to the forward problem. DC Resistivity The governing equation describing the distribution of electric potential due to the injection of a point source of current into a spatially varying conductivity structure is ) ( )} , , ( ) , , ( { s r r I z y x z y x − − = ∇ ⋅ ∇ δ φ σ (1) where σ is the electrical conductivity in units of S/m, φ is the electric potential expressed as a voltage and I is an injected current at a source location . Although the Earths conductivity structure is s r