HR: 14:55h
AN: NS13A-06    [Abstracts]
TI: 3-D Inversion of Self-Potential Data to Recover Hydraulic Head
AU: * Sheffer, M
EM: msheffer@eos.ubc.ca
AF: University of British Columbia, 6339 Stores Road, Vancouver, BC V6T 1Z4, Canada
AU: Oldenburg, D
EM: doug@eos.ubc.ca
AF: University of British Columbia, 6339 Stores Road, Vancouver, BC V6T 1Z4, Canada
AB: The self-potential method may be used to assess subsurface flow conditions in response to the electrokinetic phenomenon of streaming potential, where fluid flow through porous media generates electrical current flow. Of particular interest is inversion of the electrical potential data to evaluate the 3-D distribution of hydraulic head. As a first step, we have developed an efficient 3-D forward modelling algorithm that enables us to determine the SP distribution resulting from a saturated, or variably saturated, flow model and a known distribution of electrical properties, namely the electrical conductivity and cross-coupling conductivity coefficient. The study region is divided into a discrete rectangular mesh, in which hydraulic head and electrical properties are defined for each cell. Discrete equations are formulated using the method of finite volumes and the forward problem, which is a linear relationship between the electrical potentials and hydraulic head, is solved using a preconditioned biconjugate gradient stabilized method. In the inverse problem we are supplied with measured electrical potentials and our goal is to estimate the causative 3-D model of hydraulic head. We assume fully saturated conditions, such that the electrical properties are not a function of hydraulic head. The earth model is divided into rectangular cells, each of which is assigned constant values of the electrical properties. In practice, these must be obtained through additional analysis, but the cross-coupling conductivity coefficient may usually be estimated since it varies over a small range, and electrical conductivity may be characterized using DC resistivity survey techniques. Since the number of available SP data is usually less than the number of grid cells we are faced with a typical underdetermined inverse problem. We solve the inverse problem by minimizing an objective function that consists of a data misfit and a model objective function. The data misfit is weighted according to the measurement error. A priori information is incorporated into the solution via the model objective function. We use a Tichonov-type regularization technique to balance fitting the data with fitting a chosen reference head model. The algorithm is tested using measured data collected in a laboratory tank experiment that simulates flow under a cut-off wall.
DE: 0545 Modeling (4255)
DE: 0903 Computational methods: potential fields (1214)
DE: 0925 Magnetic and electrical methods (5109)
DE: 1835 Hydrogeophysics
DE: 3260 Inverse theory
SC: Near-Surface Geophysics [NS]
MN: 2007 Fall Meeting