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Forward modelling and inversion of streaming potential for the interpretation of hydraulic conditions from self-potential data Sheffer, Megan Rae


The self-potential method responds to the electrokinetic phenomenon of streaming potential and has been applied in hydrogeologic and engineering investigations to aid in the evaluation of subsurface hydraulic conditions. Of specific interest is the application of the method to embankment dam seepage monitoring and detection. This demands a quantitative interpretation of seepage conditions from the geophysical data. To enable the study of variably saturated flow problems of complicated geometry, a three-dimensional finite volume algorithm is developed to evaluate the self-potential distribution resulting from subsurface fluid flow. The algorithm explicitly calculates the distribution of streaming current sources and solves for the self-potential given a model of hydraulic head and prescribed distributions of the streaming current cross-coupling conductivity and electrical resistivity. A new laboratory apparatus is developed to measure the streaming potential coupling coefficient and resistivity in unconsolidated soil samples. Measuring both of these parameters on the same sample under the same conditions enables us to properly characterize the streaming current cross-coupling conductivity coefficient. I present the results of a laboratory investigation to study the influence of soil and fluid parameters on the cross-coupling coefficient, and characterize this property for representative well-graded embankment soils. The streaming potential signals associated with preferential seepage through the core of a synthetic embankment dam model are studied using the forward modelling algorithm and measured electrical properties to assess the sensitivity of the self-potential method in detecting internal erosion. Maximum self-potential anomalies are shown to be linked to large localized hydraulic gradients that develop in response to piping, prior to any detectable increase in seepage flow through the dam. A linear inversion algorithm is developed to evaluate the three-dimensional distribution of hydraulic head from self-potential data, given a known distribution of the cross-coupling coefficient and electrical resistivity. The inverse problem is solved by minimizing an objective function, which consists of a data misfit that accounts for measurement error and a model objective function that incorporates a priori information. The algorithm is suitable for saturated flow problems or where the position of the phreatic surface is known.

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