Numerical modeling of self-potential anomalies due to leaky dams: Model and field examples

Abstract

Substantial self-potential anomalies are known to be associated with zones of discharge in leaky dams. The mechanism for generating these SP anomalies. however, is not well understood. In this paper we apply a two-dimensional computer-code to calculate self-potential anomalies for a model of a leaky dam and then apply the code to some field data for a dam site in the United States. Fluid flow and electrical current flow are coupled processes; that is, there are small currents associated with fluid flow processes and small fluid flows associated with large electrical currents. The processes are connected via crosscoupling terms in Darcy's law and Ohm's law. The coupled equations have been solved numerically for two-dimensional geometry using the finite difference technique. A computer code developed by Sill (1983) is used in this study.

The two-dimensional schematic model for a leaky dam features a leakage zone, a seepage area and an earthen dam structure with physical properties similar to the field case considered below. We consider examples where the depth of the leak, the variation of anomalies with flow path, and the effect of a change in rock type within the dam are examined. In general, the SP profiles show a negative anomaly over the area where the leak is occuring and a positive anomaly over the seep. The relative magnitudes of these anomalies and the shapes of the profiles depend on the location of the sources, the geometry of the flow, and the distribution of physical parameters. Varying the source (leak) depth mainly affects the negative SP anomaly. Shallow leaks produce larger magnitude and more abrupt anomalies, while deeper leaks produce broader and lower amplitude anomalies. Variations in flow paths affect the observed voltages in complex ways. Where the fluid circulates above the leak and then downwards in the seepage area the anomalies seem to be somewhat enhanced. Where the fluid initially flows downwards into the bedrock the anomalies are smaller, especially near the source. A change in coupling coefficient within the dam structure, caused by a fault for example, mainly results in a scaling of the anomalies over the source and seepage in proportion to the magnitude of the change.

SP surveys over the Beaver dam site in Arkansas have similar characteristics to the model studies, they show positive anomalies where seepage is occuring and negative anomalies over leaks. The leakage through the dam seems to be controlled by an east-west graben fault that is associated with a string of negative SP anomalies. Although field data appear considerably more complex than the two-dimensional models considered above we attempt to fit an SP profile that connects the leakage and seepage area using the 2-d code. Model parameters were obtained from previous field surveys and “educated guesses” when no other information was available. A surprisingly good fit was obtained using a very simple model. The only complexity that the model features is a change in SP cross-coupling coefficient associated with the graben fault. The modeling suggests that the SP anomalies are dominantly controlled by the positions of the sources and sinks and not by any complex flow processes.