Cross-coupled flow modeling of coincident streaming and electrochemical potentials and application to subglacial self-potential data

This study aims to demonstrate that self-potential measurements can yield unique information about subglacial drainage conditions, which has so far been doubtful. At the bed of warm-based glaciers arborescent and distributed drainage systems interact, and streaming and electrochemical potentials coincide. A key secondary aim of this study is, therefore, the development of a mathematical framework for the analysis of self-potentials generated by such interacting flow systems. We consider cross coupling between hydraulic, electrical, and chemical driving forces, and apply the resulting model solution to self-potential data recorded beneath Haut Glacier d'Arolla, Switzerland. We find that (1) the streaming and electrochemical contributions to the total self-potential signal can be separated mathematically, (2) streaming potentials directly reflect the direction of water flow at the glacier bed, (3) combination of streaming potentials with hydraulic conductivity estimates from slug tests allows estimation of in situ subglacial water flow velocities, (4) the subglacial zeta potential, calculated from estimated values of the streaming coupling coefficient, is small (∼-0.022 V) due to systematic flushing of clay minerals from the channel area during the melt season, and (5) uncertainties in exact electrode location in the borehole are unlikely to produce self-potential noise. Self-potential measurements may therefore yield unique information about subglacial drainage conditions, and especially the direction and velocity of in situ subglacial water flow are difficult to obtain by other methods. We further anticipate that our mathematical framework will be applicable to other areas of subsurface hydrology, especially where spatially distributed seepage feeds preferential flow pathways.