Coupled hydro-electrokinetic modelling of surface self-potential signals during deep hydraulic injection

SUMMARY Electrokinetic signals, such as surface self-potential (SP) variations, offer a unique window into coupled fluid–electrical processes in the Earth’s crust, yet their quantitative interpretation remains challenging in complex geological settings. In this study, we develop an electrokinetic modelling framework by extending the modified Luco-Apsel-Chen generalized reflection and transmission method to simulate SP responses due to a fluid-injection source in layered geological media. After simulating electric signals, we apply location-specific amplification factors—derived from prior numerical investigations—that account for the effects of steel well casings. This post-processing step enables rigorous comparison with field observations. Using the well-documented deep fluid injection experiment at the Soultz-sous-Forêts geothermal site, we calibrate simulated pore pressure against downhole measurements to derive a realistic source function for direct comparison between modelled and observed SP signals. The model reproduces key spatiotemporal features of the mV-scale SP anomalies and, importantly, captures the observed slower decay of surface SP signals after shut-in despite the rapid decrease in deep pore pressure. Previous field-scale studies have qualitatively attributed this phenomenon to sustained ionic transport; here, our simulation results provide a quantitative demonstration that this process—driven by continued pore-fluid movement—is responsible for the slower SP decay, a mechanism not captured in earlier electrokinetic simulations. These findings provide new mechanistic insight into SP generation in stratified media, demonstrate the essential role of casing effects in field-scale interpretation, and establish a transferable framework for monitoring subsurface fluid flow in geothermal, hydrocarbon and groundwater systems.