Application of an extended Kalman filter approach to inversion of time-lapse electrical resistivity imaging data for monitoring recharge

We apply an extended Kalman filter (EKF) approach to inversion of time-lapse electrical resistivity imaging (ERI) field data. The EKF is a method of time series signal processing that incorporates both a state evolution model, describing changes in the physical system, and an observation model, incorporating the physics of the electrical resistivity measurement. We test the feasibility of using an EKF approach to inverting ERI data collected with 2-D surface array geometries. As a first test, we invert synthetic data generated using a simulated recharge event and water saturation distributions converted to electrical conductivity values using an Archie's law relationship. In the synthetic example we demonstrate the impact that the noise structure of the state evolution and the regularization weight have on EKF-estimated model parameters and errors. We then apply the method to inversion of field data collected to monitor changes in electrical conductivity beneath a recharge pond that is part of an aquifer storage and recovery project in northern California. Using lines of electrodes buried at a depth of 0.25 m when the base of the pond is dry, we monitor the wetting front associated with the diversion of stormflow runoff to the pond. Using field data, we demonstrate that by oversampling in time, we are able to apply the so-called random walk model for the state evolution and to build the model of observation noise directly from collected data. EKF-estimated values track changes in conductivity associated with both increasing water content in subsurface sediments and changes in the properties of the pore water, showing the method is a feasible approach for inversion of time-lapse ERI field data.