Covariance-constrained difference inversion of time-lapse electrical resistivity tomography data

Hydrogeophysics has become a major field of research in the past two decades and time-lapse electrical resistivity tomography (ERT) is one of the most popular techniques to monitor passive and active processes in shallow subsurface reservoirs. Time-lapse inversion schemes have been developed to refine inversion results, but they mostly still rely on a spatial regularization procedure based on the standard smoothness constraint. In this paper, we propose to apply a covariance-based regularization operator in the time-lapse ERT inverse problem. We first illustrate the method for surface and cross-hole ERT with two synthetic cases and compare the results with the smoothness-constrained inversion (SCI). The examples show that the covariance–constrained inversions (CCI) better image the anomaly both in terms of shape and amplitude. Although more important in low-sensitivity zones, improvements are observed everywhere in the tomograms. Those synthetic examples also show that an error made in the range or in the type of the variogram model has a limited impact on the resulting image, which still remains better than SCI. The method is then applied to cross-borehole ERT field data from a heat tracing experiment, where the comparison with direct measurements shows a strong improvement of the breakthrough curves retrieved from ERT. The proposed method could be extended to the time dimension which would allow the use of CCI in 4D inversion schemes.