4D time-lapse ERT inversion: introducing combined time and space constraints

Time-lapse Electrical Resistivity Tomography (ERT) can be used to characterize dynamic processes occurring in the subsurface of the Earth. It involves the installation of a permanent array of electrodes to monitor changes in resistivity associated with changes in pore-water properties (salinity, temperature, water content) or porosity (compaction or dilation). The interpretation of time-lapse data is complicated by both the presence of noise in the data and the influence of low sensitivity in parts of the model. A uniform space and time constraint is not able to address this problem. In this work, we propose a new approach to distinguish noise-related artefacts to true changes in resistivity, while at the same time addressing the problem of the lack of sensitivity of electrical resistivity tomography with depth. We propose transforming the space and time constraints to be active, meaning that the regularization parameters are distributed rather than being uniform for the entire model. This way, both time-related noise (assumed to be random) in the data and the lack of sensitivity are addressed and we can incorporate prior information in a natural way into the inversion scheme. Using this strategy, the inversion scheme is able to favour areas where the expected changes are likely to occur while filtering out areas where no changes should occur. The favoured areas can be either selected from a preliminary analysis of the data, or by incorporating other types of prior information into the system based on the process that is monitored.