4-D inversion of DC resistivity monitoring data acquired over a dynamically changing earth model

Geophysical monitoring is used principally to interpret the locations and amounts of ground condition changes. To achieve these objectives, differences are computed and examined using time-lapse images calculated under the time-invariant static assumption, that any material property changes during the data measurement can be practically ignored. These monitored data, however, can be contaminated with noise and frequently generate false anomalies of ground condition changes. Furthermore, the assumption of the static model can be invalid if the material property changes significantly during data acquisition. To alleviate these problems, we developed a new least-squares inversion algorithm that allows for the subsurface properties to continuously change in time. We define the subsurface structure and the entire monitoring data in the space–time domain, allowing us to obtain a four-dimensional space–time model using just one inversion process. We introduce the regularizations not only in the space domain but also in time, resulting in reduced inversion artifacts and improved stability of the inverse problem. We demonstrated the performance of the proposed algorithm through numerical experiments that assumed several scenarios of ground condition changes and data acquisition sequences. Finally, the applicability to field data was proven by applying the developed algorithm to the monitoring data of crosshole resistivity tomography jointly performed with a dye tracer flooding experiment. This experiment had a small enough scale that we could not ignore the change of material properties during the data measurement.