Predicting and tracking spatiotemporal moments in electrical resistivity tomography

Abstract:

Visualisation is an invaluable tool in the study of near sub-surface processes, whether by mathematical modelling or by geophysical imaging. Quantitative analysis can further assist interpretation of the ongoing physical processes, and it is clear that any reliable model should take direct observations into account. Using electrical resistivity tomography (ERT), localised areas can be surveyed to produce 2-D and 3-D time-lapse images. This study investigates combining quantitative results obtained via ERT with spatio-temporal motion models in tracer experiments to interpret and predict fluid flow.

As with any indirect imaging technique, ERT suffers specific issues with resolution and smoothness as a result of its inversion process. In addition, artefacts are typical in the resulting volumes. Mathematical models are also a source of uncertainty – and in combining these with ERT images, a trade-off must be made between the theoretical and the observed.

Using computational imaging, distinct regions of stable resistivity can be directly extracted from a time-slice of an ERT volume. The automated nature, as well the potential for more than one region-of-interest, means that multiple regions can be detected. Using Kalman filters, it is possible to convert the detections into a process state, taking into account pre-defined models and predicting progression. In consecutive time-steps, newly detected features are assigned, where possible, to existing predictions to create tracks that match the tracer model.

Preliminary studies looked at a simple motion model, tracking the centre of mass of a tracer plume with assumed constant velocity and mean resistivity. Extending the model to factor in spatial distribution of the plume, an oriented semi-axis is used to represent the centralised second-order moment, with an increasing factor of magnitude to represent the plume dispersion. Initial results demonstrate the efficacy of the approach, significantly improving reliability as the information in observations is increased. This is due to increased control over parameter and noise effects, and over balancing measurement with model predictions.