Time-lapse inversion of 2D resistivity monitoring data with a spatially varying cross-model constraint

The resistivity method has been used to image the electrical properties of the subsurface. This method has become particularly suitable for monitoring since data could be rapidly and automatically acquired. In this study, we developed a time-lapse inversion algorithm using a spatially varying cross-model constraint for the effective interpretation of resistivity monitoring data. The spatially varying cross-model constraint imposes a large penalty on the model parameters with small changes, but a minimal penalty on the model parameters with large changes compared to the reference model. In addition, we proposed a selective cross-model constraint that can identify all the significant changes over time. The selective cross-model constraint does not penalize the model parameters with significant changes over time regardless of the amount of changes. Through numerical experiments, we can ensure that the developed time-lapse inversion using the spatially varying and selective cross-model constraint can yield a more accurate and focused image that clearly represents the areas with significant changes over time. In addition, we confirm that two major leakage zones have not expanded seriously over time by applying the developed time-lapse inversion in an embankment dam.

Research highlights
► The spatially varying cross-model constraint imposes different weighting factor on the model parameter according to the amount of changes over time.
► The selective cross-model constraint does not penalize the model parameters with significant changes over time regardless of the amount of changes.
► The developed time-lapse inversion using the spatially varying and selective cross-model constraint can yield a more accurate and focused image.