Constrained Time-Lapse Resistivity Imaging Inversion

Abstract

Changes in the subsurface resistivity with time are frequently measured by conducting 2D or 3D resistivity imaging surveys over the same area at different times. Examples of such studies include mapping the flow of water through the unsaturated zone, changes in the aquifer saturation due to water extraction, subsurface flow of chemical pollutants and leakage from dams. One common technique to interpret the data from such surveys is carry the inversion of each data set individually and then determine the relative changes in the subsurface resistivity from the differences in the resulting models. This approach can lead to artifacts in the sections showing the relative changes in the subsurface resistivity. In order to reduce such artifacts, a joint inversion technique that uses the results from the inversion of the first data set as a reference model to constrain the inversion of the later time data sets is used. Several types of cross-model constrains are examined. They are the simple damped or Marquardt constrain, the l2 norm least-squares smoothness constrain and the l1 norm or robust constrain. By using the appropriate cross-model constrain, artifacts in the sections showing the relative changes in the subsurface resistivity can be significantly reduced. Where the changes in the model resistivity values are expected to vary spatially in a gradual manner, the l2 norm constrain is more appropriate. When the changes have sharp boundaries, the l1 norm constrain gives better results. In cases where the relationship between the resistivity of the subsurface material and water content follows Archie’s Law, the change in the water saturation can be estimated from the change in the model resistivity.