4D Inversion of the Resistivity Monitoring Data with Focusing Model Constraint

The resistivity monitoring is a practical method to resolve changes in resistivity of underground structures over time. With the advance of sophisticated automatic data acquisition system and rapid data communication technology, resistivity monitoring has been widely applied to understand spatio-temporal changes of subsurface. In this study, a new 4D inversion algorithm is developed, which can effectively emphasize significant changes of underground resistivity with time. To overcome the overly smoothing problem in 4D inversion, the Lagrangian multipliers in the space-domain and time-domain are determined automatically so that the proportion of the model constraints to the misfit roughness remains constant throughout entire inversion process. Furthermore, a focusing model constraint is added to emphasize significant spatio-temporal changes. The performance of the developed algorithm is demonstrated by the numerical experiments using the synthetic data set for a time-lapse model.