Seismic history matching is the process of modifying a reservoir simulation model to reproduce the observed production data in addition to information gained through time-lapse (4D) seismic data. The search for good predictions requires that many models be generated, particularly if there is an interaction between the properties that we change and their effect on the misfit to observed data. In this paper, we introduce a method of improving search efficiency by estimating such interactions and partitioning the set of unknowns into noninteracting subspaces. We use regression analysis to identify the subspaces, which are then searched separately but simultaneously with an adapted version of the quasiglobal stochastic neighborhood algorithm. We have applied this approach to the Schiehallion field, located on the UK continental shelf. The field model, supplied by the operator, contains a large number of barriers that affect flow at different times during production, and their transmissibilities are highly uncertain. We find that we can successfully represent the misfit function as a second-order polynomial dependent on changes in barrier transmissibility. First, this enables us to identify the most important barriers, and, second, we can modify their transmissibilities efficiently by searching subgroups of the parameter space. Once the regression analysis has been performed, we reduce the number of models required to find a good match by an order of magnitude. By using 4D seismic data to condition saturation and pressure changes in history matching effectively, we have gained a greater insight into reservoir behavior and have been able to predict flow more accurately with an efficient inversion tool. We can now determine unswept areas and make better business decisions.