Cancellation of extraterrestrial magnetic disturbances by taking simple differences between total field readings at spaced stations is imperfect. It is shown that improvement is possible when three component observatory data are available from a single station in the general, but not necessarily immediate, vicinity of an array of total field stations used in a tectonomagnetic study. The local effects of a magnetic disturbance field depend upon its orientation, so that local field differences are more effectively generated by certain orientations of the disturbance field. The orientation of the disturbance field which correlates best with a local difference field is determined by a least-squares method, so that the correlated vector signal can be routinely subtracted from the difference field record. Application of the technique to daily averages of records from three synchronised proton magnetometers on Kilauea volcano reveals a 1.5-nT change in the local field at the time of a flank eruption in May, 1973. This effect was obscured by noise in the raw difference field data. ?? 1979.