A recording obtained at the Coachella Canal Engine House No. 4 of the October 15, 1979, Imperial Valley earthquake shows a dominant 2 Hz frequency. This feature is very unusual and an attempt has been made to determine if the recording is real or spurious. As the pumping station is a small heavily constructed bunker type of structure located on material of low shear wave velocity it was considered likely that soil-structure interaction might be responsible for the 2 Hz component. However, both an experimental and theoretical investigation fail to establish this. This report describes the theoretical investigation. The experimental investigation is described in a separate open-file report.