A novel time-frequency analysis method (S-transform) capable of handling noisy non-stationary signals is applied to study the properties of geomagnetically induced current (GIC) fluctuations in the Finnish natural gas pipeline. New local time- and storm phase-dependent S-transform spectral properties of auroral region GIC fluctuations during geomagnetic superstorms are reported. More specifically, the S-transform spectra have two distinct regions containing the most of the spectral power that persisted from storm to storm: main phase-related wide-band fluctuations driven possibly by a substorm-type ionospheric activity centered around the local midnight and recovery phase-related narrow-band fluctuations associated with Pc5 range geomagnetic pulsations in the local morning region. Based on this observed "stability", a new S-transform-based statistical approach using, for example, an ensemble of different S-transform responses for known storms is proposed for GIC prediction.