Spectral analysis of gapped data: Search for mode ₁S₁ at the South Pole

The exigencies of operating an ultralong‐period seismometer/gravimeter at the South Pole have obliged us to search for evidence for the pendulum mode of the earth's inner core as a signal with poor signal‐to‐noise ratio, recorded with lengthy interruptions in the time series. In our method for identifying a weak, almost harmonic time signal in the presence of record gaps, we assume the signal is phase coherent for the full time series across the gaps and perform Fourier analysis of the full data sequence. The signal‐to‐noise ratio is improved by 1/( M ) 1/2 over the case where individual gapped segments are summed, where M is the number of segments. Analysis of the recordings from the South Pole both before and after the Sumbawa earthquake shows no spectral line identifiable with the pendulum mode that is above the noise level.