A worldwide network of superconducting gravimeters (SGs) is presently running under the coordination of the Global Geodynamics Project (GGP). SGs have proved in the past to be suited for the study of the long-period seismic and sub-seismic modes. The present paper provides some evidence of these results through the analysis of the noise levels at GGP stations in the seismic and sub-seismic frequency bands and the study of the 2001 Mw=8.4 Peru earthquake. The knowledge of the noise level at each station is important in a number of studies that combine the data of several stations to determine global Earth parameters. One example is the stacking of the data in the search for the gravity variations associated with the translational mode of the solid inner core (Slichter mode). Synthetic signals are first used to estimate the possible detection of this degree-one mode with SGs and a stacking method is tested. This method is then applied to the gravity residuals from the GGP records after the Peruvian earthquake.