Time-varying gravity signals, with their nonlinear, non-stationary and multi-scale characteristics, record the physical responses of various geodynamic processes and consist of a blend of signals with various periods and amplitudes, corresponding to numerous phenomena. Superconducting gravimeter (SG) records are processed in this study using a multi-scale analytical method and corrected for known effects to reduce noise, to study geodynamic phenomena using their gravimetric signatures. Continuous SG (GWR-C032) gravity and barometric data are decomposed into a series of intrinsic mode functions (IMFs) using the ensemble empirical mode decomposition (EEMD) method, which is proposed to alleviate some unresolved issues (the mode mixing problem and the end effect) of the empirical mode decomposition (EMD). Further analysis of the variously scaled signals is based on a dyadic filter bank of the IMFs. The results indicate that removing the high-frequency IMFs can reduce the natural and man-made noise in the data, which are caused by electronic device noise, Earth background noise and the residual effects of pre-processing. The atmospheric admittances based on frequency changes are estimated from the gravity and the atmospheric pressure IMFs in various frequency bands. These time-and frequency-dependent admittance values can be used effectively to improve the atmospheric correction. Using the EEMD method as a filter, the long-period IMFs are extracted from the SG time-varying gravity signals spanning 7 years. The resulting gravity residuals are well correlated with the gravity effect caused by the Earth's polar motion after correcting for atmospheric effects.