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Saturn's C ring contains multiple structures that appear to be density waves driven by time-variable anomalies in the planet's gravitational field. Semi-empirical extensions of density wave theory enable the observed wave properties to be translated into information about how the pattern speeds and amplitudes of these gravitational anomalies have changed over time. Combining these theoretical tools with wavelet-based analyses of data obtained by the Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft reveals a suite of structures in Saturn's gravity field with azimuthal wavenumber 3, rotation rates between 804 degrees/day and 842 degrees/day and local gravitational potential amplitudes between 30 and 150 cm^2/s^2. Some of these anomalies are transient, appearing and disappearing over the course of a few Earth years, while others persist for decades. Most of these persistent patterns appear to have roughly constant pattern speeds, but there is at least one structure in the planet's gravitational field whose rotation rate steadily increased between 1970 and 2010. This gravitational field structure appears to induce two different asymmetries in the planet's gravity field, one with azimuthal wavenumber 3 that rotates at roughly 810 degrees/day and another with azimuthal wavenumber 1 rotating three times faster. The atmospheric processes responsible for generating the latter pattern may involve solar tides.