We have analyzed data from `dense-pack' mosaics of tracked regions of Dopplergrams from each of the four annual MDI Dynamics Campaigns of 1996-99. The dense-pack mosaics consist of regions of 16° extent centred at 7.5° spacings in latitude and longitude, mapped with Postel's projection, tracked for periods of 1664 minutes centred on times when the Carrington longitude of the solar disc central meridian is a multiple of 15°, apodized around circular regions of 15° diameter, and Fourier transformed to obtain local ring-diagram power spectra. For this study we have averaged together successive sets of 8 spectra obtained for the same heliocentric location, e.g. regions at latitude 0° and Carrington longitudes 120°, 105°, ..., 15° on successive `days'. Frequencies as a function of wavenumber k are determined from fits to the average spectra.

The ring-fitting procedure does not yet provide satisfactory uncertainty estimates. In order to estimate the statistical uncertainties in the frequencies we have separately fit six sets of 8-day averaged spectra each, covering two full Carrington rotations in 1996, when the sun was almost uniformly magnetically quiet. The cumulative distribution of fits as a function of the scatter among the six sets for the region at latitude 0 and (central meridian) longitude 0 is shown in Figure 0. For the sake of comparison with succeeding years we have used only frequency estimates for which the scatter in 1996 is less than 0.5 or 0.75 microHz, depending on the number of modes being compared.


The frequencies obtained for the same region (lat 0, lon 0) in 1997 and 1999 exhibit very small differences from those in 1996, with no systematic trends (Figure 1a, c). However, there is a clear trend of increasingly large negative frequency shifts with increasing mode frequency between 1996 and 1998 (Fig. 1b). This effect is exclusively seen in the p-modes (radial order ≥ 1) and especially in those of higher order (Fig 2.); there is no systematic difference in f-mode frequencies at disc center among the years studied.