  Two series of solar-granulation images -- the La Palma series of 5 June 1993
and the SOHO MDI series of 17--18 January 1997 -- are analysed both
qualitatively and quantitatively. New evidence is presented for the existence
of long-lived, quasi-regular structures (first reported by Getling and Brandt
(2002)), which no longer appear unusual in images averaged over 1--2-h time
intervals. Such structures appear as families of light and dark concentric
rings or families of light and dark parallel strips (``ridges'' and
``trenches'' in the brightness distributions). In some cases, rings are
combined with radial ``spokes'' and can thus form ``web'' patterns. The
characteristic width of a ridge or trench is somewhat larger than the typical
size of granules. Running-average movies constructed from the series of images
are used to seek such structures. An algorithm is developed to obtain, for
automatically selected centres, the radial distributions of the azimuthally
averaged intensity, which highlight the concentric-ring patterns. We also
present a time-averaged granulation image processed with a software package
intended for the detection of geological structures in aerospace images. A
technique of running-average-based correlations between the brightness
variations at various points of the granular field is developed and indications
are found for a dynamical link between the emergence and sinking of hot and
cool parcels of the solar plasma. In particular, such a correlation analysis
confirms our suggestion that granules -- overheated blobs -- may repeatedly
emerge on the solar surface. Based on our study, the critical remarks by Rast
(2002) on the original paper by Getling and Brandt (2002) can be dismissed.
