The idea is to cross correlate two sequential images in time and to measure the shift in location of the correlation peak. By splitting the images in two and doing the analysis separately for the two parts, we can get an idea whether the shifts that we see are really motion of the whole image.

I analyzed one hour of data from Jan. 18, 1997. It was high-res data and all references to pixels are high-res pixels. The dataset is 1024x500 and so split nicely into two pieces of 512x500 in size. The center positions from the header have a variation of about 0.05 pixels over this time period. One issue is whether these variations are real image motion or are errors in the measurements.

The cross correlation between two images is sharply peaked, which I attribute to granulation. These peaks were fit to a gaussian and the shifts measured in x and y for the hour. Also shown is the first difference of the center positions from the header, which should be comparable to these measurements. We should expect an offset in x of about 0.25 pixels but it is not clear why the measured offsets for the two halves are not the same. From the high correlation between analyses done for the two halves separately, it is clear that we are seeing real image motion. The power spectrum of these signals shows a clear p-mode signature, indicating that the p-modes on the limb sensors as a likely source of the variation.

To get the real position instead of the first difference, I tried integrating the first difference. For the x case, I did the two halves separately and also the average. For the y case, I just did the average. It is difficult to measure the low frequency components from the first difference. We might conclude from this that there are real variations of order .05 pixels on time scales of an hour. There are definitely variations associated with the five-minute oscillations.