I am not sure what the question here is. If all you need to check is whether there is a correlation between mean depth and radius, just convert your Cartesian coordinates to polar using:
[THETA,RHO] = cart2pol(X,Y)
then just do not use theta ... which is effectively
So then you would just plot RHO vs Mean Depth for a scatter plot, and do any sort of correlation analysis you want with RHO as your x and Mean Depth as your y.
If then you want to plot it, you will plot using:
but instead use:
so you will plot rings instead of points.