Multiresolution analysis of active region magnetic structure and its   correlation with the Mt. Wilson classification and flaring activity
  Two different multi-resolution analyses are used to decompose the structure of active region magnetic flux into concentrations of different size scales. Lines separating these opposite polarity regions of flux at each size scale are found. These lines are used as a mask on a map of the magnetic field gradient to sample the local gradient between opposite polarity regions of given scale sizes. It is shown that the maximum, average and standard deviation of the magnetic flux gradient for alpha, beta, beta-gamma and beta-gamma-delta active regions increase in the order listed, and that the order is maintained over all length-scales. This study demonstrates that, on average, the Mt. Wilson classification encodes the notion of activity over all length-scales in the active region, and not just those length-scales at which the strongest flux gradients are found. Further, it is also shown that the average gradients in the field, and the average length-scale at which they occur, also increase in the same order. Finally, there are significant differences in the gradient distribution, between flaring and non-flaring active regions, which are maintained over all length-scales. It is also shown that the average gradient content of active regions that have large flares (GOES class 'M' and above) is larger than that for active regions containing flares of all flare sizes; this difference is also maintained at all length-scales. 
J. Ireland, C.A. Young, R.T.J. McAteer, C. Whelan, R.J. Hewett, P.T.   Gallagher