Theoretical estimation: 1
The spectral analysis introduced in the previous courses (see Spectral Analysis courses) corresponds to a second order statistics analysis, the Trace Moment analysis is performed on large range of moment
. This allows to determine the statistical moment function
of
over wide range of scale (resolution
). As we have seen in the previous courses the statistical moments of
can be expressed as :

The field
is aggregated at resolution increasingly small
( where
is the highest resolution)
Then, the
function corresponds to the slope of the moments of order
according to
in log-log plot.