If we apply fitting goals (9) in an attempt
to create multiple models with about the same level
and type of noise, we obtain the models
seen in Figure . These models
have about the right amplitude of noise but
have a higher frequency noise component than our
The reason for this discrepancy is that the
noise filter does not effectively describe the
noise spectrum in our synthetic. Figure
shows the spectrum of the noise added in our synthetic
test (the noise seen in the left panel of Figure ).
Note how the spectrum outside a very small band is zero.
Emulating this behavior with a filter is nearly impossible
and requires a prohibitively large filter. As a result,
we are limited in what type of noise we can describe by
the practicality of building a filter that accurately captures
Figure 10 Four realizations
using the fitting goals (9). Note
how the amplitude of the noise is consistent with
our synthetic experiment but the spectrum shows
more energy and large wavenumbers.
Figure 11 The spectrum of
the noise added in the synthetic problem shown
in Figures -.