LSJIMP seeks to exploit another type of multiplicity in the data, that between
multiples and primaries. I claimed in Chapter that by
adding the model regularization which differences between images (section
), we expect that information from the multiples can fill
illumination holes or missing trace and also lead to better discrimination
between signal and noise. The veracity of this claim is central to the labeling
of LSJIMP as a ``joint imaging'' algorithm. If false, then we conclude that the
multiples add nothing to the inversion. I ran a simple test to determine what,
if anything, the multiples add to the LSJIMP inversion, I ``turn off'' the
regularization which differences across images by setting
in
equation (
). Figures
-
show the results of this
test.
Figure shows the stack of the estimated
primaries,
, with
, and can be compared directly with
Figure
. Differences are apparent, although subtle.
Generally, we notice a loss of coherency in the estimated multiples (difference
panel).
![]() |
More revealing are Figures and
, which show a zoomed view of two regions
of Figure
, and are directly comparable to
Figures
and
,
respectively. Comparing Figure
to
Figure
, we again note a general decrease in
estimated multiple coherency when
. We also can see that in
regions where multiples overlap primaries, like at 3.7 seconds/1200 meters,
setting
leads to some losses in primary energy. Comparing
Figure
to Figure
, we see that setting
leads to a
generally worse result. Less multiple energy is removed, particularly from some
of the salt-related multiples, like TSPLWB and BSPLWB, and again, the subtracted
energy is less coherent.
![]() |
![]() |
Finally, Figure compares the result of setting
in the prestack sense, at CMP 55 of 750. The left-hand panels
compare the estimated primaries with
and
, while
the right-hand panels compare (after NMO) the data residuals for
and
. The panels are split in half vertically
and clipped at a different value, labeled on the plot, for display purposes.
Comparing the estimated primaries, we see from the small oval that where
multiples and primaries overlap, setting
reduces the quality of
the separation. Primaries are less coherent with offset, and the primary
panel contains some energy corresponding to the seabed pure multiple. From the
larger oval, notice that for the strongest multiples, setting
leads to poorer separation. Comparing the data residuals, we see from the top
pair of ovals that if
, we generally somewhat damage the
primaries, which we expect if we have velocity errors, mis-alignment between
imaged primaries and multiples, or incorrect reflection coefficient. This issue
was discussed earlier, in section
. However, we also
note from the lower pair of ovals, that setting
seems to have
reduced our ability to accurately model the important multiples.
![]() |