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The results of the previous sections illustrate that nondiffracted
waterbottom multiples (whether from flat or dipping waterbottom) map to
negative subsurface offsets (since in this case), whereas primaries
migrated with slower velocities would map to positive subsurface offsets.
This suggests an easy strategy to attenuate these multiples. Migrate the
data with a constant velocity that is faster than water velocity but slower
than sediment velocity. Keep only the positive subsurface offsets and
demigrate with the same velocity. In principle, the primaries would be
restored (at least kinematically) whereas the multiples would be attenuated.
Although not shown here, the same conclusion can be reached for higherorder
nondiffracted waterbottom multiples.
This strategy, however, would not work for diffracted multiples since
they may map to positive subsurface offsets even when migrated with a
velocity faster than water velocity as illustrated schematically in
Figure . We can still separate
these multiples from the primaries, but that requires the application of an
appropriate Radon transform. An apexshifted tangentsquared Radon transform
was applied by Alvarez et. al. 2004 to a real 2D section
with good results, but the basic assumption there was that of no raybending
at the waterbottom interface. It is expected that the more accurate
equations derived here will allow the design of a better Radon transform and
therefore a better degree of separation between primaries and diffracted
multiples. This is the subject of continuing research.
mul_sktch7
Figure 18 Sketch illustrating that
diffracted multiples may map to positive subsurface offsets.

 
For the nondiffracted multiple from a flat waterbottom the mapping between
the imagespace coordinates and the dataspace coordinates is essentially
2D since , which allowed the computation of closedform expressions
for the residual moveout of the multiples in both SODCIGs and ADCIGs. For
diffracted multiples in particular, it is not easy to compute equivalent
closedform expressions, but we can compute numerically the residual moveout
curves given the expression for in terms of the
dataspace coordinates (t_{m},h_{D},m_{D}), and X_{diff}. In principle,
the dip of the waterbottom can be estimated from the data and the position
of the diffractor corresponds to the lateral position of the apex of the
multiple diffraction in a shot gather as illustrated in the sketch of
Figure .
mul_sktch8
Figure 19 Sketch illustrating the raypaths
of a diffracted multiple in a shot gather. The lateral position of the
diffractor corresponds to the apex of the moveout curve.

 
Next: Conclusions
Up: Alvarez: Multiples in image
Previous: Diffracted multiple
Stanford Exploration Project
11/1/2005