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Interpolation of field data in $ f$-$ h$-$ s$

As in the Sigsbee example, we first take the pseudo-primaries in Figure 14, perform a water-velocity normal moveout, and then break the result into $ 150$ overlapping time windows of $ 32$ samples each. These time windows are then Fourier transformed into $ 150 \times 16$ source-offset frequency slices. We then estimate a $ 3
\times 4$ nonstationary PEF that varies every sample along the source and offset axes for each of these slices, and use it to interpolate the corresponding slice of the recorded data with the near-offset gap. For each frequency of each time patch, we use $ 80$ iterations of a conjugate-direction solver both to estimate the PEF and to interpolate the missing data. The data are then transformed back to time, the windows are reassembled, and the NMO correction is reversed. This result is shown in Figure 15.

fieldfx
fieldfx
Figure 15.
Interpolation of field data with a 2D f-h-s PEF using pseudo-primaries. The front face is a constant-offset section, and the side face is a shot. The near offsets appear much more reasonable than the pseudo-primaries in Figure 14. The top and side panels are zoomed in relative to earlier figures in order to emphasize the interpolated values. The image is scaled by $ t^{0.8}$ for display purposes. $ [{\bf CR}]$
[pdf] [png]

The interpolation result in Figure 15 is greatly improved over that in the pseudo-primary data. The most obvious differences between the pseudo-primaries and the interpolated result are that the ringing wavelet has been removed and the polarity of the images differ. The dipping portions of the water-bottom that were not present in the pseudo-primaries were not interpolated. While this gap is much smaller than that in the Sigsbee example, the result is not as impressive. The water bottom, top of salt, bottom of salt, and the associated multiples are reasonably well interpolated, but the subtle stratigraphic reflectors outside of the salt body and the steeply dipping portions of the water bottom are not present in the interpolated result. For example, the diffractions below the bottom of salt reflection or at the edges of salt are not present in the interpolated result. The subtler stratigraphic reflections flanking the salt body are well interpolated, even at later times.
next up previous [pdf]

Next: Pseudoprimaries in 3D Up: Field data example Previous: Pseudo-primary generation from field

2009-04-13