APPENDIX C - preprocessing details

I first applied better tuned f-k filters, then shifted the data 9 meters across offset using a frequency-domain operator. Why? The migration program Phase requires data to be regularly sampled to contain the zero offset. The minimum offset of the data was 241m and the offset sampling was 50m (interpolated to 25), so there was no way of having both the zero offset and regularly sampled data. Worse, Phase requires split-spread data, so half of the offsets would have been off by 9 meters. I then performed f-x decon to eliminate random noise. I interpolated the offsets from a sampling rate of 50m (visible aliasing) to 25m in the wavenumber domain. I performed deconvolution using Pef and Helicon. I had to apply again f-k filters with new parameters to eliminate some of the effects of former aliasing, which turned into spurious events after interpolation.

Figures and show the smallest non-extrapolated offset before and after the new preprocessing, respectively. The railroad-track reflections above 1.5 seconds, which is actually water-velocity noise, is eliminated and the geology beneath is uncovered (due to the dip filters). The strong ringing which multiplied reflectors most visibly in the high-amplitude region is gone (due to deconvolution). The signal/noise ratio between 3 and 5 seconds is highly improved (due to the f-x decon). After the new preprocessing, the stratigraphy looks much more interpretable and new, subtler FEAVO anomalies are brought to light. The V-shaped anomalies were not destroyed; on the contrary, they are clearer than ever (Figure ).

 

zofbef Figure 11 Smallest offset (241m) before reprocessing

 

zofaft Figure 12 Smallest offset (250m) after reprocessing. Railroad-track false reflections above 1.5 sec, ringing all over the section and high noise in the lower part are eliminated.

 

kshq
Figure 13 Preprocessing enhanced the V-shaped anomalies

The previous velocity model, which is already existing in the data library, is shown in the upper left panel of Figure . The geological setting of the Grand Isle survey in the Mississippi Delta shows that the Grand Isle deposits are very young and the velocity is most likely determined by compaction, making such large lateral velocity variations as pictured in the initial model implausible. The previous velocity had also been picked at only ten midpoints.

I eliminated random noise from the data with an enhanced noise attenuation method. I then transformed each CMP to velocity space, automatically picked the highest semblance values, and transformed them to interval velocity using the ``SuperDix'' inversion described by () (Figure ). The result of the inversion was then smoothed along midpoint into a more geologically plausible almost-v(z).

 

veloplot
Figure 14 Upper left: previous interval velocity model. Upper right: v(z) model constructed by smoothing it many times. Lower left: new interval velocity model for migration. Lower right: ``v(z)'' profile constructed by smoothing the new velocity model across midpoint

I migrated with the velocity shown in the lower left panel of . I also used more frequencies than in the previous migration. The new migration stack is shown in Figure . Some reflectors stack better in the newer result, and amplitude anomalies are also more consistent.

 

phw
Figure 15 Illustration of the velocity analysis for one midpoint: autopicker fairway, automatic picks, and inversion weights.

 

kaer_new Figure 16 New migrated stack

 

 

Short Note
Transformation to dip-dependent Common Image Gathers

Biondo Biondi and William Symes

biondo@sep.stanford.edu

The analysis of Common Image Gathers (CIG) is an essential tool for updating the velocity model after depth migration. When using wavefield-continuation migration methods, angle-domain CIGs (ADCIGs) are usually used for velocity analysis (). The computation of ADCIG is based on slant-stack transformation of the wavefield either before imaging () or after imaging (, , ). In either case, the slant stack transformation is usually applied along the horizontal offset axis.

However, when the geological dips are steep, this ``conventional'' way of computing CIGs does not produce useful gathers, even if it is kinematically valid for all geological dips that are milder than 90 degrees. As the geological dips increase, the horizontal-offset CIGs (HOCIGs) degenerate, and their focusing around zero offset blurs. This limitation of HOCIGs led both of the authors to independently propose a partial solution to the problem; that is, the computation of CIG along a different offset direction than the horizontal one, and in particular along the vertical direction (). Unfortunately, neither set of angle-domain gathers (HOCIG ad VOCIG) provides useful information for the whole range of geological dips, making their use for velocity updating awkward. While VOCIG are a step in the right direction, they are not readily usable for migration velocity analysis (MVA).

In this paper we present a new method to transform a set of CIGs (HOCIGs and/or VOCIGs) into another set of CIGs. The resulting image cube is equivalent to the image cube that would have been computed by aligning the offset direction along the local geological dips. This transformation applies a non-uniform dip-dependent stretching of the offset axis and can be cheaply performed in the Fourier domain. Because the offset stretching is dependent on the reflector's dip, it also automatically corrects for the image-point dispersal. It thus has the potential to improve substantially the accuracy and resolution of residual moveout analysis of events from dipping reflectors. It has been recognized for long time () that image-point dispersal is a substantial hurdle in using dipping reflections for velocity updating.

The proposed transformation is dependent on the apparent dips in the image cube, and creates an image cube in which the effective offset depends on those apparent dips in an ``optimal'' way. We will thus refer to the resulting CIGs as dip-dependent offset CIGs (DDOCIGs), and to the transformation as the ``transformation to DDOCIGs.''

The proposed method is independent from the particular migration method used to obtain the CIGs. The input offset-domain image cube can be computed by either downward-continuation migration (shot profile or survey sinking) or reverse-time migration (). The proposed transformation should also improve the accuracy and resolution of velocity analysis applied only to ``conventional'' HOCIGs. In its most immediate application, it should also improve the image obtained by stacking after a residual moveout correction.

The next section illustrates the problem of HOCIGs and VOCIGs with a real data set from the North Sea that was recorded above a steeply dipping salt edge. The following section introduces the new transformation, that is then tested on a synthetic data set.