In last
month's column we discussed the most common deleterious problems
with sonic logs, and their effect on seismic ties were outlined.
These included:
 Cycle skips and noise.
 Short logging runs,
or gaps in sonic log coverage.
 Relative pressure
differences between the drilling fluid and the confining stress
of the rocks around the wellbore.
 Shale alteration
(principally clay hydration from the drilling fluid).
This month
we cover methods to correct these problems and calibrate the sonic
log using the seismic data. Proper handling of sonic log problems
can result in high quality informative ties that can be used in
a variety of disciplines.
Solutions
Clearly,
a key to being able to correct common problems with sonic logs requires
the ability to replace questionable data with a reasonable estimate.
This is important because if we replace bad data with an estimate
that is poor, we may not have done much good with respect to the
cumulative error, and may have added false reflectivity.
Other wireline
data that have a good relationship to velocity include: density,
resistivity, gamma ray and spontaneous potential.
Unfortunately:

The density tool
has a very low tolerance to poor borehole conditions, and will
likely not be useful.

Both the gamma ray
and spontaneous potential curves are useful, but they tend to
be rather bimodal in their behavior (either sand or shale),
and do not adequately capture the dynamic range of actual rock
velocities.
The deep
resistivity is neither affected by the near borehole environment
(rugosity or invasion), nor is it bimodal, making it the best candidate
for the generation of pseudo sonic data and, in most cases, still
has adequate vertical resolution to tie to seismic data.
Low Frequency
Compaction Model
The sonic
log exhibits a large low frequency component from burial compaction,
which must be removed prior to modeling with other log data that
do not have this same feature, such as the deep resistivity.
A fast
and accurate way to model the low frequency component of a sonic
log is to fit a polynomial to the entire curve.
Figure
1 shows a typical sonic log from a continental basin with the
fitted polynomial on top. When we subtract this trend from the data,
the resulting curve will be referred to as the "high pass sonic."
Check shot
surveys, VSPs and seismic stacking velocities transformed to interval
velocities also can be used to determine the low frequency velocity
trend.
All we
need to do to make a full pseudo sonic is to add the reflectivity
from our model (based on resistivity or gamma ray data) to our burial
trend.
Replacement
Scheme
Our goal
is to make a curve from the resistivity data that looks just like
the high pass sonic.
In most
cases, a Faust transform or neural net solution will fail to have
the required accuracy for large vertical replacement intervals.
When using these techniques, one often finds that far too much transit
time is removed from the sonic log, especially in poorly constrained
intervals of the model.
Since resistivity
data are logarithmically distributed, and our high pass sonic is
normally distributed, we must transform from resistivity to conductivity
(reciprocal resistivity) before meaningful statistical work can
be done. What we wish to do is examine the shape of the histogram
of high pass sonic data compared to the shape of the conductivity
histogram over the same interval.
Now, we
will simply reshape the conductivity histogram to match the high
pass sonic. This reshaping forces the asymmetrical shalesand velocity
response of the sonic log onto the conductivity data, thus making
a pseudo sonic log. Zoning the well can improve the result, as the
model will be forced to accommodate less geologic change (three
to five zones should suffice).
Figure
2 shows the results of the redistribution.
Now we
add the low frequency component back in (from our polynomial fit
to the raw sonic) to obtain a full usable pseudo sonic log — and
replacement of poor data now can be done with some confidence.
In compacted
rocks, most of the problems described occur commonly in the shales
and much less commonly in sands. Because sands have resistivity
signatures that are highly dependant on hydrocarbon saturation,
replacement of real sonic data in sands using a model based on the
resistivity data should be done with care.
In cases
where the sonic log is poor in a sandy interval, the gamma ray or
spontaneous potential logs may be more suitable choices for modeling.
Shale Alteration
Desiccated
shales can imbibe drilling fluid, thus producing an invaded zone.
Within this invasion zone mechanical change occurs due to swelling
of the shale. This may take the form of elastic swelling, or swelling
with some fracturing. Subtle chemical alteration of the clay minerals
may also occur. Both of these phenomena cause a reduction in apparent
velocities as seen by the sonic tool.
Because
it is difficult to directly determine invasion in shales using traditional
resistivity analysis, we must try to develop an invasion indicator
that we can use to correct the data.
If we cross
plot interval transit time (high pass sonic) vs. conductivity in
an interval that is believed to be invaded, we see a nonlinear
relationship (the fitted curve is a parabola).
Figure
3 shows such a cross plot. Note the data have been mirrored
about the interval transit time axis for visual clarity.
If we assume
that the parabolic behavior is related to an invasion profile (this
is a good assumption because ray path bending in a layered media
approaches a parabolic function), we can use the fitted parabola
to correct the sonic data.
To do this,
we simply scale the sonic data toward faster velocities using the
fitted parabola. This correction alone can account for as much as
100 ms. of time in a 10,000foot well. The correction is nonlinear,
thus its affect on the synthetic seismogram is not easy to predict.
We have
found, however, that wells having had this correction applied tie
to the seismic better over larger intervals with higher frequency,
resulting in higher quality wavelet extractions.
Calibration
to the Seismic Data
Now that
we have a sonic log that has been treated with deterministic editing
and corrections, we are ready to tie it to the seismic data.
Once the
sonic log has been placed correctly in time with the seismic data,
there are frequently small residual errors in the location of correlative
events in time. If we can relate the observed errors to geologic
packages and apply corrections only to those large intervals, we
will not introduce harmful artifacts into our sonic log.
Figure
4 has raw and final synthetic seismograms from a sonic log that
required a lot of data replacement (mostly between 8,000 and 11,000
feet).
Note the
dramatically different character in the synthetics. While the raw
version bares little resemblance to the seismic data, the final
version ties quite nicely over the entire well. The drift curve
in the far right track shows the difference in cumulative time between
the raw and final corrected sonic logs.
The logging
run numbers (R1, R2, R3) at the bottom of the well correspond to
clear differences in final velocity calibration to the seismic.
Separate runs may need to be treated differently due to tool and
mud system changes.
Conclusions

Most sonic logs
have problems that need to be addressed prior to tying to seismic
data.

Due to the summing
of errors in the sonic log, correction schemes need to be robust.

Building a good
pseudo sonic log to substitute for poor or missing real sonic
data is a must if we do not wish to introduce additional problems
through nondeterministic editing.

Shale alteration
can be empirically corrected, resulting in a superior tie to
the seismic data.

The final calibration
to the seismic data through drift analysis compensates for the
effects of pressuring the nearwellbore environment with the
drilling fluid.