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Overview
We shall briefly examine the
differences in the way  seismic data and sonic logs measure "the same
thing." First, seismic velocities are deduced statistically to provide
the best stack of the reflectors in the data. Stacking is done to
collapse a volume of measurements into a single vertical reflectivity
profile. This may involve the sampling of hundreds of thousands of cubic
feet of rock for any one stacked trace. Due to the large amount of data
required to produce any single seismic trace, the statistics are quite
robust.
A sonic log, as opposed to seismic,
measures velocity more directly. The actual borehole measurement made is
interval transit time (reciprocal velocity). All sonic log measurement
methods sample a volume very near the well bore, over a short vertical
interval and amount to sampling perhaps a few thousand cubic feet of
rock for an entire well. Assuming that the well bore is in good
condition and that there are no other known problems with the logging
environment, the sonic tool is capable of recording a very accurate
interval transit time profile with depth.
Clearly, each of these measurement
techniques has sampled very different volumes of rock in order to
determine velocity and reflectivity at the same physical location.
Therefore, we should not necessarily expect there to be a 1:1
correspondence between all reflectors seen in these two data sets.
Because the well to seismic ties are
done mostly after final seismic processing, we will assume that the
seismic data are of high quality with no significant AVO effects, and
that the velocity profile associated with each trace cannot easily be
improved. However, there are several items that need to be addressed
with the sonic log velocity profile before we can expect a good tie. We
do not want to stretch and squeeze the synthetic seismogram to force a
match with the seismic, as this will litter the sonic log with
unreasonable velocity artifacts. Instead, we need deterministically to
edit and calibrate the sonic log, by comparing the sonic log to other
wireline data as well as the seismic data.
Sonic Log
Problems
It is important to note that using a
sonic log to tie to the seismic data is a very sensitive numerical
operation.Because we wish to know the cumulative time from the surface
down to any reflector, we need to sum the sonic log in time. By summing,
we greatly exaggerate any systematic problems with the sonic log.
With the exception of noise spikes,
all of the problems with sonic log data discussed below make the transit
time too slow. When combined and summed, these errors can render a sonic
log useless. Raw sonic log problems include:
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Cycle skips and noise.
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Short logging runs, or gaps in sonic log coverage.
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Relative pressure differences between the drilling fluid and the
confining stress of the rocks around the wellbore.
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Shale alteration (principally clay hydration from the drilling fluid).
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Specifics
First, in order to be useful, a sonic
log must represent actual rock velocities. Spike noise and cycle skips
do not represent true rock measurements, and therefore must be removed
from the sonic log. Spike noise can be easily removed by "de-spiking."
Cycle skips occur when the sonic tool records an arrival that is not
correct (typically one "cycle" in the wave train late). The most common
cause of cycle skipping is badly washed out zones. When they represent a
significant problem, an intelligent data replacement scheme is required.
Figure 1 illustrates a sonic log where the shales are badly washed
out, causing frequent cycle skips and some spike noise. Gaps in sonic
log coverage need to be handled smoothly. Often, there are some log data
in this gap, just not sonic data. If we can model a pseudo sonic from
another curve and then replace the missing sonic data, we will have a
well-behaved synthetic seismogram. If we must model large vertical
intervals without real sonic data, we also need to be able to accurately
estimate the low frequency component (burial trend) of the earth's
velocity profile.
Figure 2 compares actual raw sonic data with a pseudo sonic modeled
from the deep resistivity data in an interval where the borehole
conditions are not conducive to recording a good sonic log. This pseudo
sonic can now be used to replace bad sonic log data or to fill in gaps
in sonic coverage where resistivity data exist. Shale alteration is a
problem where the in-situ shales are desiccated. During the process of
drilling, these dry shales are brought into contact with the drilling
fluid, which can cause swelling and fracturing of the shales, as well as
chemical alteration of the constituent clays.
Figure 3 shows the relationship between interval transit time and
deep conductivity. This parabolic trend is used to estimate the
magnitude of shale alteration. Relative pressure differences between the
drilling fluid and the confining stress of the rocks around the wellbore
will have an effect on the sonic log. Since different logging runs
typically use different mud systems, separate sonic log runs will likely
need unique velocity calibrations to match the seismic data.
Figure 4 illustrates the difference in the corrections required for
different logging runs.
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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 bi-modal 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 bi-modal, 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.
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 5 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.
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 shale-sand 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 6 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 dependent 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.
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 determine invasion in shales directly 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 non-linear 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 10,000-foot well. The correction is
non-linear, 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.
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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
7 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.
o
Most sonic logs have problems that need to be addressed prior to tying
to seismic data.
o
Due to the summing of errors in the sonic log, correction schemes need
to be robust.
o
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 non-deterministic editing.
o
Shale alteration can be empirically corrected, resulting in a superior
tie to the seismic data.
o
The final calibration to the seismic data through drift analysis
compensates for the effects of pressuring the near-wellbore environment
with the drilling fluid.
o
High quality ties can be used for many purposes, including phase
determination, relative wavelet extractions, seismic inversions,
effective stress calculations, etc.
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Figure 1.
Figure 2.
Figure 3.
Relationship between interval transit time and deep conductivity in an
invaded shale interval.
Figure 4. This plot
illustrates the magnitude of changes required of the raw sonic log (red
curve in left track) to tie fully to the 
Figure 5. Raw sonic
log from a continental basin with fitted polynomial showing low
frequency burial trend.
Figure 6.
Distribution shapes of the high pass sonic (ms/ft), deep conductivity (mmohs)
and redistributed conductivity (ms/ft, now a pseudo sonic).
Figure
7.
Comparison of the synthetic seismogram generated from the raw sonic log
(left) vs. that made with the final corrected and calibrated sonic log
(right).