Page 114 - Well Logging and Formation Evaluation

104 Well Logging and Formation Evaluation

The AI is given by:

(6.1.3)
AI =r*V p
2
where AI is in kg/m /s.
Hence an AI trace may be derived simply from the sonic and density
logs. Prior to generating the AI, it is necessary to correct for any washouts;
if necessary, editing the logs by hand. It is also necessary to correct the
logs for any invasion. Fluid replacement is covered in Section 6.2.
The logs should also be corrected for well deviation and datum level,
such that they are true vertical and referenced to the same datum as used
for the seismic survey. Having derived an AI trace in depth, it must be
converted to seismic two-way time (TWT), which is the time that sound
takes to reach a particular depth and to return to surface. Two sets of data
are available to convert from depth to time. The first is the sonic log itself,
which can be integrated to provide a total transit time. The second are data
from WSTs (well shoot tests) or VSPs (vertical seismic profiles), which
will give the TWT to certain depths in the well.
The normal procedure is to use the integrated sonic log to provide the
conversion between checkshot or VSP points, but to calibrate the inte-
grated sonic to honor actual checkshot points where they exist. A cali-
brated sonic log will provide what is known as a TZ (time vs. depth) graph,
on which the TWT relating to any depth can be derived. The TZ graph is
used to convert the depth-based AI log to a time-based log, denoted AI(t).
The next step is usually to convert the AI(t) trace to a reflectivity trace.
This is simply done by differentiating the log with respect to time. The
reason this works can be demonstrated as follows. Consider two adjacent
samples having AI values AI 1 and AI 2 . The reflectivity R is defined as:

R = (AI 2 - AI 1 ) (AI 1 - AI 2 ). (6.1.4)

If d(AI) = (AI 2 - AI 1 ) and the sampling increment is d t , then:

R ~ d AI) d ] [ t *AI)] µ ( dt. (6.1.5)
[
d AI)
(
t * d (2
So we can derive R from the AI by simply differentiating it with respect
to time. The proportionality is not important because the trace will later
be normalized before comparing with the seismic log data.
So now we have both AI(t) and R(t). These traces contain frequencies
up to (1/dt), and the AI also contains a direct-current (DC) component.