Figures Captions
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In designing a 3-D survey, the geometry (arrangement of shots and
receivers on the surface) must measure signal correctly and must also
attenuate noise. Thus finding an optimum geometry should include the
following steps:
1.
Determine the maximum frequency required to resolve the target
formation thickness -- from synthetics derived from well logs. This is
Fmax.
2.
Estimate average inelastic attenuation Q (the quality factor)
over the interval from surface to target -- preferably using the log
spectral ratio of downgoing wavelets from zero offset VSPs.
3.
From spreading losses, transmission and reflection losses and the
estimated Q value, graphs may be constructed (an example is shown in
Figure
1), showing available frequency vs. time or depth.
The
available frequency at the target may be less than Fmax (point 1 above).
If so, we must accept this new lower Fmax - because the earth itself
will preclude higher frequencies at the target.
4.
We now establish the desired S/N at the target. For example, the
smallest change we wish to detect might be a 5 percent change in
porosity, which will show up on a seismic trace as an 8 percent change
in acoustic impedance (from petrophysical crossplots of acoustic
impedance vs. porosity).
If the
seismic noise level is higher than this value, we will not be able to
detect the change.
5.
Estimate the expected S/N of raw shot data. This can be done
either on some typical test shots or by dividing the S/N of a stack (or
migrated stack) by the square root of the fold used to make this
existing stack.
Since:
Fold =
(S/N of final migrated stack / S/N of raw data)2 ... then S/N
raw = S/N migrated / Fold0.5.
Using an
existing stack (possibly also migrated) has the advantage that the S/N
improvement due to processing is taken into account.
6.
From the desired S/N (point 4 above) and the estimated S/N of the
raw data (point 5), we determine the required fold of the survey under
design.
7.
Next, the required bin size is calculated.
The
relationship between dip (qmax),
velocity (Vrms), maximum unaliased frequency (Fmax) and bin size (Dx)
is given by:
Dx
= Vrms / (4
. Fmax
. sin(qmax)
Thus, the
optimum bin size to use for a dip of 90 degrees is given by Vrms / (4 .
Fmax) -- or one quarter of the wavelength of the maximum frequency.
In
practice, this is often relaxed (a larger bin size is used), since it is
really not practical (not to mention very expensive) to measure every
dip with the maximum frequency.
In
Figure
2, an example of a crossplot of (Bin size, Vrms) vs. frequency (Fmax)
is shown. The dip angle (qmax)
is fixed at 30 degrees. This is based on the above equation and on
Figure
1 (Fmax vs. time) above and shows how the frequency varies with
velocity for a constant bin size (horizontal line). The increase in
velocity can be related to an increase in time or depth, and the figure
may be interpreted as showing the available Fmax on a dip of 30 degrees
at increasing depths -- for different choices of bin size.
Maximum
frequency (Fmax) is critical. If Fmax is too high, then the consequent
bin size will be too small -- and money will be wasted trying to record
frequencies that are not available. Conversely, if Fmax is too low, the
bin size will be too large and high frequencies coming from dipping
events will be aliased and will not contribute to the final migrated
image.
Most
surveys today are shot with too large a bin size and are thus under
sampled!
8.
Determine the minimum and maximum offsets (Xmin and Xmax). These
are normally calculated from muting functions used in processing -- or
automatic stretch mutes derived from velocities. The minimum offset
corresponds to the shallowest target of interest -- and the maximum
offset to the deepest target of interest.
These two
values (Xmin and Xmax) will be used to determine approximate shot and
receiver line spacings (equal to Xmin multiplied by the square root of
2, for single fold at the shallowest target and equal line spacings) and
the total dimensions of the recording patch.
9.
Migration Aperture:
Each shot
creates a wavefield, which travels into the sub-surface and is reflected
upwards to be recorded at the surface.
Figure 3 shows an example of a model built for a complex sub-surface
area. Such models can be ray-traced to create synthetic 3-D data
volumes. Thus, the degree of illumination on any chosen target can be
determined.
In less
complex areas, the migration aperture (amount to add to the survey to
properly record all dipping structures of interest at the edges) is
normally calculated from a 3-D "sheet" model of the target. This shows
us how much to add on each side of the proposed survey and gives the
total surface area of shots and receivers.
10.
Now various candidate geometries can be developed. The shot and
receiver intervals (SI and RI) are simply double the required bin size.
Since fold, Xmin and Xmax are fixed, the only flexibility is to change
the shot and receiver line intervals (SLI and RLI). However, we must
have Xmin2 = SLI2 + RLI2 (assuming
orthogonal shot and receiver lines).
We can
make small changes in the line intervals (SLI and RLI), depending on
whether shots or receivers are more expensive. For example, a ratio of
4/5 can give improved noise attenuation compared to 4/4.
However,
it is not wise to stray too far from shot and receiver symmetry. As the
lack of symmetry increases, the shape of the migration response wavelet
will change -- leading to undesired differences in resolution along two
orthogonal directions.
11.
The candidate geometries can each be tested for their response to
various types of noise -- linear shot noise, back-scattered noise,
multiples, and so forth. They can also be tested for their robustness
when small moves of shot lines and receiver lines are made to get around
obstacles.
The
"winning" geometry will be the one that does the best job of noise
attenuation.
12.
Acquisition logistics and costs may now be estimated for the
"winning" geometry . Depending on the result (e.g., over or under
budget), small changes may be made.
Possible
Casualties and Concluding Statement
If large
changes are needed, the usual first casualty is Fmax. Thus, dropping our
expectations for high frequencies will lead to larger bins, which will
lead to a cheaper survey. Another possible casualty is the desired S/N
-- or, in other words, using lower fold.
Budget? Be prepared to spend some money! There
is nothing as expensive as a 3-D survey that cannot be interpreted!
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