In
designing a 3D 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:

Determine the maximum
frequency required to resolve the target formation thickness
— from synthetics derived from well logs. This is Fmax.

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.

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.

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.

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 / Fold^{0.5}.
Using an existing
stack (possibly also migrated) has the advantage that the S/N
improvement due to processing is taken into account.

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.

Next, the required
bin size is calculated.
The relationship
between dip (qmax), velocity (Vrms), maximum unaliased frequency
(Fmax) and bin size (x) is given by:
x = 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!

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.

Migration Aperture:
Each shot creates
a wavefield, which travels into the subsurface and is reflected
upwards to be recorded at the surface.
Figure
3 shows an example of a model built for a complex subsurface
area. Such models can be raytraced to create synthetic 3D
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 3D "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.

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). But we must
have Xmin^{2} = SLI^{2} + RLI^{2} (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.

The candidate geometries
can each be tested for their response to various types of noise
— linear shot noise, backscattered 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.

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.
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 3D survey that cannot be interpreted!