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Recall that in this case I chose to design the survey as a collection of
three orthogonal surveys, the definition of each requiring only 5 parameters:
source and receiver interval, source and receiver line interval and
number of receiver lines per recording patch. Other considerations such
as number of shots per salvo, number of stations to rollalong in the
inline direction and number of receiver lines to rollalong in the xline
direction are also design parameters but I fixed them to be the number of
shots between two adjacent receiver lines, the number of receivers between
two adjacent source lines and one, respectively. The upshot is that the
model space has only 5 parameters for each zone and an exhaustive search
can be employed among all candidate geometries. In more irregular geometries,
we may wish to invert for the parameters of each salvo and a microgenetic
algorithm Alvarez (2002a) will be a better choice.
The fitness function has two components: one to minimize the objectives
and one to guarantee that the constraints are honored.
 
(1) 
where i is the index that represents every trial geometry, is the
factor balancing the two contributions to the fitness function, m is the
number of objectives, o_{ij} is the figure of merit of the jth objective for ith
geometry, is the relative weight of the jth objective, n is the
number of constraints, is the relative weight of the jth constraint
and c_{ij} is the figure of merit of the jth constraint for the ith geometry.
In this case I chose which means that I am giving
equal weight to the minimization of the objectives and to the satisfaction of the
constraints.
The main objective, as mentioned before, is uniformity of target illumination, which
requires minimization of the total distance that the emergence ray positions had
to be moved to conform with each geometry. Also, since this is a land survey,
the main factor in the cost of the survey is the number of shots. Therefore, I used
the minimization of the number of shots as the second objective of the optimization.
Finally, I used the total receiver and sourceline cut as additional, though less important,
objective.
Notice that the constraints are not linear and that they may be partially fulfilled
with partial penalties applied. The figures of merit assigned to the
objectives and the constraints are normalized between 0 and 1, except when a constraint is
completely violated, for example if the required number of channels is larger than the
maximum number of available channels, as mentioned before. I made no attempt to differentiate
cost between the available recording equipments although in practice this is likely
to be an important issue.
The relative weights on each objective and on each constraint for the three zones
are summarized on Table 4.
Table 4:
Weights for the objectives and constraints applied in each zone: is for illumination, is for the number of shots, is
for receiver and sourceline cut, is for maximumminimum offset,
is for number of available channels, is for aspect ratio
and is for fold of coverage.
Zone 







1 
0.7 
0.25 
0.05 
0.4 
0.2 
0.3 
0.1 
2 
0.6 
0.3 
0.1 
0.3 
0.2 
0.3 
0.2 
3 
0.6 
0.3 
0.1 
0.1 
0.4 
0.2 
0.3 
Next: Geometry with the Proposed
Up: The Proposed Approach
Previous: Logistic Constraints
Stanford Exploration Project
7/8/2003