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For each reflecting point and azimuth, rays corresponding to
the same opening angle on opposite sides of the normal are linked together
as dual rays. Rays whose emergence point (or that of its dual) fall outside
the permit area for sources and receivers are discarded. Also discarded
are rays for which the total traveltime is longer than the trace length.
The remaining rays are assigned source or receiver positions according
to the shortest distance between their emergence point and the closest
source or receiver position for each geometry. Once a ray is classified
as, say, source, its dual will be classified as receiver. Note that this
classification is geometry-dependent. Figure shows
an example of the classification of a ray and its dual for two candidate
geometries. The classification is done for all valid rays and the total
distance that the emergence points have to be moved to conform
with each geometry is recorded and saved. Minimizing this distance is
equivalent to maximizing uniformity of illumination.
**classify2
**

Figure 7 Classification of ray emergence points
as sources or receivers. Vertical lines are source lines and horizontal
lines are receiver lines. Two geometries are represented. The left panel
illustrates a sparse geometry for which the ray in the top left would
be classified as a source. The right panel shows the same ray which will
now be classified as a receiver for this less sparse geometry.

For each geometry, I compute and save all the relevant parameters such as fold
of coverage, maximum and minimum maximum offsets, aspect ratio, number
of receiver per patch, etc. This information is saved and will be used
as geophysical constraints for the optimization as described below. I also
compute all relevant statistics of each geometry, such as number of
sources, number of receivers, and receiver- and source-line cuts. This
information is used to apply logistic constraints to the optimization.
The cost of the survey, in particular, may largely depend on those
statistics.

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Stanford Exploration Project

7/8/2003