Estimation of Pu Concentration Surface
A two-phase estimation procedure, GRID, was used in conjunction with a
nearest neighbor data search routine, NEAR (Sampson, 1975a), to estimate
the plutonium concentration surface using the 170 data points obtained
as described above.* This procedure was applied at each iteration as
described in the next section.
GRID estimated the 239°249py concentration
at each intersection point (grid node) of a grid laid over the study
site.
The grid mesh spacing was chosen to be 100 feet after trial and
error computations of the concentration surface using spacings of 50 and
200 feet.** The final grid had 73 rows (east-west) and 86 columns
(north-south) for a total of 6,278 grid nodes. The method used by GRID
to estimate the concentration surface is described in detail in Appendix
B (from Sampson, 1973).
GRID and NEAR are part of a large computer software system called SURFACE
II (Sampson, 1975b) developed for the manipulation and display of spatially distributed data.
This system is under continuing development by
the Kansas Geological Survey.
All of the contour and three-dimensional
plots presented here were prepared from plots obtained on the Cal-Comp
plotter using SURFACE II.
A disadvantage of GRID is that it does not yield estimation variances of
the estimated grid node values.
However, within the next few months, a
gridding method known as Kriging is expected to become available on
SURFACE II.*** Kriging yields best linear unbiased grid node estimates
as well as variances of these estimates if the underlying assumptions of
the method are fulfilled.
The theory and practice of kriging have too
many ramifications for discussion here, but the basic assumption involves
second order stationarity of differences between spatial data (the
"intrinsic hypothesis").
Introduction to the theory and practice of
kriging are given by Huijbregts (1975) and Delfiner and Delhomme (1975).
A detailed account of the underlying theory and a worked example are
given by Olea (1975).
Further insight into the method is given in Davis
(1973), Huijbregts and Matheron (1971), Agterberg (1970), Akima (1975),
and Olea (1974).
*The estimated plutonium contours for Area 13 (Project 57) in Gilbert
et al. (1975) were based on 166 observations; those in Gilbert et al.
(1976b) on 167 or 168. These earlier efforts exclused the datum 16,400
uCi/m* in Appendix A, the extremely large value near GZ.
**Reducing the grid mesh size from 100 to 50 feet increases the number of
grid nodes fourfold.
The computing expense is similarly increased.
In
practice, the grid mesh size is determined in part by the desired detail
in the concentration surface, the density of data points, and cost factors.
**kSince this paper was originally written, kriging has become available on
SURFACE II.
However, we have instead used the kriging program BLUEPACK
written by Dr. Pierre Delfiner (see Delfiner and Gilbert, 1978) since it
offers a more general approach to the problem.
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