Estimates Using IMP Survey Results
The IMP survey results were used to make computations of total activity removed by fitting a
funetion to the gradient of concentration with depth. The function was integrated to find the
average concentration in the soil removed, and that value was multiplied by the total volume
excised and a constant which converted pCi/g to Ci/yd3 to compute the total activity removed.
Two types of functions were considered, linear and exponential.

Combinations of these were also

considered. It was necessary only to know the form of the function, since that determines the form
of the integral. The form of the function was determined from the gradient in backhoe profile soil
samples, then the integration computations were performed on the IMP values.
The soil gradient in areas without substantial subsurface contamination is clearly of a different form
than the gradient in areas with such contamination. Therefore, the functions were fit separately to
the soil data from the two pockets of subsurface contamination, and to data from the remainder of
Kickapoo. Figures B-10-1 and B-10-2 are graphs of the soil data from the east side pocket of
subsurface contamination and from the vicinity of the pandanus tree, respectively. Figure B-10-3
shows the soil data from the remainder of the Kickapoo area. Figure B-10-4 is a map showing the
relative locations of these three areas.
The gradient in Figure B-10-3 is clearly exponential in form. Figure B-10-1 shows a rise in
concentration from the surface to 20 em, then an exponential falloff below 20 em. There was
insufficient data to model the rise with anything other than a linear function, so the chosen function
was linear to 20 em (assumed equivalent to after 1 lift), then exponential below 20 em. There was
also not sufficient data to adequately fit the Figure B-10-2 gradient, so the same assumptions, i.e.,
linear from surface to 20 em, exponential below 20 em, were made for the subsurface pocket near
the pandanustree.

Mathematical Computations

eX dx = ke i (1 - eed),

k is averaged from the IMP readings before excision.
readings after excision. Then,

Poa

Of

O Remy OL

ny

°

Under the assumption of an exponential gradient, the function is of the form ke-CX, where k is the
average concentration before excision, x is depth in em, and ¢ is a constant. Then the average after
excision is ke~C4, where is the total depth of the excision. Then the average concentration is

Let ky be the average from the IMP

ky = e-cd

k
so

ed

(e)

Then the average concentration is

s (u * ),
k

to compute either c or d. However, the assumption is made in both models that d is constant for the
area the IMP readings are averaged over.

B-10-2

w

For the linear case the average concentration is simply (1/2)(k + kj). Note thatit is not necessary

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