The estimation procedure for other sampling intervals is quite similar.
Even if the distribution of activity in undisturbed soil were exponential, it is unlikely to remain
exponential if the soil is disturbed to any appreciable extent. As an example, bulldozer disturbance
during lane clearing often causes mixing in the top 10 em or so of the soil in the lane. In these
locations, the distribution of activity is likely to be linear to the depth of the disturbance, as
indicated by Tech Notes 4, 9.0 and 9.1.
For the case of a linear distribution of activity, the average of any intervals contained within the
disturbed profile can be calculated easily. For instance, assume again that the 0 to 5 and 5 to 10 cm
intervals were sampled, with measured activities a, and ag respectively, and that the
distribution of activity is linear from the surface to 10 em. Then the activity at a depth x (x<10 em)
is represented by the equation:
TRU(x) = mex +b
where m and b are constants. These can be estimated from the data, since the average of a linear
function over an interval is the value of the function at the midpoint of the interval. That is, ay
is the activity at 2.5 em and a9 is the activity at 7.5 em. Therefore:
-'2-
"1
11
a
a
m=“ F =
7.5 - 25
1 (as
{89
)
- ay.
Also,
SO,
ay = 2.5m + b= 0.5 (ag - ay) +b,
b= 15a,
- 0.5a9.
Then the average over an interval from x, to x1 + 5 would be:
TRU(x ,) + TRUG, + 5)= mx, +b+m&+5)+b,
2
2
which simplifies to:
mk, + 2.5) +b.
If an interval contains some activity with linear distribution and some with exponential, the average
can still be estimated. The two sub-intervals can be estimated separately with appropriate
modifications to the equations above. The average for the whole interval is then the weighted sum
of the sub-interval averages, the weighting factor being the proportion of the whole contained in the
respective parts.
Example Estimates from Islands Belle and Daisy
On the islands Belle and Daisy, there were a number of locations sampled in the 0 to 5, 5 to 10 and,
in some cases, the 10 to 15 em intervals. The subsurface interval with highest activity was 2.5 to
7.5 em, so it was necessary to estimate the TRU activity in this interval.
The assumption that activity dropped exponentially with depth appeared to be generally reasonable.
Figure B-19-1 shows the 5 em average TRU activity as a function of depth at 15 sample sites in the
vicinity of one stake location on Belle; the pattern of activity is typical of both Belle and Daisy.
However, at disturbed locations with all very low activities, the distribution appeared to be linear,
at least to 10 em. See Table B-19-1 for example. Of the two obvious exceptions to the pattern in
Figure B-19-1, one is a disturbed area, the other had measured TRU activities that were barely
detectable.
B-19-2