The error term that was used for 24l!4m from the IMP included a counting error based on assuming
a Poisson distribution for photons falling in a certain channel of the spectrum. A blanket 10 percent
of the actual value was addedto this error to cover errors due to differences in soil density, depth
distribution of activity in the soil, soil composition, etc.
Other errors not included in the propagation were uncertainty on the additional correction factors
and inaccuracy of the net photopeak count computation due to gain shifts or resolution changes.
The error term on the ratio was based on the assumption that the variance of the TRU value
increased linearly with 24am activity. The counting error on the 241 am by gamma or chemistry
was not included, nor were possible errors in the peak computation. Therefore, the equation used to
compute the error on the ratio is only approximate, and not exact.
The error used with the BCF was the computed sample standard deviation on the experimental
results. The experiment was performed on only one island, which had denser brush than many
islands, and a mix of vegetation species different from some islands. It is therefore possible that
there is a bias in the factor, or that the computed error might be incorrect for other islands.
Error Propagation
As indicated above, the three types of error included in the error propagation were the counting
1.
The error on Am corrected for brush attenuation is:
Sé2s (Am2 2 x S22 + 0.152 x SZ + sZ x Se.) x Br2 + Sin
where
Am
= measured 24lam value
0.15 = brush attenuation correction factor minus one
S2
= sample variance of the BCF
u
= counting error on 24lam plus 10 percent of actual value
we
sen
estimated variance of corrected Am
and
Br
proportion of brush in dectector view
The last term in parentheses was inadvertently left out of the program which did these
computations, but the effect is in general relatively minor.
2.
The error on the final TRU number corrected for brush is then:
SZ = S32 x C2 4+ SA x R2 + sa x sé
where
R
= estimated ratio of TRU to 24lam
C
= estimated Am, corrected for brush attenuation
B-20-2
oe
error on the IMP 241 am value plus 10 percent of the actual value, the sample variance of the
TRU/Am ratio data, and the sample variance of the experimental BCF data. The three variables
involved were assumed to be independent, and the error was therefore computed in two steps: