Note that we write Equation 3 in terms of P_ and Fo rather than P and F, while the regression analysis has been carried out with P and F data. This is done because we like to think of Equation 3 as expressing a physical relationship between the actual Pu concentration in a soil sample and the integrated gamma ray radiation. The error terms, which depend on measurement techniques, are superimposed. The basic equation of the model we propose for Area 13 data is Pits) = a Fo(x) + 8 + T(x), (4) where T(x) is a random field independent of F (x) with mean zero. The independence of T and Fo is the crucial assumption. It says that given the FIDLER reading above point x, other FIDLER readings bring no supplementary information about the Pu concentration at x. This excludes the case of a preferential lagged influence, as it occurs for example in uranium deposits, where detectors measure gamma radiation from radium, even though the uranium has been washed away. Equation (4) also means that the integration effect of FIDLER measurements does not concern too large an area, otherwise a spot x would contribute signifi-~ cantly to nearby gamma ray recordings, and deconvolution would be needed. Naturally, if the regression of Po and Fy had not been linear, but say E(P(x) [F,G)] = W[F(@)] we would have written as well Po¢s) = VLE Cx) ] + Tix) , E[T)]=0 , with T and Fo independent. The problem is the determination of wy (°) in the presence of errors in both P and F variables. In the linear case used in this paper, it can be shown that approximately: a 2 _ E(a) ¥ a/[1 + 2onj/ Do (Fi(x,) - F)71 (5) i i In a very tentative manner, we can evaluate the bias term in Equation 5. First, by a method explained below (under Structural Analysis) based on an analysis of the spatial variation of FIDLER data along Line 1, an order of magnitude estimate of the FIDLER error variance is found to be E(nj) ~ x 1073. (F(x,) Thus, using the 96 data for which FIDLER > 5,000, F) - Fy)2 = 2 FC) F,) )2 + Ltn - F n)2 -n)2 = 0.191 x 96. So the denominator in Equation 5 is 1 + 0.001/(0.191 - 0.001) = 1.005. This indicates that the bias is small enough to be ignored. For FIDLER < 5,000, the noise E(n?) is much larger and cannot be evaluated accurately. Hence, it is not possible to access the bias correction for this case. 375