Soil radioactivity-depth profiles from regularized inversion of borehole gamma spectrometry data

An in situ borehole gamma logging method using a LaBr₃ gamma detector has been developed to characterize a¹³⁷Cs contaminated site. The activity-depth distribution of ¹³⁷Cs was derived by inversion of the in situ measurement data using two different least squares methods, (i) Least squares optimization (LSO) and (ii) Tikhonov regularization. The regularization parameter (λ) of the Tikhonov regularization method was estimated using three different methods i.e. the L-curve, Generalized Cross Validation (GCV) and a prior information based method (PIBM). The considered inversion method variants were first validated for a¹³⁷Cs contaminated pipe, and in most of the cases, the calculated activity of ¹³⁷Cs was found to be within the acceptable range. The calculated ¹³⁷Cs activity-depth profiles from in situ measurements were also in good agreement with the ones obtained from soil sample analysis, with an R² ranging from 0.76 to 0.82. The GCV method for estimating λ appeared to perform better than the two other methods in terms of R² and root mean squared error (RMSE). The L-curve method resulted in higher RMSE than the other Tikhonov regularization methods. Instability was observed in the activity concentration depth profile obtained from the LSO method. Therefore, we recommend the Tikhonov regularization with GCV for estimating λ for estimating the activity concentration-depth profile. The site studied showed ¹³⁷Cs activity concentrations above the exemption limit down to depths of 0.50-0.90 m.