A Deterministic Model of the Gamma Radiation at the Soil Surface–Including Soil Moisture Correction for Better Radiation Data Exploitation in Soil Mapping

Abstract

Background

During the last decades, gamma spectrometry data have increasingly been used in soil science, for example, for mapping. However, the full data potential could not be exploited due to certain constraints, among which the insufficient representation of attenuating materials (in particular, water) in correction algorithms is the most important one. Due to this problem, most often only the potassium/thorium intensity ratio is used in soil science.

Aim

However, the ultimate goal must be to derive from field gamma spectrometry the real content of the chemical elements that can be sensed (i.e., normally $K$, $U$, $\mathrm{Th}$, and $\mathrm{Cs}$). The first enabling step is to deterministically model the gamma radiation at the soil surface in order to subsequently allow for water content correction by reverse modelling.

Methods

We present here a realisation of a mathematical model that is based on the ‘King-equation’, but additionally introduces the soil science concept of horizons, that is, a finite number of strata of various vertical thicknesses, with homogeneous properties within each horizon. This approach allows the use of radial symmetry as concept for the three-dimensional integration of the gamma signal. Input data for the model are horizon vertical thickness, total content of radiating and attenuating materials, and bulk density. Additionally, used parameters concern the decay chains of the radioactive elements.

Results

Model tests with real soil produced count rates in the expected order of magnitude. Due to the instrumental setup of the field spectrometer, it was necessary to replace full spectrum analysis by the concept of regions of relevance (ROR) in order to be able to compare the counts predicted by our model and the counts registered by the spectrometer. The ROR concept is based on the computation of the relevant elements' decay steps and includes Compton scattering.

Conclusion

Using this approach, a deviation between modelled and measured gamma radiation is reasonable for $K$ and $\mathrm{Th}$. The reasons for still larger deviations with respect to the $U$-signal are discussed.