Answer to Question #10406 Submitted to "Ask the Experts"

How much does moisture saturation affect the terrestrial gamma dose rate from soil? Is there any way to relate moisture saturation in soil to the terrestrial gamma dose rate for different soil types?

The presence of moisture can have a significant impact on the transmission of terrestrial gamma radiation through soil and, hence, affect the gamma radiation dose rate above the surface of the earth. If one is using gamma spectral assessment tools that allow distinguishing specific energy photopeaks associated with primary photons, the transmission associated with a specific energy photon that is ascribed to a fixed thickness of dry soil plus water is given by a relatively simple exponential equation of the form:

I = I_o exp[(-µ_s – µ_w)x],

where I refers to the transmitted gamma ray intensity and I_o is the unattenuated gamma ray intensity; µ_s and µ_w are the effective linear attenuation coefficients for soil and water, respectively, at the gamma energy of interest, and x is the thickness of soil. Note that x is also the thickness of water, which is assumed to be distributed uniformly through the soil. It is recognized that in practical situations of measuring above the earth’s surface I₀ is not explicitly known, and gamma rays are likely originating from all depths in the soil, but the equation can be used to demonstrate the potential significance of water attenuation.

This can be done through a simple example in which we consider the effects of attenuation on the ⁴⁰K gamma rays of 1.46 MeV. If, for demonstration purposes, we assume the dry soil is all silicon dioxide with a mass density of 1.6 g cm^-3, the value of µ_s is about 0.0845 cm^-1. If we assume water is present at a nominal saturation level of 30 percent in the soil we can modify the effective value of µ_w to reflect this fact; the value of µ_w for pure water at usual volume density of 1 g cm^-3 is 0.0586 cm^-1, and adjusting for the 30 percent saturation we obtain 0.0176 cm^-1. If we considered the 1.46 MeV gamma rays coming from a nominal depth of 15 cm, we would find

I = I_o exp[(-0.0845 – 0.0176)15] = 0.216 I_o.

For the case of 0 percent water the equation would have yielded

I = I_o exp(-0.0845(15)) = 0.282 I_o.

For this simple example, the effect of the 30 percent water is to decrease the intensity of the 1.46 MeV gamma rays by about 31 percent compared to dry soil; a comparable reduction in dose rate from these primary photons would apply.

In actual measurements of water content of soil (or above the soil in the cases of snow and ice measurements), the considerations are more complex since photons originate from different depths and, depending on detector placement locations and characteristics, from different angles. The dose rate at the detector location depends on all of the photons reaching the detector and may include scattered photons as well as primary photons.

In the measurement process in which soil moisture has been correlated with gamma ray intensity, different gamma rays from terrestrial radionuclides have been used. Most common are gamma rays from ⁴⁰K and ²⁰⁸Tl (thorium series decay product), although others may also be used. You can find some information available on the internet. Publications of the National Snow and Ice Data Center (NSIDC), who perform low altitude flyover measurements to evaluate snow- and icepacks and soil moisture may be helpful in providing some insight.

Similar measurements have been made and reported by the Oak Ridge National Laboratory Distributed Active Archive Center (ORNL DAAC). They have provided information about terrestrial gamma radiation flyover measurements to assess soil moisture content in their BOREAS Experiment Plan program. There are also various publications by independent authors that deal with this subject. You might also want to review a 1993 article by Yoshioka that considers the relationship between exposure rate and moisture content of the soil.

Regarding the effects of different soil types, there have been gamma attenuation studies of different soils done in the past. In a 1964 paper by Reginato and Van Bavel the authors describe attenuation of ¹³⁷Cs (^137mBa)  gamma rays of 662 keV through nine different soil types collected from locations around the United States. They found surprisingly little differences among the values of the mass attenuation coefficients for the nine soils, with the coefficients ranging from 0.0772 cm² g^-1 to 0.0780 cm² g^-1; these compared to the value for water at this energy of 0.0862 cm² g^-1. The most important physical factor then affecting the gamma ray attenuation is likely the soil density, which can vary with soil types and packing. The presence of added water in the soil effectively serves to increase density by filling the available space in the soil.

I hope some of the above is helpful to you.

George Chabot, PhD, CHP