2.1 Relationship between gamma absorbed dose rate in air and the activity concentration of radionuclides in soil and rock

If the radionuclides are homogeneously distributed in infinite soil or rock, and gamma-ray attenuation can be ignored for 1 m of air (if the gamma ray energy is 1.0MeV, only 0.88% gamma ray is attenuated through 1 m air), the air kerma rate of a monoenergetic gamma ray 1 m above the ground surface is^[15]

where ρ (g·cm^-3) is the density of the soil or rock; c_i (Bq·g^-1) is the activity concentration of the ith radionuclide; μ_i is the linear attenuation coefficient of soil or rock for a gamma ray emitted from the ith radionuclide; and ${\Gamma }_{k,i}$ is the air kerma rate constant of the ith radionuclide, which is defined as the air kerma rate at 1 cm from a 1 Bq unfiltered point source. In air, the gamma absorbed dose rate is approximately equal to the air kerma rate. About 99% of the gamma absorbed dose in air is from the radionuclides in the soil or rock at depth of <40 cm^[6]. Geochemical prospecting data at this depth could represent the activity concentration of radionuclides in the surface soils or rocks. The conversion coefficients between the activity concentration of radionuclides and the natural gamma-ray exposure rate and gamma absorbed dose rate in air are listed in Table 2.

*1R=2.58×10^-4C/kg

2.2. Uranium–radium equilibrium

The data in Table 2 were based on the assumption that the ²³⁸U and ²³²Th series reach secular decay equilibrium. However, it may not be the case for the ²³⁸U series. Some decay products of the ²³⁸U series may dissociate from the source material, which facilitates their subsequent environmental transfer. For example, ²³⁴U may be somewhat deficient relative to ²³⁸U in soils and enhanced in rivers or the sea. ²²⁶Ra may also have slightly different activity concentration from ²³⁸U because of its greater mobility.

The ²³⁸U decay chain can be divided into two groups according to the geochemical behavior and the contributions to the gamma radiation level of the radionuclides: the uranium group and the radium group. The uranium group consists of ²³⁸U, ²³⁴Th, ²³⁴Pa, ²³⁴U and ²³⁰Th. The gamma-ray energy fluence of this group is about 2% of the total in the equilibrium ²³⁸U decay series. The radium group is composed of ²²⁶Ra and its progeny. At secular equilibrium, the radium group emits about 98% of gamma-ray energy fluence and the main gamma emitter is ²¹⁴Bi^[6]. Ignoring the emanation in soils or rocks, we find that it takes about one month for ²²⁶Ra to reach secular equilibrium with ²¹⁴Bi. Consequently, we can evaluate the gamma absorbed dose in air of the ²³⁸U decay series by measuring the total gamma count rate or gamma spectra.

Before using the concentration of uranium to evaluate the gamma absorbed dose rate of the ²³⁸U decay series, we need first to convert the concentration of uranium (C_U) to the concentration of radioactive equivalent uranium (C_eU)^[3], which is based on the Ra–U equilibrium constant (ξ). The calibration formula is as follows:

where C_eU is the concentration of radioactive equivalent uranium. ξ is the Ra–U equilibrium constant, which can be calculated by using

where C_Ra is the concentration of radium, which can be easily obtained by using in-situ gamma spectrometry. When the emanation of radon is considered, the concentration of radioactive equivalent uranium (C_eU) is given by

where η is the emanation coefficient of radon, defined as the ratio between the concentration of radon into the atmosphere (C_Rn) and that produced by ²²⁶Ra (C_Rn0). β is defined as the radioactive equivalent uranium ratio:

The ²³²Th series is a little different from the ²³⁸U series. The ²³²Th series only needs 60 years to reach secular equilibrium. The half-life of ²²⁰Rn is 54.5s; so it may not escape from the soil easily. Therefore, in this paper, a secular equilibrium is assumed for the ²³²Th series for discussion.

3.1 Geological condition of the Chengdu Plain

The Chengdu Plain lies in the west of the Sichuan Basin and to the east of the Tibetan Plateau. It is a compound alluvial fan that was washed by natural rivers originated mostly from the Tibetan Plateau (e.g., the Minjiang River, the Tuojiang River, and the Qingbai River). The western portion abuts the edge of the overthrust of the front Longmenshan Mountain, and the eastern portion borders on Longquanshan Mountain^[16,17].

There are three major tectonic units in the Chengdu Plain: the Longquanshan fault zone, the Chengdu Basin, and the Longmenshan fold. These tectonic units are bounded by two NE–SE-trending faults, i.e., the Dayi–Penguan fault and the Pujiang–Xinjing–Deyang hidden fault^[18]. The main geological tectonic units of the Chengdu Plain are shown in Fig. 1.

Fig. 1.Full-screen View

Geological map of the Chengdu Plain

3.2. Geochemical data

The geochemical prospecting data were provided by the Sichuan Geological Survey. The Chengdu Plain was divided into many small quadrate regions of 4 × 4 km and soil or rock was sampled in each quadrate region.

3.3. Determination ofβ

To obtain the concentration of radioactive equivalent uranium (C_eU), we must determine the radioactive equivalent uranium ratio β in advance. Dozens of soil samples were collected from the Chengdu Plain, the concentration of uranium was determined by laser-induced fluorometry and that of radium was determined by gamma spectrometry.

Figure 2 shows that there is a linear relationship between the radioactive equivalent uranium ratio and the concentration of uranium in soil or rock, and the adjusted R Square(R²) is 0.64. When the concentration of uranium falls in the range of (0-5) ×10^-6g/g (representing 99% of the collected samples), this linear relationship can be written as follows:

Fig. 2.Full-screen View

Relationship between the concentration of uranium and the radioactive equivalent uranium ratio β.

Where β is the radioactive equivalent uranium ratio and C_U is the concentration of uranium in soil or rock. The concentration of uranium can be converted to the concentration of equivalent uranium (C_eq) as follows: