**2. Radon production and transport**

The production of 222Rn depends on the activity concentrations of 226Ra in the earth's crust, in soil, rock and water.

molecular diffusion or by convection and enters the atmosphere where his behavior and

The radon decay products are radioactive isotopes of Po, Bi, Pb and Tl and they are easily attached to aerosol particles present in air. In table 1 are shown the principal decay characteristics of 222Rn and 220Rn, including properties of their respective parent

**Radionuclide Half-life Radiation E(MeV) E(MeV)**  226Ra 1600 y 4.78(94.3%) 0.186 (83,3%)

214Pb 26.8 m 0.295 (19%) 0.352 (36%) 214Bi 19.7 m 0.609 (47%) 1.120 (15%) 1,760 (16%)

224Ra 3.66 d 5.45 (6%) 0.241(3.9%)

212Pb 10.64 h 0.239 (47%) 0.300 (3.2%) 212Bi 1.01 h 6.05 (25%) 0.727 (11.8%) 6.09 (10%) 1.620 (2.8%)

208Tl 3.05 m 0.511 (23%)

The release of radon from natural minerals has been known since 1920's (*Spitsyn, 1926*) but its monitoring has more recently been used as a possible tool for earthquake prediction, because the distribution of soil-gas radon concentration is closely related to the geological structure, fracture, nature of rocks and distribution of sources. Therefore, surveying of radon concentration can prospect fracture trace, earthquake forecast, environment

The production of 222Rn depends on the activity concentrations of 226Ra in the earth's crust,

0.583 (86%) 0.860 (12%) 2.614 (100%)

 4.69 (5.7%) 222Rn 3.824 d 5.49(100%) 218Po 3.05 m 6.00(100%)

241Po 164 s 7.69 (100%)

 5.68 (94%) 220Rn 55 s 6.29 (100%) 216Po 0.15 s 6.78 (100%)

212Po 298 ns 8.78 (100%)

Table 1. Principal decay Characteristics of 222Rn and 220Rn

**2. Radon production and transport** 

monitoring, etc.

in soil, rock and water.

distribution are mainly governed by meteorological processes.

radionuclides and their short-lived decay products.

When radium decays in a mineral substance, the resulting radon atoms must first emanate from the grains into the air-filled pore space. The fraction of radon that enters the pores, commonly known as *emanation fraction*, consists of two components due to recoil and diffusion mechanisms. Since the diffusion coefficient of gases in solid materials is very low, it is assumed that the main portion of the emanation fraction comes from the recoil process. From the alpha decay of radium, radon atoms possess sufficient kinetic energy (86 keV) to move from the site where radon is generated. The range of 222Rn is between 20 to 710 nm in common materials, 100 nm for water and 63 m for air. (*Sabol et al., 1995*)

The emanation fraction can be strongly influenced by water content in the material, increasing with soil moisture, up to saturation in the normal range of soil moisture content. A representative estimate of the fraction of radon that leaves solid grains is 25%.

The increase in the emanation fraction can be explained by the lower recoil range of radon atoms in water than in air. A radon atom entering a pore that is fully or partially filled with water has a very good chance of being stopped by the water in the pore. Generally, the presence of water increases the emanation fraction, but this trend may show a saturation effect or the effect may even later reverse as the water content becomes greater.

In addition to the moisture effect, dependence of the emanation fraction on grain size and temperature has also been observed. Small grain size soils, such as clay, display maximum emanation at about 10%-15% water content. The ratio of the maximum emanation fraction to that of a dry sample also decreases as the grain size increases. A rise in temperature also causes an increase in the emanation fraction, which is probably due to the reduced adsorption of radon.

Different types of soil show different emanation fractions for 222Rn, which are generally in the range 0.01-0.5 (*Sabol et al., 1995*).

Some emanated radon atoms, after their penetration trough the pore of a material, may finally reach the surface before decaying. Radon behaves as a gas and its movement in material follows some well-known physical laws. There are essentially two mechanisms of radon transport in material: (1) molecular diffusion and (2) forced advection.

In diffusive transport, radon flows in a direction opposite to that of the increasing concentration gradient. Fick's law describes this process. Expressions for the radon fluence rate, in Bq m-2 s-1 , can be derived for specified geometric conditions.

If one assumes the earth as a semi-infinite homogeneous material, with density and porosity the fluence rate JD of radon emerging at the earth surface can be given by (*Sabol et al., 1995*):

$$J\_D = \mathbb{C}\_{Ra} \mathcal{A}\_{Rn} f \, \rho \left[ \frac{D\_\varepsilon}{\mathcal{A}\_{Rn} \varepsilon} \right]^{0.5} \tag{1}$$

where *CRa* is the activity concentration of 226Ra in earth material (Bq/kg); *Rn* is the decay constant of 222Rn (2.1 10-6 s-1); *f* and *De* are the emanation fraction and the effective diffusion coefficient for earth material (m2/s) respectively.

After crossing soil-air interface radon exhales into the atmosphere. The exhalation rate, that is the amount of radon activity released from the surface, depends on meteorological parameters. In particular the exhalation of radon is positively correlated with moisture content, temperature and wind speed and negatively with pressure, so that these factors

Radon as Earthquake Precursor 147

which is the Fick's second law expressed for the function K(z, t). Nevertheless the solution of equation (6) cannot be merely obtained by combining the solution of the general Fick's second law (2) with the substitution (5) because the two functions *K(z, t)* and *CRn (z, t)* do not

(7)

,0 for a z a,t 0

, 0 for z a,z a

(the atmosphere is considered as a reservoir of concentration *C* = 0) which means for *K(z, t)*:

( ,0) 0 for a z a,t 0 ( , ) exp for z a,z a *RnEq Rn*

Fick's law is usually solved for plane sheet geometry by separation of variables but this method is unsuccessful for such initial and boundary conditions. Several studies have been done for heat conduction in a slab having an initial zero temperature and surfaces

cosh

cosh

*Rn*

*Rn*

*z D*

*a D*

4 4 2 1

By multiplying by Rn both sides of the equation (10), one obtains the activity of CRn (z, t)

<sup>2</sup> <sup>0</sup>

2 1 1 exp

*<sup>n</sup> Rn*

<sup>2</sup> <sup>0</sup>

*<sup>n</sup> Rn*

*Rn*

*Rn*

*z D*

*a D*

*C a n z*

2 1 1 exp <sup>4</sup> <sup>4</sup> 2 1

2 2 2

 

*n D*

*C a n z*

 

2 1

2 2

<sup>2</sup> <sup>4</sup> 2 11

*n D*

*Rn*

*t*

*a a*

<sup>2</sup> <sup>4</sup> 2 11 2 1

 

*n Dt*

2 2 2

*n D*

2 2

(8)

cos

*a a*

cos

(9)

(10)

*t*

maintained at the temperature *f(t) = V exp(vt)* (*Gauthier et al.,1999*), obtaining:

*n*

*n*

*n*

cosh

cosh

*n*

admit the same initial and boundary conditions. These conditions are for *CRn (z, t)* :

*Ra*

*Rb*

*Rn RnEq Ra*

*Cz C C*

*Kzt C*

, exp

*K zt C t*

*RnEq Rn*

and therefore, combining with (6):

given in equation:

,

*RnEq*

*Rn RnEq RnEq*

*C zt C C*

*RnEq*

*Rn*

*K z*

*C zt*

must be considered in the determination of exhalation rates in environmental measurements. Since the main mechanism governing the entry of radon into the atmosphere from the surface of the earth is diffusion, the radon fluence rate can be calculated by using appropriate parameters in equation (1). Representative values of these parameters and *CRa* = 40 Bq m-3 yield *JD*= 0.026 Bq m-2 s-1 which is quite close to the average value experimentally obtained for some regions (*Sabol et al. ,1995*).

#### **2.1 Theory of radon diffusion**

In order to understand how radon anomalies could be correlated to geodynamic events radon transport mechanisms in soil must be considered. Different models to describe radon diffusion have been proposed. In this section we will give a brief review.

#### **2.1.1 Plate sheet model**

One of the most reliable models to describe radon diffusion is the plane sheet model. The molecular diffusion is considered in only one direction and, for any stable element, can be described by Fick's second law as follows (*Gauthier et al.,1999*):

$$\frac{\partial \mathbf{C}}{\partial t} = D \frac{\partial^2 \mathbf{C}}{\partial z^2} \tag{2}$$

where *C* is the concentration of the element and *D* the diffusion coefficient along *z*. This equation admits a solution C(z, t) which is constrained by the initial and boundary conditions (C = C0 at t = 0 and –a < z < a; C = 0 at t > 0 and z = +a):

$$\mathcal{C}(z,t) = \frac{4C\_0}{\pi} \sum\_{n=0}^{x} \left| \left( \frac{(-1)^n}{2n+1} \right) \times \cos\left(\frac{(2n+1)\pi z}{2a}\right) \times \exp\left(\frac{-D\left(2n+1\right)^2 \pi^2 t}{4a^2}\right) \right| \tag{3}$$

where *a* is the half-width of the slab.

In order to take into account radioactivity, equation (3) has to be modified for radon by adding a production term from its parent 226Ra and a decay term, which leads to:

$$\frac{\partial \mathbf{C}\_{Rn}}{\partial t} = \mathcal{A}\_{Ra} \mathbf{C}\_{Ra} - \mathcal{A}\_{Rn} \mathbf{C}\_{Rn} + D \frac{\partial^2 \mathbf{C}\_{Rn}}{\partial z^2} \tag{4}$$

where *CRa* and *CRn* represent the concentrations (in atoms g-1) and Ra and Rn the decay constants of 226Ra and 222Rn, respectively. Defining the function *K(z, t)* as:

> Rn (,) C , exp *Ra Ra Rn Rn Kzt zt C t* (5)

and introducing *K(z, t)* in equation (4) gives:

$$\frac{\partial \mathcal{K}}{\partial t} = D \frac{\partial^2 \mathcal{K}}{\partial z^2} \tag{6}$$

must be considered in the determination of exhalation rates in environmental measurements. Since the main mechanism governing the entry of radon into the atmosphere from the surface of the earth is diffusion, the radon fluence rate can be calculated by using appropriate parameters in equation (1). Representative values of these parameters and *CRa* = 40 Bq m-3 yield *JD*= 0.026 Bq m-2 s-1 which is quite close to the average value experimentally

In order to understand how radon anomalies could be correlated to geodynamic events radon transport mechanisms in soil must be considered. Different models to describe radon

One of the most reliable models to describe radon diffusion is the plane sheet model. The molecular diffusion is considered in only one direction and, for any stable element, can be

adding a production term from its parent 226Ra and a decay term, which leads to:

<sup>4</sup> 1 21 2 1 (,) cos exp 21 2 <sup>4</sup>

where *C* is the concentration of the element and *D* the diffusion coefficient along *z*. This equation admits a solution C(z, t) which is constrained by the initial and boundary

2 2 *C C <sup>D</sup> t z*

2 2

*<sup>t</sup> <sup>z</sup>* (6)

*Ra Rn*

*Kzt zt C t* (5)

*n a a*

In order to take into account radioactivity, equation (3) has to be modified for radon by

 

where *CRa* and *CRn* represent the concentrations (in atoms g-1) and Ra and Rn the decay

 Rn (,) C , exp *Ra*

*Rn*

2 2 *K K <sup>D</sup>*

*Rn Rn Ra Ra Rn Rn C C C CD t z*

*C n z Dn t*

(2)

 

2 2

(4)

(3)

2

diffusion have been proposed. In this section we will give a brief review.

described by Fick's second law as follows (*Gauthier et al.,1999*):

conditions (C = C0 at t = 0 and –a < z < a; C = 0 at t > 0 and z = +a):

*n*

obtained for some regions (*Sabol et al. ,1995*).

*Czt*

where *a* is the half-width of the slab.

constants of 226Ra and 222Rn, respectively.

and introducing *K(z, t)* in equation (4) gives:

Defining the function *K(z, t)* as:

0

*n*

0

**2.1 Theory of radon diffusion** 

**2.1.1 Plate sheet model** 

which is the Fick's second law expressed for the function K(z, t). Nevertheless the solution of equation (6) cannot be merely obtained by combining the solution of the general Fick's second law (2) with the substitution (5) because the two functions *K(z, t)* and *CRn (z, t)* do not admit the same initial and boundary conditions. These conditions are for *CRn (z, t)* :

$$\begin{aligned} \mathbf{C}\_{Rn} \left( z, \mathbf{0} \right) &= \mathbf{C}\_{RnEq} = \frac{\lambda\_{Ra}}{\lambda\_{Rb}} \mathbf{C}\_{Ra} \qquad & \text{for } -\mathbf{a} < \mathbf{z} < \mathbf{a}, \mathbf{t} = \mathbf{0} \\ \mathbf{C}\_{Rn} \left( z, \mathbf{t} \right) &= \mathbf{0} \qquad & \text{for } -\mathbf{z} = -\mathbf{a}, \mathbf{z} = \mathbf{a} \end{aligned} \tag{7}$$

(the atmosphere is considered as a reservoir of concentration *C* = 0) which means for *K(z, t)*:

$$\begin{aligned} \mathbf{K}(\mathbf{z},0) &= 0 & \text{for } -\mathbf{a} < \mathbf{z} < \mathbf{a}, \mathbf{t} = \mathbf{0} \\ \mathbf{K}(\mathbf{z},t) &= -\mathbf{C}\_{\mathrm{RnEq}} \exp\left(\lambda\_{\mathrm{Rn}}t\right) & \text{for } \quad \mathbf{z} = -\mathbf{a}, \mathbf{z} = \mathbf{a} \end{aligned} \tag{8}$$

Fick's law is usually solved for plane sheet geometry by separation of variables but this method is unsuccessful for such initial and boundary conditions. Several studies have been done for heat conduction in a slab having an initial zero temperature and surfaces maintained at the temperature *f(t) = V exp(vt)* (*Gauthier et al.,1999*), obtaining:

$$\begin{split} K(z,t) &= -C\_{RnEq} \exp(\lambda\_{Rn}t) \frac{\cosh\left(z\sqrt{\frac{\lambda\_{Rn}}{D}}\right)}{\cosh\left(a\sqrt{\frac{\lambda\_{Rn}}{D}}\right)} + \\ &+ \frac{4C\_{RnEq}}{\pi} \sum\_{n=0}^{\infty} \frac{(-1)^{n} \exp\left(\frac{-\left(2n+1\right)^{2}\pi^{2}Dt}{4a^{2}}\right)}{\left(2n+1\right)\left[1+\left(\frac{4\lambda\_{Rn}a^{2}}{\left(2n+1\right)^{2}\pi^{2}D}\right)\right]} \cos\frac{(2n+1)\pi z}{2a} \end{split} \tag{9}$$

and therefore, combining with (6):

$$\begin{split} \mathbf{C}\_{Rn} \left( z, t \right) &= \mathbf{C}\_{RnEq} - \mathbf{C}\_{RnEq} \frac{\cosh \left( z \sqrt{\frac{\lambda\_{Rn}}{D}} \right)}{\cosh \left( a \sqrt{\frac{\lambda\_{Rn}}{D}} \right)} + \\ &+ \frac{4 \mathbf{C}\_{RnEq}}{\pi} \sum\_{n=0}^{\infty} \frac{\left( -1 \right)^{n} \exp \left[ - \left( \frac{\left( 2n + 1 \right)^{2} \pi^{2} D}{4a^{2}} + \lambda\_{Rn} \right) t \right]}{\left( 2n + 1 \right) \left[ 1 + \left( \frac{4 \lambda\_{Rn} a^{2}}{\left( 2n + 1 \right)^{2} \pi^{2} D} \right) \right]} \cos \frac{(2n + 1) \pi z}{2a} \end{split} \tag{10}$$

By multiplying by Rn both sides of the equation (10), one obtains the activity of CRn (z, t) given in equation:

Radon as Earthquake Precursor 149

c. **Activated charcoal**: this type of detectors is based on the capability of the charcoal to adsorb Radon gas. The analysis is carried out by means of the gamma spectrometry of the Radon products. However with this kind of device measurements can be performed

d. **Thermoluminescent detector**: Radon is allowed to enter the detection device volume containing the TLD. A metallic plate, placed at short distance in front of the TLD, can be electrically charged for a better collection efficiency. Radon daughters deposited on the plate decay producing energy storage in the TLD. After appropriate exposition, the

e. **Scintillation detector**: the most widely used is the ZnS(Ag) scintillation cell for grab sampling. It is a metal container internally coated with silver activated zinc solphide. Light photons are detected, resulting from the interaction of the alpha particles from radon decaying. For counting the photons, the scintillation cell is coupled to a

In the last years active devices have been used for continuous measurements of in soil Radon gas. They use prevalently detectors as ionization chamber or silicon detectors. The devices have a probe placed in the soil at a certain depth, the gas Radon enters into the detection chamber or by means of a pump with a fixed flow rate or they can be placed inside the soil and the gas enters into the detection chamber via natural diffusion. This kind of measurements need power supply, not always available in active fault areas, but in the last years the detection systems have been implemented with solar panels, overcoming the problem. These devices have more performance respect to the previous ones because they allow continuous measurements and on-line reading by means of remote data transfer and

Accordingly, the choice among the different possibilities can be guided by the particular interest in radon measurements, whether in time-dependent or in space-dependent variations of the concentrations. In particular, spot measurements (with portable detectors) of soil–gas Radon are useful for the quick recognition of high emission sites to be later monitored for Radon variations in time. SSNTD allow for the temporal monitoring of a relatively large number of sites, but cannot distinguish short-term changes due to their long integration times. Continuous monitoring probes are optimal for defining detailed changes in soil–gas Radon activities, but are expensive and can thus be used to complete the

Most of the researchers define radon anomaly as the positive deviation that exceeds the

The origin and the mechanisms of the radon anomalies and their relationship to earthquakes are yet poorly understood, although several in-situ and laboratory experiments have been performed and mathematical modelings have been proposed. The radon observed in case of anomalies correlated with geophysical events may be considered as having two possible

sensitivity also to gamma radiations.

photomultiplier.

only for 3 – 5 days and they are affected by humidity.

TLD is recovered and read out in a TLD apparatus.

so they allow to monitor continuously the Radon temporal trend.

information acquired with SSNTD in a network of monitored sites.

**4. Origin and mechanisms of radon anomalies** 

mean radon level by more than twice the standard deviation.

changing in the total charge of the electret. This kind of detector offers several advantages: possibility to store information over relatively long period, independence from moisture in its envelop and ease to read. The main problems are linked to its response curve that does not cover efficiently the very low and very high doses and its

$$\begin{split} \mathcal{C}\_{Rn}(z,t) &= \mathcal{C}\_{Ra} - \mathcal{C}\_{ra} \frac{\cosh\left(z\sqrt{\mathcal{L}\_{Rn}}\right)}{\cosh\left(a\sqrt{\mathcal{L}\_{Rn}}\right)} + \\ &+ \frac{4\mathcal{C}\_{Ra}}{\pi} \sum\_{n=0}^{\infty} \frac{\left(-1\right)^{n} \exp\left[-\left(\frac{\left(2n+1\right)^{2}\pi^{2}D}{4a^{2}} + \mathcal{\lambda}\_{Rn}\right)t\right]}{\left(2n+1\right)\left[1 + \left(\frac{4\mathcal{L}\_{Rn}a^{2}}{\left(2n+1\right)^{2}\pi^{2}D}\right)\right]} \cos\frac{(2n+1)\pi z}{2a} \end{split} \tag{11}$$

where CRn and CRa represent the activity of 222Rn and 226Ra, respectively.

#### **2.1.1 Infinite source model**

In another earth model an infinite source C0 is overlain by an overburden of thickness *h*, where no radon source exists. In this case the radon transportation equation in the overburden, where radon production rate is zero, can be written as (*Wattanikorn et al,1998*):

$$\frac{d^2\mathbf{C}}{dz^2} + \frac{v}{D}\frac{d\mathbf{C}}{dz} - \frac{\lambda\_{Rn}}{D}\mathbf{C} = 0\tag{12}$$

where *C* is the radon concentration at depth *z*, *v* is the gas flow velocity; *D* is the diffusion coefficient of radon, and Rn is the decay constant. The solution of (12) is:

$$\mathbf{C}\_{Rn} = \mathbf{C}\_{Rn0} \exp\left[\frac{v(h-z)}{2D}\right] \frac{\sinh\left[\left(\sqrt{\left(\frac{v}{2D}\right)^2 + \frac{\lambda\_{Rn}}{D}}\right)z\right]}{\sinh\left[\left(\sqrt{\left(\frac{v}{2D}\right)^2 + \frac{\lambda\_{Rn}}{D}}\right)h\right]}\tag{13}$$

#### **3. Radon measurements**

In general Radon measurements can be performed in continuous, integrating or discrete mode, regarding the time duration of measurement, and by using passive devices, when Radon enters the detection system by natural diffusion, or active technique, when gas is pumped in the device, that require electric power.

Some types of the most used detectors for in-soil radon measurements are the following:


2 2 2

 

*n D*

*a C n z*

 

In another earth model an infinite source C0 is overlain by an overburden of thickness *h*, where no radon source exists. In this case the radon transportation equation in the overburden, where radon production rate is zero, can be written as (*Wattanikorn et al,1998*):

<sup>2</sup> <sup>0</sup> *Rn d C v dC <sup>C</sup>*

where *C* is the radon concentration at depth *z*, *v* is the gas flow velocity; *D* is the diffusion

sinh

In general Radon measurements can be performed in continuous, integrating or discrete mode, regarding the time duration of measurement, and by using passive devices, when Radon enters the detection system by natural diffusion, or active technique, when gas is

Some types of the most used detectors for in-soil radon measurements are the following: a. **Solid State nuclear track detectors**: the most used SSNTD are Cr-39 type or LR-115 one. They are particularly sensitive to alpha particles that, passing trough, produce tracks visible in optical microscope after chemical etching. The main advantages of this kind of detectors, especially for the first type, is that they are cheap, are sensitive only to alpha particles, are unaffected by humidity, low temperature, moderate heating and light.

b. **Electret detector**: an electret is a dielectric material that exhibits a permanent electrical charge. The particles from Radon decay produce ions within the device that determine

Moreover these passive devices don't need electrical power supply.

sinh

2 1

2 2

<sup>2</sup> <sup>4</sup> 2 11

*n D*

*Rn*

*t*

*a a*

*dz D dz D* (12)

*Rn*

*z*

(13)

2

2

*v*

2

2

*<sup>v</sup> <sup>h</sup> D D*

*Rn*

*Rn*

*Rn*

 

*z D*

*a D*

2 1 1 exp <sup>4</sup> <sup>4</sup> 2 1

 

cos

(11)

*<sup>n</sup> Rn*

cosh

*n*

*n*

where CRn and CRa represent the activity of 222Rn and 226Ra, respectively.

2

coefficient of radon, and Rn is the decay constant. The solution of (12) is:

exp <sup>2</sup>

0

*Rn Rn*

pumped in the device, that require electric power.

*D D vh z C C D*

cosh

<sup>2</sup> <sup>0</sup>

,

*Rn Ra ra*

*C zt C C*

**2.1.1 Infinite source model** 

**3. Radon measurements** 

*Ra*

changing in the total charge of the electret. This kind of detector offers several advantages: possibility to store information over relatively long period, independence from moisture in its envelop and ease to read. The main problems are linked to its response curve that does not cover efficiently the very low and very high doses and its sensitivity also to gamma radiations.


In the last years active devices have been used for continuous measurements of in soil Radon gas. They use prevalently detectors as ionization chamber or silicon detectors. The devices have a probe placed in the soil at a certain depth, the gas Radon enters into the detection chamber or by means of a pump with a fixed flow rate or they can be placed inside the soil and the gas enters into the detection chamber via natural diffusion. This kind of measurements need power supply, not always available in active fault areas, but in the last years the detection systems have been implemented with solar panels, overcoming the problem. These devices have more performance respect to the previous ones because they allow continuous measurements and on-line reading by means of remote data transfer and so they allow to monitor continuously the Radon temporal trend.

Accordingly, the choice among the different possibilities can be guided by the particular interest in radon measurements, whether in time-dependent or in space-dependent variations of the concentrations. In particular, spot measurements (with portable detectors) of soil–gas Radon are useful for the quick recognition of high emission sites to be later monitored for Radon variations in time. SSNTD allow for the temporal monitoring of a relatively large number of sites, but cannot distinguish short-term changes due to their long integration times. Continuous monitoring probes are optimal for defining detailed changes in soil–gas Radon activities, but are expensive and can thus be used to complete the information acquired with SSNTD in a network of monitored sites.
