**5. Case study**

168 Earthquake Research and Analysis – Statistical Studies, Observations and Planning

rock and radon volatilized into the gas phase. Stage 3 started at the point of minimum radon concentration when water saturation in cracks and pores began to increase and radon increased and recovered to the background level. The main shock produced a sharp coseismic anomalous decrease (~300 pCi/L). After the earthquake, some irregular variations were observed, which we attribute to strain release as some accumulation and release of

Radon partitioning into the gas phase can explain the anomalous decreases of radon precursory to the earthquakes (Kuo et al., 2006). To support the hypothesis of radon volatilization from ground water into the gas phase, radon-partitioning experiments were conducted to determine the variation of the radon concentration remaining in ground water with the gas saturation at formation temperature (60 ℃) using formation brine from the Antung hot spring. Five levels of gas saturation were investigated, specifically *Sg* = 5 %, 10 %, 15 %, 20 %, and 25 % where *Sg* is gas saturation. Triplicate experiments were conducted for each level of gas saturation. Every experiment started with 40-ml of formation brine. Five levels of headspace volume at 2 ml, 4 ml, 6 ml, 8 ml, and 10 ml were then created above the liquid phase for five levels of gas saturation at 5 %, 10 %, 15 %, 20 %, and 25 %, respectively. Two-phase equilibrium was achieved for each experiment in 30 minutes at the formation

A kinetic study of radon volatilization from ground water into the gas phase was conducted to determine the time required to reach equilibrium. In the kinetic experiment, formation brine from the Antung hot spring with an initial radon concentration of 479 ± 35 pCi/L was used. Every sample started with 40-ml formation brine and a headspace volume at 6 ml was then created above the liquid phase. A total of five samples were prepared. The radon concentration remaining in ground water was determined at various volatilization times (i.e., 2 min, 5 min, 15 min, 30 min, and 60 min). The time required to reach equilibrium for

Data from the vapor-liquid two-phase equilibrium radon-partitioning experiments (Fig. 8) were regressed with the two-phase partitioning model to determine Henry's coefficient as

where 0 *C* is initial radon concentration in groundwater precursory to each radon anomaly, pCi/L; *Cw* is the radon minimum in groundwater observed in well D1 during an anomalous decline, pCi/L; *Sg* is gas saturation, fraction; *H* is Henry's coefficient for radon at formation temperature (60 ℃), dimensionless. Fig. 8 shows the regressed line with *H* = 12.8 and R2 = 0.9919 (regression coefficient). Henry's coefficient for radon at 60 ℃ determined for the Antung formation brine (12.8) is higher than the value (7.91) for water at 60 ℃ (Clever, 1979). Fig. 8 can be used to estimate the amount of gas saturation required for various decreases in concentration of radon. For example, the anomalous decrease of radon concentration from 780 pCi/L to 330 pCi/L required a gas saturation of

<sup>0</sup> ( 1 ) *C CHS w g* (1)

strain continued in the region.

temperature (60 ℃).

follows.

10 % in cracks in the rock.

**4. In-situ radon volatilization mechanism** 

radon volatilization was only about 5 minutes.

We have monitored groundwater radon since July 2003 at well D1 at the Antung hot spring that is located about 3 km southeast of the Chihshang fault (Fig. 9). The Chihshang fault is part of the eastern boundary of the present-day plate suture between the Eurasia and the Philippine Sea plates. The Chihshang fault ruptured (Hsu, 1962) during two 1951 earthquakes of magnitudes M = 6.2 and M = 7.0. The annual survey of geodetic and GPS measurements has consistently revealed the active creep of the Chihshang fault that is moving at a rapid steady rate of about 2-3 cm/yr during the past 20 years (Angelier et al., 2000; Yu & Kuo, 2001; Lee et al., 2003).

Fig. 10 shows the radon concentration data since July 2003 at the monitoring well (D1) in the Antung hot spring. Radon-concentration errors are ±1 standard deviation after simple averaging of triplicates. Recurrent groundwater radon anomalies were observed to precede the earthquakes of magnitude *Mw* = 6.8, *Mw* = 6.1, *Mw* = 5.9, and *Mw* = 5.4 that occurred on December 10, 2003, April 1, 2006, April 15, 2006, and February 17, 2008 at the Antung D1 monitoring well. We consider the *Mw* 5.9 earthquake that occurred on April 15, 2006 triggered by stress transfer in response to the 2006 *Mw* 6.1 Taitung earthquake. All the three recurrent anomalous decreases observed at Antung follow the same v-shaped progression and are marked with green inverted triangles in Fig. 10. Environmental records such as atmospheric temperature, barometric pressure, and rainfall were examined to check whether the radon anomaly could be attributed to these environmental factors. The

Application of Recurrent Radon Precursors

for Forecasting Local Large and Moderate Earthquakes 171

the other hand, the radon anomalous minima, recorded precursory to strong earthquakes ( *Mw* > 6.0), the 2003 *Mw* = 6.8 Chengkung and 2006 *Mw* = 6.1 Taitung earthquakes, are

The radon minima, measured prior to local moderate earthquakes, are easily masked by the noisy background. Fig. 10 also shows the large background variation in radon data following the 2003 *Mw* = 6.8 Chengkung, 2006 *Mw* = 6.1 Taitung, and 2008 *Mw* = 5.4 Antung earthquakes. Four local earthquakes with magnitudes ( *Mw* ) of 5.5, 5.2, 6.2, and 5.2 occurred on 12/11/2003, 1/1/2004, 5/19/2004, and 9/26/2005, respectively. Based upon their magnitudes and locations, we consider these as aftershocks and induced events of the 2003 Chengkung earthquake. The large scatter in radon data between the 2003 *Mw* = 6.8 Chengkung and 2006 *Mw* = 6.1 Taitung earthquakes can be related to these aftershocks. The 2006 Mw 6.1 Taitung earthquake also triggered the Mw 5.9 earthquake that occurred on April 15, 2006. One local earthquake of magnitude *Mw* = 4.9 that occurred on 6/4/2006 can be considered as an aftershock of the 2006 *Mw* = 6.1 Taitung earthquake. The *Mw* = 4.9 aftershock also caused a large scatter in radon data following the 2006 *Mw* = 6.1 Taitung earthquake. The large background variation in radon data following the 2008 *Mw* = 5.4 Antung earthquake can also be attributed to local earthquakes, such as a local earthquake of

**2003/7/1 2004/7/1 2005/7/1 2006/7/1 2007/7/1 2008/7/1 2009/7/1 2010/7/1** 

**3**

**5.3**

**5.4**

**4.9**

**Year/Month/Day**

**2**

Fig. 10. Radon concentration data at well D1 in the Antung hot spring (open inverted triangles: anomalous radon minima; green inverted triangles: v-shaped pattern; long arrows: mainshocks; short arrows: aftershocks; earthquake magnitude *Mw* shown beside

**6.1 5.9**

**456**

**692 764 849**

**1077**

low enough to be clearly distinguished from the background noise.

magnitude *Mw* = 5.3 that occurred on 12/2/2008.

**222Rn (pCi/L)**

**222Rn (Bq/L)**

**0.0 3.7 7.4 11.1 14.8 18.5 22.2 25.9 29.6 33.3 37.0 40.7 44.4**

arrows).

**6.8**

**1**

**5.2 6.2**

**5.5 5.2**

atmospheric temperature, barometric pressure, and rainfall are periodic in season. It is difficult to explain such a large radon decrease by these environmental factors. There was also no heavy rainfall responsible for the radon anomaly.

Fig. 9. Map of the epicenters of the earthquakes that occurred on December 10, 2003, April 1 and 15, 2006, February 17, 2008 near the Antung hot spring. (a) Geographical location of Taiwan. (b) Study area near the Antung hot spring.

The box-and-whisker plot is used on the right-hand side in Fig. 10. It shows the median (50th percentile, 764 pCi/L) as a center bar, and the quartiles (25th and 75th percentiles, 692 pCi/L and 849 pCi/L) as a box. The whiskers (456 pCi/L and 1077 pCi/L) cover all but the most extreme values in the data set. Based on the box-and-whisker plot, the threshold concentration of anomalous radon minima at the Antung D1 monitoring well is estimated as 456 pCi/L. The radon minimum recorded prior to the 2008 *Mw* = 5.4 Antung earthquake is close to the threshold concentration and can be easily masked by the noisy background. On

atmospheric temperature, barometric pressure, and rainfall are periodic in season. It is difficult to explain such a large radon decrease by these environmental factors. There was

Fig. 9. Map of the epicenters of the earthquakes that occurred on December 10, 2003, April 1 and 15, 2006, February 17, 2008 near the Antung hot spring. (a) Geographical location of

The box-and-whisker plot is used on the right-hand side in Fig. 10. It shows the median (50th percentile, 764 pCi/L) as a center bar, and the quartiles (25th and 75th percentiles, 692 pCi/L and 849 pCi/L) as a box. The whiskers (456 pCi/L and 1077 pCi/L) cover all but the most extreme values in the data set. Based on the box-and-whisker plot, the threshold concentration of anomalous radon minima at the Antung D1 monitoring well is estimated as 456 pCi/L. The radon minimum recorded prior to the 2008 *Mw* = 5.4 Antung earthquake is close to the threshold concentration and can be easily masked by the noisy background. On

Taiwan. (b) Study area near the Antung hot spring.

also no heavy rainfall responsible for the radon anomaly.

the other hand, the radon anomalous minima, recorded precursory to strong earthquakes ( *Mw* > 6.0), the 2003 *Mw* = 6.8 Chengkung and 2006 *Mw* = 6.1 Taitung earthquakes, are low enough to be clearly distinguished from the background noise.

The radon minima, measured prior to local moderate earthquakes, are easily masked by the noisy background. Fig. 10 also shows the large background variation in radon data following the 2003 *Mw* = 6.8 Chengkung, 2006 *Mw* = 6.1 Taitung, and 2008 *Mw* = 5.4 Antung earthquakes. Four local earthquakes with magnitudes ( *Mw* ) of 5.5, 5.2, 6.2, and 5.2 occurred on 12/11/2003, 1/1/2004, 5/19/2004, and 9/26/2005, respectively. Based upon their magnitudes and locations, we consider these as aftershocks and induced events of the 2003 Chengkung earthquake. The large scatter in radon data between the 2003 *Mw* = 6.8 Chengkung and 2006 *Mw* = 6.1 Taitung earthquakes can be related to these aftershocks. The 2006 Mw 6.1 Taitung earthquake also triggered the Mw 5.9 earthquake that occurred on April 15, 2006. One local earthquake of magnitude *Mw* = 4.9 that occurred on 6/4/2006 can be considered as an aftershock of the 2006 *Mw* = 6.1 Taitung earthquake. The *Mw* = 4.9 aftershock also caused a large scatter in radon data following the 2006 *Mw* = 6.1 Taitung earthquake. The large background variation in radon data following the 2008 *Mw* = 5.4 Antung earthquake can also be attributed to local earthquakes, such as a local earthquake of magnitude *Mw* = 5.3 that occurred on 12/2/2008.

Fig. 10. Radon concentration data at well D1 in the Antung hot spring (open inverted triangles: anomalous radon minima; green inverted triangles: v-shaped pattern; long arrows: mainshocks; short arrows: aftershocks; earthquake magnitude *Mw* shown beside arrows).

Application of Recurrent Radon Precursors

before the main shock.

radon anomaly.

for Forecasting Local Large and Moderate Earthquakes 173

The observed v-shaped pattern prior to the three main shocks clearly progresses in a sequence of three stages (Kuo et al. 2006). The sequence of events for radon anomalies prior to the 2003 *Mw* = 6.8 Chengkung, 2006 *Mw* = 6.1 Taitung, and 2008 *Mw* = 5.4 Antung earthquakes were characterized into three stages in Figs. 11a, 11b, and 11c, respectively (Kuo et al. 2006, 2010a). During Stage 1, the radon concentration in ground water was fairly stable; there was an accumulation of tectonic strain and a slow, steady increase of regional stress. The Antung hot spring is a fractured aquifer with limited recharge surrounded by ductile mudstone (Chen & Wang 1996). When the regional stress increased under these geological conditions, dilation of brittle rock masses occurred at a rate faster than the rate at which ground water could recharge into the newly created rock cracks (Brace et al. 1966; Nur 1972; Scholz et al. 1973). During this stage (Stage 2 in Fig. 11), gas saturation and two phases (vapor and liquid) developed in the rock cracks. The radon in ground water volatilized into the gas phase and the radon concentration in ground water decreased. Stage 3 started at the point of minimum radon concentration when the water saturation in cracks and pores began to increase again. During this stage (Stage 3 in Fig. 11), the radon concentration in groundwater increased and recovered to the previous background level

Figs. 11a, 11b, and 11c show that during Stage 2 prior to the 2003 *Mw* = 6.8 Chengkung, 2006 *Mw* = 6.1 Taitung, and 2008 *Mw* = 5.4 Antung earthquakes the radon concentration in ground water kept decreasing for a significantly long period of 45, 47, 31 days, respectively. Combining the use of box-and-whisker plot, the v-shaped radon pattern shown in Figs. 10 and 11 prior to the 2003 *Mw* = 6.8 Chengkung, 2006 *Mw* = 6.1 Taitung, and 2008 *Mw* = 5.4 Antung earthquakes can be clearly distinguished from other scattering radon data which

As shown in Fig. 11, radon decreased from background levels of 787 ± 42, 762 ± 57, and 700 ± 57 pCi/L to minima of 326 ± 9, 371 ± 9, and 480 ± 43 pCi/L prior to the 2003 *Mw* = 6.8 Chengkung, 2006 *Mw* = 6.1 Taitung, and 2008 *Mw* = 5.4 Antung earthquakes, respectively. Kuo et al. (2010b) recognized that the observed precursory minimum in radon concentration decreases as the local earthquake magnitude increases. Kuo et al. (2010b) also proposed an

where *Cw* is the radon minimum in groundwater observed in well D1 during an anomalous decline, pCi/L; *Mw* is the earthquake magnitude. Eq. (2) did not take the initial stable radon concentration in groundwater precursory to each radon anomaly into account. Our observations in well D1 indicate that the initial stable radon concentration in groundwater precursory to each radon anomaly does vary occasionally. Eq. (2) will be improved by taking into account the initial stable radon concentration in groundwater precursory to each

Based on radon phase behavior and rock dilatancy, Kuo et al. (2006, 2010a) developed a mechanistic model correlating the observed decline in radon with the volumetric strain change. The model consists of two parts, i.e., the radon-volatilization model and the rock-

dilatancy model. The radon-volatilization model can be expressed as follows.

1063 110 *C M w w* (2)

appear to be related to smaller local earthquakes and aftershocks.

empirical correlation for local applications as follows.

Fig. 11. Observed radon anomalies at well D1 prior to (a) 2003 Chengkung, (b) 2006 Taitung, and (c) 2008 Antung earthquakes. Stage 1 is buildup of elastic strain. Stage 2 is development of cracks. Stage 3 is influx of ground water.

**Radon concentration (pCi/L)**

**Radon concentration (Bq/L)**

**Radon concentration (Bq/L)**

**Radon concentration (Bq/L)**

**0.0**

**7.4**

**14.8**

**22.2**

**29.6**

**37.0**

**0.0**

**7.4**

**14.8**

**22.2**

**29.6**

**37.0**

**Radon concentration (pCi/L)**

**Radon concentration (pCi/L)**

**0**

of cracks. Stage 3 is influx of ground water.

**200**

**400**

**600**

**800**

**1000**

**(c)**

**0.0**

**7.4**

**14.8**

**22.2**

**29.6**

**37.0**

**3**

**0**

**200**

**400**

**600**

**800**

**1000**

**2**

**0**

**200**

**400**

**600**

**800**

**1000**

**(a)**

**1**

**2003/8/1 2003/9/1 2003/10/1 2003/11/1 2003/12/1** 

**(b)** ▼

787 42 pCi/L

( 29.3 1.7 Bq/L )

762 57 pCi/L

( 28.2 2.1 Bq/L )

700 57 pCi/L

( 27.2 1.8 Bq/L )

**2005/11/1 2005/12/1 2006/1/1 2006/2/1 2006/3/1 2006/4/1** 

**2007/10/1 2007/11/1 2007/12/1 2008/1/1 2008/2/1** 

Fig. 11. Observed radon anomalies at well D1 prior to (a) 2003 Chengkung, (b) 2006 Taitung, and (c) 2008 Antung earthquakes. Stage 1 is buildup of elastic strain. Stage 2 is development

480 43 pCi/L ( 17.8 1.6 Bq/L )

**Year/Month/Day**

**Stage 1 2 3**

**Stage 1 2 3**

371 9 pCi/L

( 13.7 0.3 Bq/L )

31 days

56 days

326 9 pCi/L ( 12.1 0.3 Bq/L )

47 days

61 days

45 days

65 days

**Stage 1 2 3**

**Strain change (ppm)**

**2003** *M***w = 6.8 Chengkung Main shock** ▼

 **2006** *M***w = 6.1 Taitung Main shock**

**Strain change (ppm)**

**2008** *M***w = 5.4 Antung Main shock**

▼

**Strain change (ppm)**

The observed v-shaped pattern prior to the three main shocks clearly progresses in a sequence of three stages (Kuo et al. 2006). The sequence of events for radon anomalies prior to the 2003 *Mw* = 6.8 Chengkung, 2006 *Mw* = 6.1 Taitung, and 2008 *Mw* = 5.4 Antung earthquakes were characterized into three stages in Figs. 11a, 11b, and 11c, respectively (Kuo et al. 2006, 2010a). During Stage 1, the radon concentration in ground water was fairly stable; there was an accumulation of tectonic strain and a slow, steady increase of regional stress. The Antung hot spring is a fractured aquifer with limited recharge surrounded by ductile mudstone (Chen & Wang 1996). When the regional stress increased under these geological conditions, dilation of brittle rock masses occurred at a rate faster than the rate at which ground water could recharge into the newly created rock cracks (Brace et al. 1966; Nur 1972; Scholz et al. 1973). During this stage (Stage 2 in Fig. 11), gas saturation and two phases (vapor and liquid) developed in the rock cracks. The radon in ground water volatilized into the gas phase and the radon concentration in ground water decreased. Stage 3 started at the point of minimum radon concentration when the water saturation in cracks and pores began to increase again. During this stage (Stage 3 in Fig. 11), the radon concentration in groundwater increased and recovered to the previous background level before the main shock.

Figs. 11a, 11b, and 11c show that during Stage 2 prior to the 2003 *Mw* = 6.8 Chengkung, 2006 *Mw* = 6.1 Taitung, and 2008 *Mw* = 5.4 Antung earthquakes the radon concentration in ground water kept decreasing for a significantly long period of 45, 47, 31 days, respectively. Combining the use of box-and-whisker plot, the v-shaped radon pattern shown in Figs. 10 and 11 prior to the 2003 *Mw* = 6.8 Chengkung, 2006 *Mw* = 6.1 Taitung, and 2008 *Mw* = 5.4 Antung earthquakes can be clearly distinguished from other scattering radon data which appear to be related to smaller local earthquakes and aftershocks.

As shown in Fig. 11, radon decreased from background levels of 787 ± 42, 762 ± 57, and 700 ± 57 pCi/L to minima of 326 ± 9, 371 ± 9, and 480 ± 43 pCi/L prior to the 2003 *Mw* = 6.8 Chengkung, 2006 *Mw* = 6.1 Taitung, and 2008 *Mw* = 5.4 Antung earthquakes, respectively. Kuo et al. (2010b) recognized that the observed precursory minimum in radon concentration decreases as the local earthquake magnitude increases. Kuo et al. (2010b) also proposed an empirical correlation for local applications as follows.

$$C\_w = 1063 - 110M\_w \tag{2}$$

where *Cw* is the radon minimum in groundwater observed in well D1 during an anomalous decline, pCi/L; *Mw* is the earthquake magnitude. Eq. (2) did not take the initial stable radon concentration in groundwater precursory to each radon anomaly into account. Our observations in well D1 indicate that the initial stable radon concentration in groundwater precursory to each radon anomaly does vary occasionally. Eq. (2) will be improved by taking into account the initial stable radon concentration in groundwater precursory to each radon anomaly.

Based on radon phase behavior and rock dilatancy, Kuo et al. (2006, 2010a) developed a mechanistic model correlating the observed decline in radon with the volumetric strain change. The model consists of two parts, i.e., the radon-volatilization model and the rockdilatancy model. The radon-volatilization model can be expressed as follows.

$$\mathcal{C}\_{\mathfrak{o}} = \mathcal{C}\_{\mathfrak{w}} \left( H \times S\_{\mathfrak{z}} + 1 \right) \tag{1}$$

Application of Recurrent Radon Precursors

0.0

Fig. 12. Calculated crust-strain ( *d*

conclusions can be drawn from this study.

**6. Conclusions** 

0.5

1.0

Dimensionless radon-decline

1.5

2.0

for Forecasting Local Large and Moderate Earthquakes 175

recognized in all the three recurrent radon anomalies and the threshold concentration are useful for the early warning of potentially disastrous earthquakes ( *Mw* > 6.0) in the

5 5.5 6 6.5 7 7.5 Earthquake magnitude, Mw

occurred on December 10, 2003, April 1, 2006, February 17, 2008 as a function of earthquake

Since July 2003, we have recorded three recurring radon anomalies (precursory to the 2003 *Mw* = 6.8 Chengkung, 2006 *Mw* = 6.1 Taitung, and 2008 *Mw* = 5.4 Antung earthquakes) at well D1, located at the Antung hot spring. The local geological conditions near the Antung hot spring with well D1 situated in a fractured aquifer surrounded by ductile mudstone and the in-situ volatilization of groundwater radon were attributed for causing the recurrent radon anomalies precursory to the nearby large and moderate earthquakes. The following

) and observed radon-decline ( <sup>0</sup> 1

*w C*

*<sup>C</sup>* ) at well D1 that

magnitude ( *Mw* ). Radon-concentration errors are ±1 standard deviation.

0

1

2

3

4

Calculated crust-strain (ppm)

5

6

7

southern segment of coastal range and longitudinal valley of eastern Taiwan.

where 0 *C* is initial radon concentration in groundwater precursory to each radon anomaly, pCi/L; *Cw* is the radon minimum in groundwater observed in well D1 during an anomalous decline, pCi/L; *Sg* is gas saturation, fraction; *H* is Henry's coefficient for radon at formation temperature (60 ℃), dimensionless. The radon-volatilization model correlates the radon decline to the gas saturation for a given fracture porosity.

The rock-dilatancy model can be expressed as follows.

$$d\mathfrak{a} \; \equiv \; \oint \; \mathcal{S}\_{\mathfrak{g}} \tag{3}$$

where *d* is volumetric strain, fraction; is initial fracture porosity before rock dilatancy, fraction; *Sg* is gas saturation, fraction. The rock-dilatancy model correlates the volumetric strain to the gas saturation for a given fracture porosity.

Combining the radon volatilization and rock dilatancy models, equations (1) and (3), the groundwater radon concentrations can be correlated to the strain changes associated with earthquake occurrences as follows.

$$dx \triangleq \frac{\phi}{H} \left( \frac{\mathbb{C}\_0}{\mathbb{C}\_w} - 1 \right) \tag{4}$$

where 0 1 *w C C* is normalized radon decline, dimensionless. The Henry's coefficients ( *H* ) at

formation temperature (60 ℃) is 7.91 for radon (Clever, 1979). Given an average fracture porosity of 0.00003 for the Antung hot spring, Eq. (4) can be used to calculate the crust strain.

Using the radon minima precursory to the 2003, 2006, and 2008 quakes, the calculated crust –strain and observed dimensionless radon-decline are plotted as a function of earthquake magnitude in Fig. 12. The best-fitting straight line is obtained by means of the least-square method with a high value of the sample correlation squared regression coefficient (i.e., R2 = 0.9802). The regressed equations are as follows.

$$d\varepsilon = 2.5893M\_w - 12.0948\tag{5}$$

$$\left(\frac{C\_o}{C\_w} - 1\right) = 0.6827M\_w - 3.189\tag{6}$$

where 0 *C* is initial radon concentration in groundwater precursory to each radon anomaly, pCi/L; *Cw* is the radon minimum in groundwater observed in well D1 during an anomalous decline, pCi/L; *Mw* is the earthquake magnitude; *d* is volumetric strain, fraction. Eq. (6) would be quite useful locally in predicting earthquake magnitude nearby the Chihshang fault from the radon minimum observed in well D1 during an anomalous decline.

Three precursory radon minima associated with nearby large and moderate earthquakes have been recorded from the same monitoring well (D1). The same v-shaped pattern

where 0 *C* is initial radon concentration in groundwater precursory to each radon anomaly, pCi/L; *Cw* is the radon minimum in groundwater observed in well D1 during an anomalous decline, pCi/L; *Sg* is gas saturation, fraction; *H* is Henry's coefficient for radon at formation temperature (60 ℃), dimensionless. The radon-volatilization model correlates the

> *<sup>g</sup> d S*

fraction; *Sg* is gas saturation, fraction. The rock-dilatancy model correlates the volumetric

Combining the radon volatilization and rock dilatancy models, equations (1) and (3), the groundwater radon concentrations can be correlated to the strain changes associated with

formation temperature (60 ℃) is 7.91 for radon (Clever, 1979). Given an average fracture porosity of 0.00003 for the Antung hot spring, Eq. (4) can be used to calculate the crust

Using the radon minima precursory to the 2003, 2006, and 2008 quakes, the calculated crust –strain and observed dimensionless radon-decline are plotted as a function of earthquake magnitude in Fig. 12. The best-fitting straight line is obtained by means of the least-square method with a high value of the sample correlation squared regression coefficient (i.e., R2 =

2.5893 12.0948 *<sup>w</sup> d M*

*<sup>C</sup> <sup>M</sup>*

fault from the radon minimum observed in well D1 during an anomalous decline.

<sup>0</sup> 1 0.6827 3.189 *<sup>w</sup>*

where 0 *C* is initial radon concentration in groundwater precursory to each radon anomaly, pCi/L; *Cw* is the radon minimum in groundwater observed in well D1 during an anomalous

would be quite useful locally in predicting earthquake magnitude nearby the Chihshang

Three precursory radon minima associated with nearby large and moderate earthquakes have been recorded from the same monitoring well (D1). The same v-shaped pattern

*w*

*C* 

*<sup>C</sup> <sup>d</sup> H C* 

<sup>0</sup> 1 *w*

is normalized radon decline, dimensionless. The Henry's coefficients ( *H* ) at

 

radon decline to the gas saturation for a given fracture porosity.

The rock-dilatancy model can be expressed as follows.

strain to the gas saturation for a given fracture porosity.

is volumetric strain, fraction;

0.9802). The regressed equations are as follows.

decline, pCi/L; *Mw* is the earthquake magnitude; *d*

earthquake occurrences as follows.

where *d*

where 0 1 *w C C* 

strain.

<sup>0</sup> ( 1 ) *C CHS w g* (1)

(3)

(4)

is initial fracture porosity before rock dilatancy,

(5)

(6)

is volumetric strain, fraction. Eq. (6)

recognized in all the three recurrent radon anomalies and the threshold concentration are useful for the early warning of potentially disastrous earthquakes ( *Mw* > 6.0) in the southern segment of coastal range and longitudinal valley of eastern Taiwan.

Fig. 12. Calculated crust-strain ( *d* ) and observed radon-decline ( <sup>0</sup> 1 *w C <sup>C</sup>* ) at well D1 that occurred on December 10, 2003, April 1, 2006, February 17, 2008 as a function of earthquake magnitude ( *Mw* ). Radon-concentration errors are ±1 standard deviation.
