**4.3.2 Decision trees**

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

training and cross-validation set, while the test set was used to verify its performance. The

Fig. 3. The ANN topology for learning radon concentration dependency on environmental

In the testing phase, the correlation between the measured (m-*C*Rn) and predicted (p-*C*Rn) radon concentration in NSA periods was compared to the correlation between the measured and predicted radon concentration in the entire dataset (NSA and SA). The difference between the correlation coefficients might indicate a period of seismically induced radon anomaly. The ratio between the measured and predicted values (m-*C*Rn/p-*C*Rn)1 represents

Fig. 4. The ratio between the measured and predicted radon concentration (m-*C*Rn/p-*C*Rn)1 using an ANN in the case of soil gas radon in the Krško basin for a seismic window of ±7 days. A radon anomaly, possibly caused by a seismic event, is observed when the signal

A radon anomaly is held to be when the absolute value of signal (m-*C*Rn/p-*C*Rn)1 exceeds the predefined threshold of 0.2. The ANN in this case performed the best in the case of a seismic window of ±7 days (indicating the length of the period of pre- and post-seismic changes).

topology of the ANN generated for each NSA dataset is shown in Fig. 3.

parameters.

the discrepancy between both values (Fig. 4).

exceeds the threshold value of 0.2.

Decision trees are machine-learning methods for constructing prediction models from data. The models are obtained by recursively partitioning the data space and fitting a simple prediction model within each partition. As a result, the partitioning can be represented graphically as a decision tree, where each internal node contains a test on an attribute, each branch corresponds to an outcome of the test, and each leaf node gives a prediction for the value of the class variable (Džeroski, 2001; Loh, 2011). Regression trees are designed for dependent variables that take continuous or ordered discrete values. Like classical regression equations, they predict the value of a dependent variable (called the class) from the values of a set of independent variables (called attributes).

Fig. 5. A schematic description of the different stages of radon data series analysis with machine learning methods.

The model in each leaf can be either a linear equation or just a constant; trees with linear equations in the leaves are also called model trees. Tree construction proceeds recursively, starting with the entire set of training examples. At each step, the most discriminating attribute is selected as the root of the sub-tree and the current training set is split into subsets according to the values of the selected attribute. For continuous attributes, a threshold is selected and two branches are created, based on that threshold. The attributes that appear in the training set are considered to be thresholds. Tree construction stops when the variance of the class values of all examples in a node is small enough. These nodes are called leaves and are labelled with a model for predicting the class value. An important mechanism used to prevent the tree from over-fitting data is tree pruning.

Regression (RT) and model trees (MT), as implemented with the WEKA data mining suite (Witten & Frank, 1999), were used for predicting radon concentration from meteorological parameters in the case of radon time series in soil gas at the Krško basin (Zmazek et al., 2003; Zmazek et al., 2005) and in the thermal spring water in Zatolmin (Zmazek et al., 2006).

Radon as an Earthquake Precursor – Methods for Detecting Anomalies 189

days was chosen. The performance was estimated with 10-fold cross-validation in order to evaluate the predictability of the radon concentration in the NSA periods. The model built on the NSA data set was then applied to the SA data set and the performance change was determined using two different measures, the correlation coefficient (*r*) and the root mean square error (RMSE). For the purposes of prediction, the measured performance in NSA periods should be higher than the performance in SA periods. In these periods, when the discrepancy between the measured and predicted radon concentration is low, no seismic activity is anticipated (Fig. 6a), while in the periods with a higher discrepancy, a radon anomaly can be ascribed to increased seismic activity, rather than to the effect of atmospheric parameters (Fig. 6b). This discrepancy is clearly shown in form of the ratio between both values (m-*C*Rn/p-*C*Rn)1, as shown in Fig. 6c. A radon anomaly is held to be when the absolute value of the signal (m-*C*Rn/p-*C*Rn)1 exceeds the predefined threshold of 0.2. Besides regression trees, other machine learning methods were also tested (e.g., linear regression and instance-based regression). However, model trees have been shown to

The results of all of the approaches used for the identification of radon anomalies caused by seismic events in the case of soil gas radon at the Krško basin are shown in Fig. 7 for the period of 1/9 – 30/12/2000. Among all of the approaches – and although not very exact – the ±xσ method (I) is the most frequently used. The threshold of anomalous concentrations (e.g., ±1σ, ±2σ, ±3σ) should be chosen in order to minimise the number of false anomalies (FA: anomalies in seismically non-active periods) and so as not to miss the correct ones (CA). Generally, a range of ±2σ from the related seasonal mean value is chosen. Furthermore, a cyclic behaviour of radon concentration has to be taken into account in order to accurately define the period of standard deviation and the calculation of the mean value. For this purpose different methods of time series analyses – for example, Fourier transform

In the case shown in Fig. 7a, three radon anomalies exceeding 2σ above the mean value may be noticed. The first, in the beginning of September, cannot be assigned to a seismic event (FA). About a week before a weak earthquake of local magnitude *M*L=1.1, 5 km away from the measurement location – which is the first of five earthquakes over a period of 2 months – the second anomaly is observed. And finally, the third one can be noticed soon after a weak

The first of the anomalies mentioned above as FA is also visible by applying the method of pressure gradients (II) (Fig. 7b). A positive correlation between the time gradient of radon concentration and the time gradient of barometric pressure is considered to be a radon anomaly, and corresponds to the anomaly observed through method (I) which preceded the first earthquake (*M*L=1.1). A radon anomaly can also be noticed a few days before the last earthquake, as with the analysis of method (I). Additionally, the anomalous behaviour of the radon concentration as regards the gradient approach is observed during the period starting a few days before the earthquake with *M*L=2.7 and lasting until the earthquake with *M*L=1. More often than not, swarms of anomalies are observed over longer periods, with a higher number of anomalies in a swarm observed for approach (II) than for approach (I). As an additional criterion, a threshold of Δ*P*/Δ*t* > 2 hPa d1 is introduced by this approach in order to optimise the identification of anomalies caused by seismic events. However, by increasing the threshold value above 2 hPa d1, the ratio between correct and false anomalies cannot be

outperform other approaches.

**4.4 Comparison of the results** 

(Ramola, 2010) – can be applied.

earthquake 6 km away (*M*L=1).

significantly improved (Zmazek et al., 2005).

Fig. 6. Measured and predicted radon concentration using model trees in the case of soil gas radon at the Krško basin for a seismic window ±7 days; a) low discrepancy in the period without seismic activity; b) high discrepancy starting 10 days before a group of earthquakes; c) the ratio between the measured and predicted radon concentration (m-*C*Rn/p-*C*Rn)1 for the same SA period. A radon anomaly, possibly caused by earthquakes, is observed when the signal exceeds the threshold value of 0.2 (marked by the green lines).

As presented in Fig. 5 the first stage of data analysis comprises the selection of attributes – i.e. environmental parameters – and the partitioning of the whole data set to the periods with and without seismic activity, SA and NSA respectively. After inspecting the correlation changes between radon concentration and barometric pressure, a seismic window of ±7 days was chosen. The performance was estimated with 10-fold cross-validation in order to evaluate the predictability of the radon concentration in the NSA periods. The model built on the NSA data set was then applied to the SA data set and the performance change was determined using two different measures, the correlation coefficient (*r*) and the root mean square error (RMSE). For the purposes of prediction, the measured performance in NSA periods should be higher than the performance in SA periods. In these periods, when the discrepancy between the measured and predicted radon concentration is low, no seismic activity is anticipated (Fig. 6a), while in the periods with a higher discrepancy, a radon anomaly can be ascribed to increased seismic activity, rather than to the effect of atmospheric parameters (Fig. 6b). This discrepancy is clearly shown in form of the ratio between both values (m-*C*Rn/p-*C*Rn)1, as shown in Fig. 6c. A radon anomaly is held to be when the absolute value of the signal (m-*C*Rn/p-*C*Rn)1 exceeds the predefined threshold of 0.2. Besides regression trees, other machine learning methods were also tested (e.g., linear regression and instance-based regression). However, model trees have been shown to outperform other approaches.

### **4.4 Comparison of the results**

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

Fig. 6. Measured and predicted radon concentration using model trees in the case of soil gas radon at the Krško basin for a seismic window ±7 days; a) low discrepancy in the period without seismic activity; b) high discrepancy starting 10 days before a group of earthquakes; c) the ratio between the measured and predicted radon concentration (m-*C*Rn/p-*C*Rn)1 for the same SA period. A radon anomaly, possibly caused by earthquakes, is observed when

As presented in Fig. 5 the first stage of data analysis comprises the selection of attributes – i.e. environmental parameters – and the partitioning of the whole data set to the periods with and without seismic activity, SA and NSA respectively. After inspecting the correlation changes between radon concentration and barometric pressure, a seismic window of ±7

the signal exceeds the threshold value of 0.2 (marked by the green lines).

The results of all of the approaches used for the identification of radon anomalies caused by seismic events in the case of soil gas radon at the Krško basin are shown in Fig. 7 for the period of 1/9 – 30/12/2000. Among all of the approaches – and although not very exact – the ±xσ method (I) is the most frequently used. The threshold of anomalous concentrations (e.g., ±1σ, ±2σ, ±3σ) should be chosen in order to minimise the number of false anomalies (FA: anomalies in seismically non-active periods) and so as not to miss the correct ones (CA). Generally, a range of ±2σ from the related seasonal mean value is chosen. Furthermore, a cyclic behaviour of radon concentration has to be taken into account in order to accurately define the period of standard deviation and the calculation of the mean value. For this purpose different methods of time series analyses – for example, Fourier transform (Ramola, 2010) – can be applied.

In the case shown in Fig. 7a, three radon anomalies exceeding 2σ above the mean value may be noticed. The first, in the beginning of September, cannot be assigned to a seismic event (FA). About a week before a weak earthquake of local magnitude *M*L=1.1, 5 km away from the measurement location – which is the first of five earthquakes over a period of 2 months – the second anomaly is observed. And finally, the third one can be noticed soon after a weak earthquake 6 km away (*M*L=1).

The first of the anomalies mentioned above as FA is also visible by applying the method of pressure gradients (II) (Fig. 7b). A positive correlation between the time gradient of radon concentration and the time gradient of barometric pressure is considered to be a radon anomaly, and corresponds to the anomaly observed through method (I) which preceded the first earthquake (*M*L=1.1). A radon anomaly can also be noticed a few days before the last earthquake, as with the analysis of method (I). Additionally, the anomalous behaviour of the radon concentration as regards the gradient approach is observed during the period starting a few days before the earthquake with *M*L=2.7 and lasting until the earthquake with *M*L=1.

More often than not, swarms of anomalies are observed over longer periods, with a higher number of anomalies in a swarm observed for approach (II) than for approach (I). As an additional criterion, a threshold of Δ*P*/Δ*t* > 2 hPa d1 is introduced by this approach in order to optimise the identification of anomalies caused by seismic events. However, by increasing the threshold value above 2 hPa d1, the ratio between correct and false anomalies cannot be significantly improved (Zmazek et al., 2005).

Radon as an Earthquake Precursor – Methods for Detecting Anomalies 191

Both machine learning approaches, artificial neural networks (III) and decision trees (IV) give promising results, with a low number of false anomalies. The two distinctive anomalies – observed in Fig. 7c and Fig. 7d, for ANN and MT, respectively – confirm the anomalies identified by approaches (I) and (II). Additionally, a relatively long negative anomaly was observed using the ANN approach at the end of November, accompanying the earthquake with *M*L=1.6. On the other hand, the same negative anomaly is only weakly expressed using the MT approach. A FA observed at the beginning of September using approaches (I) and (II) was also noticed using the MT approach but not by the ANN approach. Approaches (III) and (IV) do not appear to greatly depend upon the choice for the threshold of (m-*C*Rn/p-

Since the appropriate interpretation of field measurements plays an important role in any research, the purpose of this work was to combine and evaluate the different approaches applied by our research group for differentiating the radon anomalies caused by increased seismic activity from those caused solely by environmental parameters. The application of four different approaches – standard deviation from the related mean value (I), the correlation between time gradients of barometric pressure and radon concentration (II), artificial neural networks (III) and decision trees (IV) – was presented. Radon anomalies based on approach (I) have been less successful in predicting earthquakes than those based on the other three approaches. Secondly, approaches (I) and (II) greatly depend upon the values of the ±xσ and Δ*P*/Δ*t* thresholds, respectively, while the dependence of approaches (III) and (IV) on the threshold of (m-*C*Rn/p-*C*Rn)1 is very weak. The number of false anomalies for approach (II) points to the disturbance of radon exhalation by other environmental parameters and not just by barometric pressure. The assumption that radon exhalation is only directly influenced by barometric pressure is further suggested by different forms of radon transport at compression and dilatation zones (Ghosh et al., 2009). Promising results are achieved by applying approaches (III) and (IV), which make it possible to simultaneously incorporate all of the available environmental parameters. Furthermore, in using these techniques, the relation between radon concentration and environmental parameters does not necessarily have to be presumed linear. And finally, in taking into account the scale of the earthquake magnitudes observed during the time of radon measurements, one may speculate that the performance of the applied approaches

This study was done within the program P1-0143: Cycling of substances in the environment,

Anderson, O.L., & Grew, P.C. (1977). Stress-corrosion theory of crack-propagation with applications to geophysics. *Reviews of Geophysics,* Vol. 15, No. 1, pp. 77–104 Atkinson, B.K. (1980). Stress corrosion and the rate-dependent tensile failure of a fine-

grained quartz rock. *Tectonophysics,* Vol. 65, No. 3–4, pp. 281–290

mass balances, modelling of environmental processes and risk assessment.

*C*Rn)1 and can, therefore, be used with less hesitation.

would be better in the case of stronger earthquakes.

**6. Acknowledgement** 

**7. References** 

**5. Conclusion** 

Fig. 7. A comparison of different approaches for the identification of radon anomalies: a) standard deviation (I); b) the relationship between radon exhalation and barometric pressure (II); c) artificial neural networks (III); and d) model trees (IV).

Both machine learning approaches, artificial neural networks (III) and decision trees (IV) give promising results, with a low number of false anomalies. The two distinctive anomalies – observed in Fig. 7c and Fig. 7d, for ANN and MT, respectively – confirm the anomalies identified by approaches (I) and (II). Additionally, a relatively long negative anomaly was observed using the ANN approach at the end of November, accompanying the earthquake with *M*L=1.6. On the other hand, the same negative anomaly is only weakly expressed using the MT approach. A FA observed at the beginning of September using approaches (I) and (II) was also noticed using the MT approach but not by the ANN approach. Approaches (III) and (IV) do not appear to greatly depend upon the choice for the threshold of (m-*C*Rn/p-*C*Rn)1 and can, therefore, be used with less hesitation.
