Monte Carlo Aggregating Method for Radon Precursor-Based Earthquake Parameter Prediction in Java, Indonesia

Earthquake early prediction technology is an exciting innovation to develop, especially in Indonesia. Indonesia is at the meeting point of the world's active tectonic plates, causing high seismic activity. Earthquakes with large magnitudes have the potential to create damage that impacts the lives of affected communities. If not anticipated, infrastructure damage, chaos, and even loss of human life are examples of the impacts of natural disasters. Early prediction technology is built to provide earlier information before an earthquake occurs. With this technology, mitigation can be achieved to reduce the impact of the disaster.

Before an earthquake occurs, several natural phenomena can be used as precursors. Potential earthquake precursors that can be used are the Earth’s magnetic field anomalies, radon gas emissions, and soil temperature. Radon is a naturally occurring radioactive gas found in Earth’s crust. Radon is a potential seismic precursor because it is released from the Earth’s cavity during a seismic event. The radon gas anomaly is internationally recognized as one of the seven seismic precursors [1]. One significant advantage is its ability to serve as a short-term pre-seismic indicator due to its rapid emission changes preceding earthquakes [2].

In comparison to other seismic precursors like electromagnetic anomalies and soil temperature, radon emissions provide a distinct geochemical signal directly linked to subsurface stress changes [3]. This geochemical nature allows radon monitoring to detect stress accumulations that may not produce immediate electromagnetic responses or soil temperature changes. Moreover, when used in conjunction with other precursors, radon data can enhance the robustness of earthquake forecasting models by providing complementary information [3]. The monitoring of radon gas concentrations for earthquake precursors has been established as a valuable approach given the abundance of this radioactive gas in groundwater with a short half-life, making it a suitable indicator for seismic activity [4]. However, the reliability of radon as a sole predictor is challenged by its sensitivity to environmental factors such as precipitation and atmospheric pressure changes, which can obscure seismic-related anomalies [5].

Radon anomalies observed before earthquakes have been a focal point of research, with findings suggesting that changes in radon release rates could be key precursory phenomena for earthquakes [6]. Previous studies have shown that changes in radon concentrations in groundwater and soil can be an early sign of an earthquake, because sudden changes in radon concentrations often occur before seismic events [7]. This is reinforced by many recent studies that showed changes in radon concentrations before major earthquakes [8]. Radon gas emissions can be a short-term pre-seismic precursor [9]. Radon concentration anomalies indicate impending earthquakes. This is reinforced by research that highlights the

correlation between radon gas concentrations, meteorological data, hydrology, and seismic activity [10]. Radon gas concentration fluctuations can also be used as medium and long-term indicators to reveal abnormal underground air changes before an earthquake occurs [2]. Radon-based earthquake precursors in Indonesia have also been reported [11, 12]. The phenomenon of anomalous radon gas concentrations before the 5.6 M earthquake on June 8, 2023, south of Java Island, Indonesia, is shown in Figure 1.

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Figure 1. Radon concentration anomaly phenomenon

Earthquake parameter prediction using artificial intelligence (AI) technology is being increasingly developed along with advances in the field of computing. In particular, the application of machine learning as a branch of AI has great potential for the development of prediction algorithms that can provide more accurate and faster results. However, one of the main challenges in applying machine learning to earthquake prediction is the requirement for a large amount of high-quality data. These data are required for the model training process and for validating the accuracy of the algorithm. An earthquake is a natural event that occurs suddenly and in limited quantities; therefore, collecting sufficient data for machine learning is a challenge. In addition, specifically for data on radon gas concentration fluctuations, one of the precursors of earthquakes, this data collection takes a long time because significant changes in radon concentration occur only before an earthquake.

Earthquake event simulation efforts have been conducted previously [13-15]. Simulations were conducted using the Monte Carlo method. This work modified the machine learning method using the Monte Carlo approach to predict earthquakes based on radon gas precursors. This study is expected to increase the accuracy of predictions, so that earthquake early warning technology can be created to benefit the community. This study modified the limited training data to develop a more accurate prediction model. This modification was performed by increasing the training data using the Monte Carlo method to produce variations close to real conditions. The training data generated from this method is then used to build a more robust prediction model. The prediction model was then subjected to an aggregation process to produce more reliable prediction results.

The main contribution of this study is to solve the issue of limited datasets to improve the prediction accuracy of earthquake parameters based on radon gas precursors. This paper is divided into four sections. The first Section, the Introduction, discusses the background and objectives of the problem. The second Section, Related Work, provides a review of previous studies that have been conducted in earthquake prediction. Section Proposed Method describes the steps for implementing the Monte Carlo method and aggregation techniques. The fourth Section, Results and Discussion, presents the simulation results using radon-based earthquake precursor data and the analysis of these results. Finally, the Conclusion Section summarizes the main findings of this study.

3.1 Monte Carlo Aggregating

Fluctuations in radon gas concentrations at the radon monitoring station prior to the earthquake exhibited a sudden and significant increase. The gain at the monitoring station was defined as the ratio of the peak fluctuation value to the average radon gas concentration measured over the seven days preceding the fluctuation. This station gain value was used to predict the earthquake parameters. A visualization of the station gain is shown in Figure 2. Figure 2 shows that a single fluctuation occurred, which has been identified as a precursor to earthquakes [20]. The gain of the monitoring station is expressed by Eq. (1).

$G_S=\frac{R_{\max }}{\frac{1}{n} \sum_{i=0}^{i=n} R_{t-i}}$                    (1)

where,

G_S = Gain of the monitoring station,

R_max = Maximum Radon value (Bq/m³),

R_t-i = Daily average Radon value (Bq/m³).

In this study, an algorithm was designed to predict earthquake parameters using the gain of the Radon Monitoring Station. Owing to the random nature of earthquakes, with a distribution that is challenging to determine, the algorithm was required to account for this randomness and uncertainty. One approach employed was the use of a Monte Carlo simulation. A simulation was conducted to obtain all possible output values of the prediction. The illustration of the Monte Carlo approach is presented in Figure 3.

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Figure 2. Gain monitoring of radon concentration anomaly

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Figure 3. Monte Carlo approach in data training

The Monte Carlo method applied in this study utilized probability distributions derived from historical data of radon concentration anomalies and seismic activity. To ensure that the generated synthetic data closely aligned with observed patterns, an empirical distribution was selected, providing a more accurate representation of the variability present in real-world data. Random samples were subsequently generated based on the empirical distribution to simulate variations in prediction errors of earthquake parameters. These samples were specifically designed to replicate the potential uncertainties inherent in earthquake prediction. The proposed method was trained on historical data, ensuring that the simulations accurately captured the relationships present in the observed data. This approach was implemented to ensure the robustness and relevance of the Monte Carlo simulations for earthquake prediction, grounding the methodology in empirical data and realistic patterns to enhance its reliability.

The first step in the proposed method involved creating a probability distribution of prediction errors. At this stage, the prediction error (e) was obtained at this stage by measuring the difference between the output training data (Y train) and the predicted value using a prediction model with the input training data (X train). This probability distribution is then formed into a probability mass function (f(e)) expressed in Eq. (2).

$f\left(e_i\right)=\left\{\begin{array}{lll}P_1 & \text { for } & e_1 \\ P_2 & \text { for } & e_2 \\ \cdots & \cdots & \cdots \\ P_m & \text { for } & e_m\end{array}\right.$                      (2)

P is the probability of a prediction error occurring, and i is an index with values ranging from 1 to m. The probability mass function was then used to create random prediction errors. The probability mass function is then used to form the cumulative probability function (F(e)), which is written as:

$F\left(e_i\right)=\left\{\begin{array}{ccc}P_1 & \text { for } & e_1 \\ P_1+P_2 & \text { for } & e_2 \\ \ldots & \ldots & \ldots \\ 1 & \text { for } & e_m\end{array}\right.$                   (3)

The random number U (Uniform(0,1)) determines the prediction error value. If the random number value is $P_1 \leq U \leq P_1+P_2$, then the prediction error value is e₂. The resulting prediction error was then added to the output training data (Y train). The prediction model is then created using the Y train, which has added errors. The prediction model can then predict the Y-test with the input X-test.

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Figure 4. Monte Carlo Aggregating method

Given that an earthquake is a random event with significant uncertainty in its prediction, the Monte Carlo approach was implemented to enhance prediction accuracy. Prediction errors, which were generated randomly through n iterations, produced n prediction models, allowing the prediction output to be approximated as the average of the predicted outputs from each model. By simulating all possible outcomes based on the probability distribution, the predictive capability was expected to improve. Based on this approach, the Monte Carlo Aggregating (MCA) method for earthquake prediction was developed. The Monte Carlo aggregation method is drawn in Figure 4.

3.2 Data collection

The monitoring station was located in the Special Region of the Yogyakarta Province (lat. -7.7531627 S, long. 110.4215244 E), Indonesia. This area is located in the central part of Java. Java Island is adjacent to the subduction zone at the bottom of the Indian Ocean along the southern coast of Java. Therefore, the island is prone to earthquakes and tsunamis. The sensor used is the ion chamber RD200 sensor, and radon data can be accessed at http://dataalamdiy.com/dataview/, whereas earthquake data can be accessed from https://earthquake.usgs.gov/earthquakes/map/. The data used were earthquake and radon gas data from December 11, 2022, to August 8, 2023. The data were collected based on the radius of the earthquake event at the radon monitoring station. The earthquake profile used in this study is summarized in Table 1.

Table 1. Earthquake profile

The earthquake data used in this study are presented in Table 1. This table provides a summary of seismic events based on three radial distances from the monitoring station: 200, 300, and 400 km. The table shows that the minimum earthquake magnitude recorded was 4, with the maximum magnitude being 5.9 at a radius of 200 km and 7 at radii of 300 km and 400 km. The distance of the closest earthquake event to the monitoring station was 92.87 km, while the maximum distance was 197.21 km at a radius of 200 km, 285.85 at a radius of 300 km and 393.19 km at a radius of 400 km. The time of occurrence of earthquakes after the anomaly with minimum time was recorded between 2 h and a maximum time of 168 h. Meanwhile, the number of earthquake events recorded was 12 at 200 km, 32 at 300 km, and 46 at 400 km.

3.3 Evaluation and validation

The prediction evaluation was performed using the RMSE metric [29]. RMSE is the square root of the mean of the squares of the prediction errors, which provides a measure of the error in native units. RMSE is expressed by:

$R M S E=\sqrt{\frac{\sum_{i=1}^n\left(Y_i-\hat{Y}_i\right)^2}{N}}$                      (4)

$\hat{Y}_i$ is the predicted value, $Y_i$ is the recorded earthquake parameter value and $N$ denotes the number of data points to be evaluated. Model validation was performed using a 5-fold cross-validation technique. The average RMSE is used to evaluate the performance of the proposed method.

3.4 Baseline method

One of the challenges in earthquake prediction using radon gas as a precursor is the lack of a representative radon precursor dataset and appropriate baseline methods that could help researchers compare their approaches and results [28]. To compare our study, we selected a baseline regression method from previous research based on performance results and data characteristics, enabling our approach to be applied to other studies. Random Forest has been previously used for earthquake prediction and produced good results [30]. In earlier studies, XGBoost [31] and linear regression [32] were also developed to predict earthquake events.

From the research conducted, it is proven that the proposed Monte Carlo Aggregating algorithm for dataset limitation in earthquake parameter prediction performs better than several other methods. This algorithm can provide more accurate predictions, which is often the main obstacle to earthquake prediction. The findings demonstrate the performance of Monte Carlo Aggregating, particularly in managing uncertainty and achieving high accuracy with limited data. This approach offers significant potential for enhancing earthquake early warning systems, especially in scenarios with sparse or incomplete data monitoring. Moreover, this method accelerates the development of earthquake early warning systems without requiring prolonged radon observation periods, particularly in the Java Island region. By providing a reliable method for modeling and predicting earthquake parameters, this study contributes to mitigating the impacts of earthquake disasters and improving preparedness through timely and accurate warnings.

At a prediction radius of 200 km, the proposed method shows the best performance in time predictions, with RMSE values of 41.98 hours, respectively, compared to other methods. Meanwhile, the Random Forest has the lowest RMSE value (0.49) in the magnitude parameter and 13.5 km in distance prediction. For a prediction radius of 300 km, the proposed method also shows better performance in magnitude, distance, and time predictions with RMSE values of 0.48, 60.60 km and 57.85 hours, respectively. At a prediction radius of 400 km, the proposed method remains better in magnitude, distance, and time prediction, with RMSE values of 0.61, 76.29 km and 46.69 hours, respectively.

However, additional research is necessary to enhance the performance of this algorithm further. The current method cannot adapt to and learn when more data are available. The actual probability distribution may not be accurately represented when the data are limited. This leads to the potential use of an incorrect distribution, thereby reducing prediction accuracy. Future research should focus on developing an adaptive process that enables the algorithm to improve its prediction accuracy when more data are collected. With this adaptive component, the algorithm is expected to be more responsive to changes in the data patterns, resulting in greater accuracy over time. This advancement will elevate Monte Carlo Aggregating-based earthquake prediction technology, significantly mitigating natural disaster risk.