Seismic Microzonation and Future Forecasting of Earthquakes in Western Anatolia through K-Means Clustering Analysis with Magnitude Volatility Detection by Entropy Approaches

Seismic Microzonation and Future Forecasting of Earthquakes in Western Anatolia through K-Means Clustering Analysis with Magnitude Volatility Detection by Entropy Approaches | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Seismic Microzonation and Future Forecasting of Earthquakes in Western Anatolia through K-Means Clustering Analysis with Magnitude Volatility Detection by Entropy Approaches Hatice Nur Karakavak, Hatice Oncel Cekim, Gamze Ozel Kadilar, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3979686/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Western Anatolia stands out as one of the globally active seismic regions. The paleoseismic history of numerous significant faults in this area, including information about recurrence intervals of damaging earthquakes, magnitude, displacement, and slip rates, remains inadequately understood. The extensive crustal extension at the regional level has given rise to significant horst-graben systems delineated by kilometer-scale normal faults, particularly in carbonate formations, where vertical crustal displacements have taken place. We categorize earthquakes with a k-means clustering algorithm in Western Anatolia from 1900 to 2021 based on specific characteristics or patterns present in the data. Additionally, we explore the volatility in depth and size within each cluster using approximate and sample entropy methods. These entropy measures offer valuable insights into the complexity and irregularity of earthquake patterns in different zones. The findings indicate that to understand seismic activity in the Aegean region comprehensively, it needs to be analyzed by dividing it into three regions using the k-means clustering algorithm. Entropy procedures are implemented to validate that the identified regions accurately depict the seismic patterns. The long-short-term memory (LSTM) method obtains separate earthquake magnitude predictions for each of the three regions. When these values are evaluated with the root mean squared error (RMSE) criterion for the three regions with the actual values, the train data gives strong results with 0.30 and the test data with 0.49 on average. The outcomes demonstrate that the future forecast for each region exhibits unique trends, predicting larger earthquakes in the second segment. earthquake k-means clustering sample entropy approximate entropy long-short term memory Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 1. Introduction Turkey is in a region known as the Alpine-Himalayan seismic belt, which is one of the most active earthquake zones globally. According to the former earthquake zonation map, approximately 42% of the country's land area falls within the first-degree earthquake zone. Most of the country is situated on the Anatolian tectonic plate, positioned between the Eurasian, African, and Arabian tectonic plates (Bonev and Beccaletto 2007 ). This tectonic and geological setting has led to the occurrence of numerous destructive earthquakes throughout both historical and instrumental periods in Turkey. The western region of Turkey is of great geological and tectonic significance, making it an area of interest for further investigation. This region is highly susceptible to seismic activity due to its high maximum ground acceleration values related to earthquake hazards. The movement of Anatolia towards the west induces east-west compression and north-south expansion, which activates faults in the Aegean Region. Particularly, the Marmara Region in the western provinces of Turkey is exceptionally prone to earthquakes. The North Anatolian Fault Zone (NAFZ), tracing along the Marmara Sea, is a crucial active fault line with the potential to generate major earthquakes (Kalafat and Görgün, 2017 ). Notably, the western part of Turkey represents not only the country's most densely populated region but also its industrial heartland. This area comprises major cities and industrial centers with dense populations, holding significant economic importance. Cities such as Istanbul, Izmir, Bursa, and Ankara are pivotal trade hubs, experiencing robust commercial, tourism, and industrial activities. However, it's imperative to analyze these commercial areas concerning earthquakes, as seismic events can profoundly impact commercial activities. A large-scale earthquake has the potential to damage infrastructure, destroy buildings, and cause significant losses, thereby negatively affecting trade and the economy (Ocal, 2019 ). Major cities such as Istanbul, Bursa, and Izmir, along with the surrounding provinces, face a significant risk of experiencing large earthquakes. These areas are located in close proximity to the North Anatolian Fault Zone (NAFZ) and other active fault lines in the Aegean region. Istanbul is highly vulnerable to a major earthquake due to its location near the Marmara Sea and its position on the NAFZ. The Marmara Region was struck by a catastrophic earthquake on August 17, 1999, measuring 7.4 in magnitude, tragically leading to the loss of more than 17,000 lives (McClusky et al. 2000 ; Erdik 2001 ). Cities such as Istanbul, Gölcük, and Sakarya experienced significant damage, with numerous buildings collapsing or sustaining severe damage. The confirmed number of fatalities was recorded at 17,480, accompanied by approximately 44,000 injuries. The earthquake caused extensive damage, with nearly 300,000 homes either damaged or completely collapsed, and over 40,000 business establishments impacted. Other cities, including Düzce, Bolu, Sakarya, and Bursa, are situated on the southern segment of the NAFZ and are at risk of significant seismic activity. On November 12, 1999, a 7.2 magnitude earthquake occurred in Düzce, located approximately 110 km (70 miles) east of the August 17 earthquake epicenter, resulting in further casualties and damage. Provinces such as Balikesir and Canakkale are also located in earthquake-prone zones. On March 18, 1953, a 7.4 magnitude earthquake struck the Yenice-Gönen region of Balıkesir, causing an estimated death toll of around 265 people and extensive damage to buildings (Pinar 1953 ; Çağatay 2005 ). Izmir, situated in the Aegean region, faces significant risk due to its proximity to active fault lines. On June 6, 1970, a 7.2 magnitude earthquake struck the Gediz River valley near Izmir, resulting in an estimated death toll of approximately 1,086 people (Bayrak and Bayrak 2012 ). The town of Gediz and nearby regions experienced significant destruction, with widespread damage to buildings. In a more recent event, on October 30, 2020, a powerful earthquake measuring 6.9 on the moment magnitude scale struck near Izmir, off the coast of Samos. This earthquake, one of the largest in the Aegean Region, lasted around 16 seconds and was followed by a series of aftershocks. The earthquake affected the town of Seferihisar, which is located 27 km away from the epicenter, making it the closest area in Turkey to be impacted. The event also triggered a tsunami in the town of Sigacik kwon as ancient Teos (Karadaş and Öner 2021 ). Earthquake catalogues are an important tool for earthquake hazard assessment thus they convey information on seismic characteristics of a region. Accordingly, earthquake catalogues are frequently utilized in seismic hazard analysis to model earthquake sources particularly for areal source models. However, delineation of seismic sources is an important issue in seismic source modeling as there exits considerable epistemic uncertainty in defining boundaries of source zones. This issue is mostly handled by combining different source models as different branches in seismic source characterization (SSC) logic tree with variable weights based on expert judgments. Nevertheless, a statistical approach to delineate sources attributed to diffused seismicity may decrease uncertainty related to the boundaries of the seismic sources as well as address inaccuracy of expert judgments. Cluster analysis is a widely utilized research technique in data mining, emphasized by Yuan and Yang ( 2019 ). Its main objective is to categorize distinct groups where observations or objects within each cluster demonstrate similarities (homogeneity) and differences from those in other clusters (heterogeneity), as highlighted by Novianti et al. ( 2017 ). The k-means algorithm stands as a prominent clustering approach extensively discussed in the literature, as referenced by Sinaga and Yang ( 2020 ) and Yuan and Yang ( 2019 ). In earthquake data analysis, researchers extensively apply cluster analysis techniques to group earthquakes based on specific characteristics. For example, Novianti et al. ( 2017 ) used clustering to study earthquake epicenters in Bengkulu province and adjacent areas, utilizing tectonic earthquake data from January 1970 to December 2015. Kamat and Kamath ( 2017 ) employed k-means clustering to categorize earthquakes in India based on their location and magnitude. Likewise, Rifa et al. ( 2020 ) utilized k-medoids and k-means algorithms to classify earthquake data in Indonesia, considering magnitude and depth as criteria. These studies demonstrate how cluster analysis techniques are valuable for comprehending earthquake patterns and characteristics, playing a pivotal role in earthquake prediction, classification, and hazard assessment. Entropy, a measure of disorder and randomness within a system, has found valuable application in evaluating regularity and patterns in data series. Notably, approximate entropy (ApEn) and sample entropy (SampEn) algorithms are commonly employed to estimate the randomness in a data series without prior knowledge of its source (Pincus, 1991 ; Unal et. al., 2023 ). Recent research has delved into the relationship between entropy and seismicity, especially concerning earthquake prediction. Studies have revealed that changes in the complexity measure associated with entropy in seismicity can demonstrate discernible patterns preceding major earthquakes (Kalimeri et al., 2008 ). Seismic events are considered as microstates, and the Tsallis Entropy framework has been utilized to analyze seismic data. The entropic index 'q' within this framework reflects the magnitude-frequency distribution, spatiotemporal properties of earthquake swarms, asperities, and the presence of regional hydrothermal features (Balasis et al., 2008 ). This approach, in conjunction with long-range temporal correlations, has proven effective in describing real seismic data in regions such as Japan (Sigalotti et al., 2023 ). Additionally, temporal alterations in the entropic index 'q' have been observed to gradually increase and then sharply rise prior to a major earthquake (Balasis et al., 2011 ). After seismic microzonation of earthquakes and determination of regional volatility with entropy approaches, predicting the future forecasts for each region plays a very important role for seismic hazard assessment studies. At this stage, long-short term memory (LSTM is an effective method for estimating earthquake magnitudes due to its ability to comprehend the complex dynamics of time series data arranged chronologically. The memory cells in LSTM can capture long-term dependencies and learn hidden relationships that can be used to predict future earthquake magnitudes. Wang et al. ( 2017 ), Berhich et al. ( 2021 ) and Cekim et al. ( 2023 ) attempted to predict earthquakes magnitudes with high accuracy using LSTM. The main goal of this study is to cluster earthquakes based on their epicentral location using the k-means algorithm. A secondary objective is to evaluate the regularity and predictability of the resulting clusters. To achieve this, we conduct a comparative analysis by calculating approximate and sample entropy measures. It's noteworthy that the western part of Turkey has not been extensively examined regarding earthquake volatility using entropy-based approaches. Lastly, LSTM method is conducted to predict magnitude of earthquakes in each zone.Through the application of these methods, our aim is to deepen our understanding of seismic characteristics and patterns in this region. This paper are organized as follows: Section 2 provides a detailed description of the study area and the data utilized in this research. Section 3 outlines the methodology employed for the study. The research findings are presented in Section 4. Finally, Section 5 concludes the paper by summarizing the key findings and their implications. 2. Study Area Turkey, situated in Western Asia and part of Eurasia, is positioned within the Alpine-Himalayan belt, globally recognized as a highly earthquake-prone region (Okay et al., 1991 ). The country's geological structure and geodynamic location give rise to a multitude of active faults (Şengör and Yılmaz, 1981; Janssen et al., 2009 ). A particularly active and tectonically significant area in Turkey is the Aegean Region, depicted in Fig. 1 . Situated at one end of the Gediz graben system and influenced by the Western Anatolian Expansion Regime, this region has witnessed numerous seismic events throughout its history (Flerit et al., 2004 ; Bohnhoff et al., 2005 ; Kalafat and Görgün, 2017 ). This study focuses on evaluating earthquakes in the Aegean Region with a moment magnitude of 3.0 (Mw) or higher, encompassing the period from January 1970 to September 2021. The Aegean Region has a complicated tectonic structure marked by numerous independent fault lines. According to Şengör (1979a, b), there are four main neotectonic provinces in Turkey, namely the North Anatolian province, the East Anatolian contraction province, the Central Anatolian 'Ova' province and the West Anatolian extensional province, each of which has specific tectonic properties. To begin, we conducted an analysis to assess the active faults in the region, considering their tectonic and geological characteristics. Active fault data within Turkey's land boundaries were sourced from the Activ ault Map of Turkey (Emre et al., 2018 ). By using these datasets with predefined data standards, we created a comprehensive compilation of linear seismic sources. Figure 2 illustrates the raw earthquake catalog events spanning from 1970 to 2021 in the region The primary objective of this study is to compile a comprehensive earthquake catalog for the designated study area. This catalog was meticulously crafted by reviewing three earthquake catalogs that collectively cover the study area. The fundamental source utilized is the Disaster and Emergency Management Presidency, Earthquake Department DDA catalog (AFAD-DDA). Additionally, two other reputable earthquake catalogs were considered: The Kandilli Observatory Earthquake Catalogue (KOERI) and the Tan ( 2021 ) earthquake catalog. The study area encapsulates a total of 202,080 earthquakes recorded from 1900 to 2021, meticulously documented in the AFAD-DDA catalog. However, this catalog does not exhibit homogeneity concerning earthquake magnitude, encompassing the smallest recorded magnitude of M l = 0.5. On the other hand, the KOERI catalog highlights 13,950 earthquakes recorded within the study area from 1900 to 2021. While this catalog is also not homogeneous in magnitude, it includes earthquakes of magnitude M 3.5 and above. Moreover, the Tan ( 2021 ) catalog, another critical source considered for the study catalog, encompasses earthquakes recorded between 1905 and 2018. Within this catalog, out of the total 337,429 earthquakes recorded, an impressive 252,594 were situated within the study area. The primary objective was a comparative analysis to identify common earthquakes in the AFAD-DDA, KOERI, and Tan ( 2021 ) catalogs, focusing on earthquake parameters within the AFAD-DDA catalog. Specific criteria, including a time difference of ≤ 3 minutes and position differences (longitude and latitude) ≤ 0.5 degrees, were applied to compare earthquake parameters. The analysis, based on 153,533 earthquakes, revealed a robust correlation between the AFAD-DDA and Tan ( 2021 ) catalogs, particularly for magnitudes of 3.0 and above. This affirmed the reliability of the AFAD-DDA catalog, indicating any observed disparities with the KOERI catalog could be attributed to the latter. The merged catalogs underwent refinement to correct parameters for matching earthquakes and identify potential omissions in the AFAD-DDA catalog. Each earthquake was uniquely numbered, listed chronologically, and duplicates were removed. Parameter corrections were applied to matching earthquakes, and any absent from the AFAD-DDA catalog were included, cross-verified with ISC and ISC_EHB catalogs. To standardize magnitude, original magnitudes were converted to the Mw scale using conversion equations from Kadirioğlu and Kartal ( 2016 ), Tan ( 2021 ), and Scordilis ( 2006 ), selected for their derivation from earthquake catalogs and frequent use in the region. The Gardner and Knopoff ( 1974 ) declustering analysis was employed to remove foreshocks and aftershocks from the catalog. This widely used method, which involves a standard time-space window approach, was applied using the ZMAP program. Following the declustering process, the catalog was refined to comprise 16,503 earthquakes, with a total of 5,284 identified clusters and 30,107 associated earthquakes removed. To visually represent the epicentral distribution and Kernel density of the earthquakes in the declustered earthquake catalog, maps were generated using ArcGIS and are showcased in Figs. 3 and 4 , respectively. These steps were pivotal in ensuring the compilation of a reliable and declustered earthquake catalog for the study. 3. Methodology 3.1. K-means clustering algorithm The k-means clustering algorithm stands as a popular technique in data mining, particularly for clustering large datasets (Na et al., 2010 ). Its fundamental objective is to group observations in a manner that minimizes the difference within each cluster while maximizing the difference between clusters (Sinaga and Yang, 2020 ). Diverse methods have been devised for clustering data based on specific criteria. These encompass partitional methods like k-medoids, k-means, and fuzzy c-means, density-based methods such as OPTICS, DBSCAN, and DBCLASD, hierarchical methods including BIRCH, CURE, and ROCK, model-based approaches like EM, COBWEBSC, and LASSIT, and grid-based methods like STING, CLIQUE, and OptiGrid. These methods constitute the primary clustering approaches available in the literature (Rehioui et al., 2016 ; Fahad et al., 2014 ). Non-hierarchical and partitional clustering, like k-means, segments data via partitioning (Govender and Sivakumar, 2020 ). It's a widely adopted unsupervised technique that generates clustering results without a predetermined outcome (Dubey and Choubey, 2017 ; Zeebaree et al., 2017 ). In k-means, we start by randomly assigning k cluster centers (desired clusters). The algorithm iterates, assigning each data point to the nearest cluster center using Euclidean distance. Cluster centers are updated by calculating the mean of the data points within each cluster. This continues until convergence, determined by a predefined stopping criterion. K-means is valued for its simplicity and efficiency, crucial for large datasets. However, initial cluster center selection and the need to predefine the number of clusters (k) can affect its performance. The assumption of spherical, equal-sized clusters might not always match the data. Still, k-means is vital for pattern discovery, especially when cluster count is known or estimable, owing to its simplicity and scalability, widely used in data mining, pattern recognition, and image analysis. The k-means clustering algorithm is illustrated in Fig. 5 . In k-means clustering algorithm, first of all, ' k ' cluster number is determined and clusters are created. Then, each data is assigned to a cluster. Cluster center points \({(C}_{i})\) are obtained by calculating the average values for all data in the relevant cluster as follows: $${C}_{i}=\frac{1}{N}{\sum }_{j=1}^{N}{X}_{j}$$ 1 The k-means clustering algorithm uses distance metrics like Euclidean, Manhattan, Canberra, Correlation, or Minkowski to calculate center-to-data distances. Euclidean distance, commonly employed, gauges similarity through squared coordinate differences. Smaller Euclidean distance signifies similarity, while larger implies dissimilarity. Metric choice depends on data and clustering task (Ghazal et al., 2021 ; Syakur et al., 2018 ; Sony et al., 2011 ). Euclidean distance is widely used due to its simplicity and intuitive interpretation, especially with numerical data. However, for categorical or ordinal variables, Hamming or Jaccard distance might be more suitable. Different distance metrics, including Euclidean, play a crucial role in determining data point similarity and cluster assignment in k-means. Choosing the right metric helps identify patterns and group similar data points effectively. The Euclidean distance ( d ) between the points \({(x}_{1},{y}_{1})\) and \({(x}_{2},{y}_{2})\) in 2-dimensional space is given by $$d=\sqrt{{({x}_{2}-{x}_{1})}^{2}+{({y}_{2}-{y}_{1})}^{2}}$$ 2 After computing the distances, the data points are reassigned to the most appropriate cluster based on the distance between the data point and the centroid of each cluster. This iterative process continues until no further changes in cluster assignments occur or a maximum number of iterations is reached (Kumar et al., 2014 ; Dubey and Choubey, 2017 ). Determining the optimal number of clusters is a critical aspect of the k-means clustering algorithm for a given dataset (Shahapure and Nicholas, 2020 ). Two common methods used to decide the optimal number of clusters are the Elbow criterion and the Silhouette method. The Elbow criterion assesses the sum of squared errors (SSE) for various cluster counts (k). By plotting SSE against k, the "elbow" point, indicating a significant decrease in SSE, helps determine the optimal number of clusters (Nainggolan et al., 2019 ; Humaira and Rasyidah, 2020 ). On the other hand, the Silhouette score evaluates the cohesion and separation of resulting clusters. A score close to 1 signifies correct clustering, while near − 1 implies incorrect clustering. Higher Silhouette scores indicate the appropriateness of the k-means model for the dataset (Yuan and Yang, 2019 ; Ogbuabor and Ugwoke, 2018 ). Both the Elbow criterion and the Silhouette method provide valuable insights into determining the suitable number of clusters for a given dataset. The choice between the two methods depends on the specific characteristics of the dataset and the objectives of the clustering analysis. 3.2. Entropy Measures Entropy, originating from thermodynamics, quantifies system disorder or randomness. Introduced by Clausius in 1864, it measures unusable thermal energy in a system. Beyond thermodynamics, entropy finds applications in fields like information theory and data analysis. Claude Shannon extended it in 1948 to measure information content in signals, representing uncertainty or randomness. Higher entropy means more disorder or unpredictability. Entropy varies with the system's state; ordered systems have entropy zero. On a universal scale, entropy tends to increase, reducing available energy for work. It's widely used in predictive modeling and analyzing complex systems. Common entropy metrics include Shannon, Approximate, Sample, Tsallis, and Renyi entropy (Renyi, 1961; Tsallis, 1998 ). Shannon entropy, a measure of the uncertainty or diversity of a probability distribution, is often used to analyse the distribution of samples in a data set and to measure the amount of information in the data set. Therefore, Shannon entropy measures how uncertain or regular the distribution of a data set is and provides information about its predictability. The mathematical function for calculating the Shannon entropy of a set of non-negative random variables X with distribution function F(x) and probability density function f(x) is as follows: $$H\left(X\right)=-\underset{0}{\overset{\infty }{\int }}f\left(x\right)logf\left(x\right)dx$$ 3 Tsallis entropy, a generalized form of Shannon entropy in information theory, is defined by the parameter α. It offers a flexible diversity measure, allowing more precise measurements than Shannon entropy. It is a generalization of Shannon entropy, offering versatility in entropy calculations capturing both negative and positive values based on the chosen α, enhancing its versatility. The Tsallis entropy can be computed as $${H}_{\alpha }\left(X\right)=\frac{1}{1-\alpha }\underset{0}{\overset{\infty }{\int }}{f}^{\alpha }\left(x\right)dx -1$$ 4 where all \(\alpha \in {D}_{\alpha }=\left(\text{0,1}\right)\cup (1,\infty )\) and it is clear that \(H\left(X\right)=\underset{\alpha \to 1}{\text{lim}}{H}_{\alpha }\left(X\right)\) . This is why it is reduced to the Shannon entropy. Rényi entropy, a flexible alternative to the Shannon entropy, measures data set information using parameter α. It's a generalization of Shannon entropy, offering versatility in entropy calculations. The Rényi entropy of the random variable X can be given as $${H}_{\alpha }\left(X\right)=\frac{1}{1-\alpha }log\underset{0}{\overset{\infty }{\int }}{f}^{\alpha }\left(x\right)dx$$ 5 where, \(\alpha >0\) and \(\alpha \ne 1\) . It can also be seen that \(H\left(X\right)=\underset{\alpha \to 1}{\text{lim}}{H}_{\alpha }\left(X\right)\) again, as in the Tsallis entropy. Approximate entropy (ApEn) and sample entropy (SampEn) are mathematical algorithms specifically designed to quantify the repeatability or predictability within a time series dataset. These entropy measures aim to estimate the level of randomness or irregularity in a dataset without prior knowledge about the underlying data generation process. ApEn, developed by Pincus ( 1991 ), assesses the complexity and regularity of real-life time series data without the need for coarse-graining techniques. SampEn, introduced by Richman and Moorman ( 2000 ), improves upon the limitations of ApEn by mitigating the influence of time series length on the analysis results, thereby reducing errors. The ApEn algorithm is an entropy-based method used to assess the complexity and predictability of earthquake time series data. It quantifies the irregularity or complexity of a time series by evaluating the probability that similar patterns within the data will persist as the pattern length increases. The calculation involves determining the logarithm of the conditional probability that two sequences of a specified length, with a maximum tolerance level, will remain similar within a defined range. A lower ApEn value indicates a more regular and predictable time series, while a higher ApEn value indicates greater complexity and irregularity. The ApEn can be obtained as follows: $$ApEn\left(x,m,r\right)=\frac{1}{N-m+1}\left[\sum _{i=1}^{N-m+1}log\left(\frac{\left|{j}_{i}\right|}{N-m+1}\right)\right]-\frac{1}{N-m}\left[\sum _{i=1}^{N-m}log\left(\frac{\left|{k}_{i}\right|}{N-m}\right)\right],$$ 6 where $${j}_{i}=\left\{\zeta \left|‖{y}_{i}-{y}_{\zeta }‖\right.\le r\wedge \zeta \in ⟨1,N-m+1⟩\right\},$$ $${k}_{i}=\left\{\zeta \left|‖{z}_{i}-{z}_{\zeta }‖\right.\le r\wedge \zeta \in ⟨1,N-m⟩\right\}$$ $${y}_{i}=\left[{x}_{i},{x}_{i+1},\dots ,{x}_{i+m-1}\right], {z}_{i}=\left[{x}_{i},{x}_{i+1},\dots ,{x}_{i+m}\right], N=\left|x\right|.$$ Eq. ( 6 ) searches for similar subsequences \({y}_{i}\) and \({z}_{i}\) of length \(m\) and \(m+1\) . Assuming that the evaluation \(‖{y}_{i}-{y}_{\zeta }‖\le r\) is a basic operation, \(N-m+1\) operations are required to compute each \(\left|{j}_{i}\right|\) . The total number of operations would then be \(2{N}^{2} + N(6 - 4m) + 2{m}^{2} - 6m + 7\) , so the time complexity of the approximate entropy is \({\Theta }\left({N}^{2}\right)\) . SampEn, an enhancement over ApEn, overcomes the limitations associated with dataset length. It evaluates the regularity and complexity of a time series by assessing the probability of similar patterns in the data remaining similar, while considering the length of the time series. By accounting for dataset length, SampEn provides a more accurate estimation of complexity without the bias introduced by dataset length. Like ApEn, a lower SampEn value indicates a more regular and predictable time series, while a higher SampEn value signifies increased complexity and irregularity. The SampEn is obtained as $$SampEn\left(x,m,r\right)=log\left(\frac{\sum _{i=1}^{N-m+1}\left|{b}_{i}\right|}{\sum _{i=1}^{N-m}\left|{a}_{i}\right|}\right)$$ 7 . Here, we have $${b}_{i}=\left\{\zeta \left|‖{y}_{i}-{y}_{\zeta }‖\right.\le r\wedge \zeta \in ⟨1,N-m+1\setminus i⟩\right\},$$ $${a}_{i}=\left\{\zeta \left|‖{z}_{i}-{z}_{\zeta }‖\right.\le r\wedge \zeta \in ⟨1,N-m\setminus i⟩\right\}$$ , $${y}_{i}=\left[{x}_{i},{x}_{i+1},\dots ,{x}_{i+m-1}\right], {z}_{i}=\left[{x}_{i},{x}_{i+1},\dots ,{x}_{i+m}\right], N=\left|x\right|.$$ In terms of ApEn, the sets \({b}_{i}\) and \({a}_{i}\) are different from the sets \({j}_{i}\) and \({k}_{i}\) . They do not include the index \(i\) , so the computation of \(\left|{b}_{i}\right|\) and \(\left|{a}_{i}\right|\) only requires \(N-m\) and \(N-m-1\) operations. It also introduces the possibility that all \(\left|{a}_{i}\right|\) can sum to zero. Then the total number of operations is \(2{N}^{2}+N(2-4m)+2{m}^{2}-2m+1\) and the time complexity is again \({\Theta }\left({N}^{2}\right)\) . 3.3. LSTM (Long Short-Term Memory) Model Recurrent Neural Network (RNN) effectively deals with long-term dependencies but faces issues like gradient fading (Cao et al., 2019 ). To tackle this, Hochreiter and Schmidhuber ( 1997 ) introduced LSTM, a variant of RNN, which became widely used in time series forecasting (Cho et al., 2014 ; Gers and Schmidhuber, 2000 ). LSTM overcomes gradient vanishing using memory cells and control gates, outperforming classical RNNs (Livieris et al., 2020 ). It excels in addressing time series forecasting challenges (Chimmula and Zhang, 2020 ). LSTM cells consist of three primary structures: the input gate, the memory gate and the output gate. The cell state, represented by a horizontal line, carries information throughout the network (Yadav et al., 2020 ). The input gate determines the relevance of new input, the forget gate manages information retention, and the output gate organizes the transmitted information (Yamak et al., 2019 ; Livieris et al., 2020 ). The LSTM algorithm is highly efficient for time series modelling due to its ability to capture long-term dependencies, store relevant information in memory cells, and regulate the flow of information through gates. Its general structure is depicted in Fig. 6 . Input Gate It is the stage of determining what new information will be stored in the cell state. It consists of two basic components, the sigmoid layer and the tanh layer. The sigmoid layer decides which information will be stored in the cell state. The tanh layer creates a vector of new candidate values that can be added to the cell state. The outputs of the sigmoid layer and tanh layer are calculated, respectively, as follows $${i}_{t}=\sigma \left({W}_{{i}_{h}}\left[{h}_{t-1}\right]+{W}_{{i}_{x}}\left[{X}_{t}\right]+{b}_{i}\right)$$ 8 , $$\stackrel{\sim}{{c}_{t}}=tanh\left({W}_{{c}_{h}}\left[{h}_{t-1}\right]+{W}_{{c}_{x}}\left[{X}_{t}\right]+{b}_{c}\right)$$ 9 The outputs of the sigmoid layer and the tanh layer are then combined to calculate new information to be added to the cell state: $${c}_{t}={f}_{t}\odot {c}_{t-1}+{i}_{t}*\stackrel{\sim}{{c}_{t}}$$ 10 Here, ⊙ is the element-wise multiplication and \({f}_{t}\) is the forget gate output. Forget Gate It is the stage to determine the information to be extracted from the cell state. The values and are obtained and a sigmoid layer is used. The output of the forget gate takes a value between 0 and 1. 0 means that the information corresponding to the value should be completely forgotten, while 1 means that the information corresponding to the value should be retained. The output of the forget gate is calculated as follows $${f}_{t}=\sigma \left({W}_{{f}_{h}}\left[{h}_{t-1}\right]+{W}_{{f}_{x}}\left[{X}_{t}\right]+{b}_{f}\right)$$ 11 The output of the forget gate \({f}_{t}\) is then used to modulate the previous memory cell state \({c}_{t-1}\) . It performs an element-wise multiplication (⊙) with \({c}_{t-1}\) to determine which information to keep and which to forget: $${c}_{t}={f}_{t}\odot {c}_{t-1}$$ 12 Output Gate This stage determines which information will be output and plays a crucial role in deciding which part of the LSTM memory contributes to the final output. Similar to the input gate, it employs a sigmoid layer followed by a tanh layer. This layer determines the degree of contribution, which is then multiplied element-wise by the output of the sigmoid layer using a non-linear tanh function. The operations in the process are calculated as follows $${o}_{t}=\sigma \left({W}_{{o}_{h}}\left[{h}_{t-1}\right]+{W}_{{o}_{x}}\left[{X}_{t}\right]+{b}_{o}\right)$$ 13 , $${h}_{t}={o}_{t}\odot \text{t}\text{a}\text{n}\text{h}\left({c}_{t}\right)$$ 14 , Here, \({i}_{t}\) represents the vector of the input gate, \({f}_{t}\) represents the vector of the forget gate, o t represents the output gate, \(\stackrel{\sim}{{c}_{t}}\) is the vector of the candidate values added to the new cell state, and \({c}_{t}\) represents the vector of the memory cell. The weight matrices are \({W}_{i}\) , \({W}_{f}\) , \({W}_{o}\) and \({W}_{c}\) . The bias vectors are \({b}_{i}\) , \({b}_{f}\) , \({b}_{o}\) , \({b}_{c}\) . In Eq. ( 13 ), the sigmoid function designated by \(\sigma\) and finally, the output matrix represented by \({h}_{t}\) . The final output \({ h}_{t}\) is the result of element-wise multiplication between the output gate \({o}_{t}\) and the hyperbolic tangent of the current memory cell state \({(c}_{t})\) . This output represents the information that the LSTM model decides to pass on to the subsequent time step or use for prediction. LSTM gives effective results in earthquake magnitude estimation. For this reason, it is frequently applied to forecast future earthquake magnitudes by analyzing past data (Lakshmi and Tiwari, 2009 ; Berhich et al., 2023 ; Sadhukhan et al., 2023 ; Zhang and Wang, 2023 ). 4. Results The descriptive statistics obtained from earthquake magnitude and depth data, covering the period between January 1970 and September 2021, are presented in Table 1 . Q 1 , Q 2 , and Q 3 denote the first, second, and third quartiles correspondingly. The histogram graphs in Fig. 7 a and b also illustrate earthquake magnitude and depth data, respectively. Analyzing the data from Table 1 and the visual representation in Fig. 7 reveals essential characteristics of earthquakes in the Aegean Graben System. Table 1 The descriptive statistics for the Depth (km) and Magnitude (Mw) of earthquakes that occurred between January 1970 and September 2021 Depth (km) Magnitude (Mw) Depth (km) Magnitude (Mw) Min. 0.00 3.00 Max. 183.80 7.60 Q 1 6.81 3.10 St. Deviation 21.25 0.54 Median 10.00 3.30 Skewness 3.84 1.54 Mean 16.06 3.48 Kurtosis 20.79 5.38 Q 3 16.32 3.70 The minimum magnitude recorded stands at 3.0, representing the smallest earthquake magnitude within this dataset. Conversely, the maximum magnitude observed is 7.6, indicating the highest earthquake magnitude documented in the Aegean Graben System. The first quartile at 6.81 km reveals that 25% of earthquakes have depths below or equal to this value. The median, set at 10 km, marks the midpoint where 50% of earthquakes fall below or equal to this depth. Moving further, the third quartile is at 16.32 km, indicating that 75% of earthquakes have depths less than or equal to this value. The average depth stands at 16.06 km, giving a central tendency estimate and portraying a typical depth for earthquakes in the dataset. Additionally, the standard deviation of 21.25 km signifies the spread or variability around the average, implying a wider range of depth values when higher. The skewness value of 3.84 indicates a right-skewed distribution, suggesting a longer tail on the right side. Lastly, the kurtosis value of 20.79 denotes a highly peaked distribution with heavy tails, providing insights into the distribution's shape. The statistics given in Table 1 also shed light on earthquake magnitude distribution. The first quartile at 3.10 indicates 25% below this, median at 3.30 shows 50% below, and third quartile at 3.70 means 75% below. The average magnitude, 3.48, gives a central tendency measure. A standard deviation of 0.54 signifies variability around the average, higher values implying greater dispersion. Skewness (1.54) indicates right-skewed distribution with a longer tail on the right, and kurtosis (5.38) implies a highly peaked distribution with heavy tails. Figure 8 presents the box plots for the magnitude (km) of earthquakes between years 1970 and 2021. When examining this graph, two distinct patterns in earthquake magnitudes between 1970 and 2021 are noteworthy. It is observed that from 1970 to 1990, the annual earthquake magnitudes were higher, and after 1990, earthquake magnitudes decreased compared to the previous years. The decline observed between 1990 and 2021 may imply a shift or decrease in stress distribution over that timeframe. However, it's essential to emphasize the significance of precise and thorough earthquake data collection. The lack of a clear trend between 1970 and 1990 may be due to limitations in data sources or observation systems during this period. However, advancements in technology and the expansion of monitoring networks in later years likely led to the acquisition of more accurate and reliable data. After exploratory data analysis, a k-means clustering analysis is applied to analyze earthquakes between January 1970 and September 2021 using earthquake magnitude, latitude, and longitude as input variables from the declustered catalog. The objective is to uncover distinct clusters within the dataset. The Silhouette score and the Elbow criterion are used to determine the ideal number of clusters for the k-means method. These aid in selecting the most appropriate number of clusters that effectively capture the inherent patterns in the data. The Silhouette score assesses clustering quality by examining the compactness of data points within clusters and the separation between different clusters. Higher Silhouette scores indicate well-defined and separated clusters. Additionally, the Elbow criterion is employed to pinpoint the number of clusters that explain the most significant portion of variance in the data. This involves plotting the percentage of variance explained against the number of clusters. The "Elbow" point on the plot signifies the optimal number of clusters, where the additional gain in explained variance becomes minimal. Figure 9 illustrates the outcomes of both the Silhouette score and the Elbow criterion, assisting in the determination of the optimal number of clusters. The Silhouette score plot provides insights into the clustering quality for various numbers of clusters, while the Elbow criterion plot demonstrates the explained variance as a function of the number of clusters. By examining these plots, one can determine the number of clusters that maximizes the Silhouette score or identifies the point where the explained variance levels off significantly (indicating diminishing improvements in clustering). This chosen number of clusters will be utilized for conducting the k-means clustering analysis on the earthquake dataset. Figure 9. Graphs for Silhouette score and Elbow criterion for earthquake between years 1970 and 2021. Upon analyzing Fig. 9.a, it's clear that the model with three clusters achieves the highest Silhouette score, indicating distinct and well-separated clusters. The two-cluster model follows with the second-highest Silhouette score, succeeded by the models with four and five clusters. This suggests the dataset can be effectively grouped into three or four distinct clusters based on earthquake magnitude, latitude, and longitude. Figure 9.b, illustrating the elbow criterion, demonstrates the most significant decrease in within-cluster sum of squares at three clusters. Moreover, there's a notable decrease from three to five clusters, with diminishing decreases for higher cluster numbers. The alignment of the Silhouette score and the elbow criterion strongly suggests the optimal cluster number is likely three or four. Both criteria consistently point to these numbers, affirming they represent the underlying patterns in the data. This convergence boosts confidence in selecting either three or four clusters for the k-means clustering analysis of the earthquake dataset. Figure 10 shows clustering results from the k-means algorithm. Each cluster is represented by a unique color, allowing for easy analysis of earthquake spatial distribution based on latitude and longitude. The x-axis represents longitude, and the y-axis represents latitude. This plot provides insights into how earthquakes are distributed and clustered across the study area. Figure 10 further reveals distinct spatial patterns and earthquake groupings within the selected clusters. Many earthquakes in the Aegean Region concentrate in the sea due to islands and the indented coastline. Through k-means clustering, earthquake magnitudes were effectively grouped into three clusters, revealing distinct patterns and enhancing our understanding of seismic behavior in the region. In Table 2 , the characteristics of each cluster, derived from the k-means clustering with an optimal cluster number of 3, are presented. Figure 10 .b visually validates the presence of these three clusters, aligning with the optimal cluster number identified through the average Silhouette width value. A deeper look into Table 2 provides additional insights. The first cluster (blue in Fig. 10 .b) comprises 4352 observations with an average magnitude of approximately Mw = 3.4. The second cluster encompasses 5382 earthquakes, while the third cluster includes 6111 earthquakes. Analysis of Table 2 shows that the mean magnitudes for the second and third clusters are around Mw = 3.4 and Mw = 3.6, respectively. Table 2 Characteristics of each cluster when the optimal number is 3 via k-means clustering Cluster Magnitude Mean Longitude Mean Latitude Mean Number of Events Variance 1 3.4 30.63 38.15 4352 0.281 2 3.4 27.43 39.72 5382 0.209 3 3.6 27.02 36.83 6111 0.336 In Fig. 10 .b, Cluster 3 displays earthquakes with magnitudes ranging from Mw = 3.0 to Mw = 6.9 and depths up to 183.8 km. Notably, the destructive Izmir earthquake of October 30, 2020, falls within this cluster, marked by its shallow depth and severe impact in the Aegean and Marmara regions, especially Izmir province. In Cluster 2, earthquakes are predominantly land-based, with magnitudes spanning from Mw = 3.0 to Mw = 6.5 and maximum depth recorded at 78 km. Many of these quakes occurred on the mainland. Cluster 1 showcases earthquakes occurring on both land and islands. With 4352 earthquakes and an average magnitude of Mw = 3.4, this cluster has the fewest observations but extends to depths of 159.2 km. In Table 3 , the calculated ApEn and SampEn values are also provided for each cluster of earthquakes. These entropy values reflect the complexity or irregularity of the time series patterns within each cluster. The ApEn and SampEn values offer insights into the predictability and regularity of the seismic activity within the analyzed clusters. Table 3 Entropy measures of earthquake magnitudes for each cluster with k-means clustering Cluster 1 Cluster 2 Cluster 3 ApEn 0.9584647 0.9754377 1.276853 SampEn 0.7440741 0.766529 1.355065 Analyzing the entropy values presented in Table 3 , we can deduce distinct patterns within the three clusters. Notably, Cluster 1 displays a higher degree of regularity and uniformity than the other clusters. This suggests a consistent and predictable pattern in seismic activity for this cluster. Conversely, Cluster 3 exhibits lower predictability with higher entropy values, indicating a less regular and more unpredictable seismic pattern. These observations shed light on the diverse characteristics of earthquake clusters in the Aegean Region. Cluster 1 showcases a homogenous seismic activity pattern, emphasizing its predictability. Conversely, Cluster 3 presents a more intricate and unpredictable pattern, highlighting the variability and complexity its seismic events. Figure 11 illustrates monthly average earthquake magnitudes for each cluster, aiding in the visualization of temporal variations and trends. Connecting these insights from the entropy analysis to the temporal variations illustrated in Fig. 11 , we can discern a compelling correlation. Cluster 2, demonstrating higher regularity in seismic activity, aligns with a smoother and more consistent trend in earthquake magnitudes over the months. This reinforces the notion of predictability within this cluster, as the seismic events follow a uniform pattern. Conversely, in Cluster 3 where seismic activity is less predictable, the monthly average earthquake magnitudes depict a more erratic pattern. The higher entropy values observed in Cluster 3 might indeed be reflected in these fluctuations, showcasing a dynamic and less homogeneous seismic activity scenario. These plots offer insights into seismic activity dynamics, aiding in the identification of patterns or notable changes over time. The smoothed monthly averages provide a clear overview of magnitude behavior. In Fig. 11 , the time series plots have been visually examined and they show noticeable trends. This observation is further supported in Fig. 12 by analyzing the autocorrelation function (ACF) and partial autocorrelation function (PACF) plots for each cluster. The first differences of the series in each cluster are calculated to address this issue. This differencing process effectively removes the trend component and transforms the series into a stationary form. Examination of the resulting differenced series confirms that the trends have been successfully removed from all three clusters. We also perform the LSTM method to consider memory mechanisms to capture and learn complex relationships of earthquakes. In the application of the LSTM method to k-means-clustered three sub-catalogs, a series of steps are followed to build and train the model. First, the data is prepared by dividing it into training (70%) and testing (30%) sets. Subsequently, the data is normalized using Min-Max normalization to make sure that the data falls within a certain range. Moving on to the model architecture, the LSTM model is employed in the second step. The Tanh activation function is utilized, and the parameter "return_sequences = True" is set to maintain the output sequence, which is crucial for capturing temporal dependencies. The third step involves the training process, where an optimization algorithm, stochastic gradient descent, is utilized. This algorithm helps to determine the optimal batch size and the number of epochs needed for effective training. The loss function chosen for this training phase is the mean squared error, a common choice for regression tasks. In the final step, the LSTM model is trained using the specified parameters and the prepared training data. Once trained, the model can be employed to make predictions, forecasts, and even estimate confidence intervals for future time periods based on the patterns and information captured during the training phase. The values of batch size and epoch number values mentioned in Step 3 used for the clusters are given in Table 4 . Table 4 The LSTM parameters values for all clusters Cluster 1 Cluster 2 Cluster 3 Batch size 32 128 32 Epoch number 1000 750 1000 Figure 13 displays the number of iterations for each cluster alongside its corresponding loss function value. This value represents the error between the predicted and actual values calculated using the Mean Squared Error (MSE) criterion. The objective is to achieve the best possible predictions with minimal error, in other words, with minimum loss. It is worth noting that Cluster 1 approaches this value with a higher number of iterations. On the contrary, Cluster 3 achieves the greatest loss function value by employing the highest number of iterations, whereas Cluster 2 attains a lower value after 750 iterations. Figure 13 . Loss vs iterations graph for all clusters The appropriateness of these figures for training and testing data is assessed via the mean square error (RMSE) criterion. In addition, the RMSE values presented in Table 5 corroborate the parameter sizes established in Table 4 . Correspondingly, the parameters in Table 4 with the lowest RMSE values among the parameters are deemed the most suitable. When the above LSTM steps are applied, the predicted values for each cluster are first shown in Fig. 14 . Later, Fig. 15 shows the forecast and confidence limits of the average earthquake magnitude obtained up to March 2028 for the clusters. Table 5 The RMSE values of all clusters The RMSE values Cluster 1 Cluster 2 Cluster 3 Train data 0.32 0.31 0.27 Test data 0.45 0.34 0.59 Figure 15 illustrates a clear comparison of the actual series and the forecast series. The fit appears to be satisfactory for all clusters. It is challenging to forecast the sudden changes in the three clusters that occurred in the average magnitudes of earthquakes between 1970 and 1990, which marked the beginning of the period. It is observed that the average earthquake magnitudes of the second cluster after 1990 are close to the predictions. This supports the findings presented in Table 5 . In this regard, it appears that the mean earthquake magnitudes and predicted values in the test dataset of the third cluster are significantly distinct from the other clusters. Based on the findings, we anticipate distinctive average earthquake magnitudes within each cluster until the year 2028. Cluster 1 is expected to maintain lower-than-average magnitudes, indicating a relatively subdued seismic activity pattern. In contrast, Cluster 2 is foreseen to exhibit significantly higher-than-average magnitudes, highlighting a heightened level of seismic activity characterized by substantial events. Cluster 3, falling somewhere in between, is projected to sustain an average magnitude trend, underscoring a balanced seismic activity pattern. These projections offer valuable insights into the expected seismic behavior within the respective clusters, aiding in proactive measures for seismic risk assessment and preparedness. In general, earthquake magnitudes that decreased after the 2000s are expected to continue after the 2020s, with different seismic movements depending on the region covered by each cluster. This is due to various seismic movements that rely on the region covered by each cluster. Future estimations of earthquake magnitude averages have been attempted whilst considering the impacts of geological structures of each cluster, determined by region. 5. Conclusion Earthquakes are seismic activities that can cause significant loss and destruction. Turkey, being located in a highly seismic region hosted by dense active faults from west to east, experiences frequent and intense earthquakes. Cluster analysis is a powerful tool for advancing our understanding of earthquakes and improving our ability to manage associated risks. By analyzing the resulting clusters, we can gain valuable insights into magnitude ranges, spatial distribution, and potential relationships between earthquake events in the region. This information is instrumental for studying seismic hazards, assessing risks, and implementing effective mitigation strategies in the Aegean Region. Our study aims to contribute to a deeper understanding of earthquake dynamics in Turkey. We conducted a comprehensive analysis of earthquake classification and detection of volatilities concerning depth and size. This knowledge is crucial for assessing seismic hazards, enhancing disaster preparedness, and implementing effective mitigation strategies. The use of entropy-based measures, including approximate entropy and sample entropy provides significant insights into the regularity, complexity, and patterns present in seismic data. These methods enhance our understanding of seismic behavior and potentially aid in earthquake forecasting and hazard assessment. Sample entropy, specifically, is utilized to quantify the fluctuation degree of earthquake magnitudes. By grouping seismic events using k-means, researchers can uncover patterns and relationships within the data, leading to improved earthquake analysis and a better understanding of seismic activity. The LSTM method, with its ability to capture ordered relationships in earthquake magnitude estimation, adapt through parameter adjustments, and effectively handle complex and multidimensional data, stands out. This approach allows for accurate predictions and contributes to earthquake risk management. In this study, we utilized the LSTM method to calculate future earthquake magnitude predictions for the clusters obtained in the last stage. As a result, the region in the 2nd cluster is anticipated to experience more severe earthquakes in the coming years. Understanding the tectonic and geological characteristics of the region, combined with observed seismicity patterns, provides valuable insights into earthquake processes in Turkey. This knowledge is critical for seismic hazard assessment, earthquake preparedness, and the implementation of effective mitigation strategies to minimize the devastating impacts of future earthquakes. Declarations Acknowledgements The research presented in this study received funding from The Scientific and Technical Research Council of Türkiye (TÜBİTAK) under project number 121F208. We would like to express our gratitude to Assoc. Prof. Dr. Senem Tekin for her contribution in preparing the dataset. 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A spatiotemporal model for global earthquake prediction based on Convolutional LSTM. IEEE Transactions on Geoscience and Remote Sensing. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3979686","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":282948132,"identity":"fc2f8dd9-f2db-4087-b0b9-9ccd67ba1063","order_by":0,"name":"Hatice Nur Karakavak","email":"data:image/png;base64,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","orcid":"","institution":"Hacettepe University: Hacettepe Universitesi","correspondingAuthor":true,"prefix":"","firstName":"Hatice","middleName":"Nur","lastName":"Karakavak","suffix":""},{"id":282948133,"identity":"8ced960b-abf7-4a5a-b442-d0141276d4b9","order_by":1,"name":"Hatice Oncel Cekim","email":"","orcid":"","institution":"Hacettepe University: Hacettepe Universitesi","correspondingAuthor":false,"prefix":"","firstName":"Hatice","middleName":"Oncel","lastName":"Cekim","suffix":""},{"id":282948134,"identity":"51c1b747-daf1-4372-82ad-91198e23a31e","order_by":2,"name":"Gamze Ozel Kadilar","email":"","orcid":"","institution":"Hacettepe University: Hacettepe Universitesi","correspondingAuthor":false,"prefix":"","firstName":"Gamze","middleName":"Ozel","lastName":"Kadilar","suffix":""},{"id":282948135,"identity":"c978f2d6-a44e-426d-859e-a24c6a020bba","order_by":3,"name":"Senem Tekin","email":"","orcid":"","institution":"Adiyaman University: Adiyaman Universitesi","correspondingAuthor":false,"prefix":"","firstName":"Senem","middleName":"","lastName":"Tekin","suffix":""}],"badges":[],"createdAt":"2024-02-22 20:05:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3979686/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3979686/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":53562832,"identity":"d61a6a80-9e6f-4c5f-8c7b-b46774187812","added_by":"auto","created_at":"2024-03-27 13:55:17","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2206739,"visible":true,"origin":"","legend":"\u003cp\u003eLocation map of the study area\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/589bf6a39f772a074d346ebf.png"},{"id":53562785,"identity":"c1f0eb58-7ee4-47e9-b917-f5dc3b513c79","added_by":"auto","created_at":"2024-03-27 13:55:13","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":2297352,"visible":true,"origin":"","legend":"\u003cp\u003eEarthquakes in the raw catalog between 1970 and 2021 in the region\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/0827a45cc567662ff39b0d6e.png"},{"id":53562951,"identity":"f07ba610-c7f3-45ae-9c48-ea474a2ba0a5","added_by":"auto","created_at":"2024-03-27 13:55:31","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":769833,"visible":true,"origin":"","legend":"\u003cp\u003eEpicentral distribution map of the declustered catalog with Mw ≥ 3.0\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/86f9cab6631cec653645acef.png"},{"id":53562900,"identity":"47edc97a-e40d-4ece-91fc-fa824ecb4c26","added_by":"auto","created_at":"2024-03-27 13:55:25","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":498307,"visible":true,"origin":"","legend":"\u003cp\u003eKernel density map of earthquakes in the declustered project catalog\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/2a970902d4d5fe7ad678c30f.png"},{"id":53562949,"identity":"ad8d3a7f-6621-47b5-91b3-eaa763f578a4","added_by":"auto","created_at":"2024-03-27 13:55:30","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":46388,"visible":true,"origin":"","legend":"\u003cp\u003eFlowchart of k-means Clustering Algorithm\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/5ef1d90b6f00cbe90baa42bd.png"},{"id":53562825,"identity":"6e44eae9-8412-4480-b87e-431f38ac95b3","added_by":"auto","created_at":"2024-03-27 13:55:15","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":102931,"visible":true,"origin":"","legend":"\u003cp\u003eFlowchart of a basic LSTM architecture\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/d2cb5d0470a6cd4f1b30901b.png"},{"id":53562955,"identity":"83e0a836-070c-413d-b3d2-4ef70f64e16c","added_by":"auto","created_at":"2024-03-27 13:55:31","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":236997,"visible":true,"origin":"","legend":"\u003cp\u003eFor earthquakes that occurred between January 1970 and September 2021, a) histogram for Magnitude (Mw), b) scatter graph for Magnitude (Mw) and Depth (km), c) histograms for Depth (km) at different Magnitude (Mw) values.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/ad02b0bde816ef10cb3c627e.png"},{"id":53562954,"identity":"da63200c-962e-4d56-945e-086ec3c3897a","added_by":"auto","created_at":"2024-03-27 13:55:31","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":68746,"visible":true,"origin":"","legend":"\u003cp\u003eBox plot for the Magnitude (Mw) of earthquakes during January 1970 - September 2021.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/99272b08b0fb58d4ca08a758.png"},{"id":53562899,"identity":"8981d3a0-bc8f-489d-aad3-7f55c32a2332","added_by":"auto","created_at":"2024-03-27 13:55:24","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":5077345,"visible":true,"origin":"","legend":"\u003cp\u003eGraphs for Silhouette score and Elbow criterion for earthquake between years 1970 and 2021.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/7197a7903248ff1eb5c8cc70.png"},{"id":53562953,"identity":"14852ab3-e1ac-41f2-9e3c-e97a9723c993","added_by":"auto","created_at":"2024-03-27 13:55:31","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":229683,"visible":true,"origin":"","legend":"\u003cp\u003eClustering of the earthquakes in declustered catalog with k-means algorithm\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/bf032e3fa491d806c0b6e650.png"},{"id":53562782,"identity":"9a52b0c0-2917-4a24-bc2d-b71148ed027c","added_by":"auto","created_at":"2024-03-27 13:55:13","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":214430,"visible":true,"origin":"","legend":"\u003cp\u003eTime series plots of magnitude (Mw) in each K-means cluster\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/db3558a1b683990b67cbfe7b.png"},{"id":53562824,"identity":"d5789aec-5390-4322-8512-6d3af609b924","added_by":"auto","created_at":"2024-03-27 13:55:15","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":328879,"visible":true,"origin":"","legend":"\u003cp\u003eThe ACF and PACF plots of each k-means cluster\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/92a099c6828ae3d075cb0c99.png"},{"id":53562841,"identity":"e5aac0c3-4af6-4e14-b0fd-f70dadd260a8","added_by":"auto","created_at":"2024-03-27 13:55:19","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":275755,"visible":true,"origin":"","legend":"\u003cp\u003eLoss vs iterations graph for all clusters\u003c/p\u003e","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/befc425db694ac3e6a7af312.png"},{"id":53563913,"identity":"82248d79-0db9-4e3d-81ad-48b21f8ddaef","added_by":"auto","created_at":"2024-03-27 14:03:15","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":173831,"visible":true,"origin":"","legend":"\u003cp\u003eThe predicted values of the average earthquake magnitude for all cluster\u003c/p\u003e","description":"","filename":"floatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/1c77f0793614e16ac5aa2e83.png"},{"id":53562898,"identity":"a4d93124-8c8f-4ad3-b1de-e737a8e2eaf2","added_by":"auto","created_at":"2024-03-27 13:55:23","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":3829145,"visible":true,"origin":"","legend":"\u003cp\u003eThe forecast and confidence limit values of the average earthquake magnitude for all cluster during October 2021- March 2028.\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/6ef1664ab8e65876c4bc9578.png"},{"id":56335209,"identity":"5db143c4-f215-4f6b-ad6f-5bc17436a0fe","added_by":"auto","created_at":"2024-05-12 15:53:27","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10004246,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3979686/v1/fd6a689f-d1b1-4314-b32f-b0554f6c02cc.pdf"}],"financialInterests":"","formattedTitle":"Seismic Microzonation and Future Forecasting of Earthquakes in Western Anatolia through K-Means Clustering Analysis with Magnitude Volatility Detection by Entropy Approaches","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eTurkey is in a region known as the Alpine-Himalayan seismic belt, which is one of the most active earthquake zones globally. According to the former earthquake zonation map, approximately 42% of the country's land area falls within the first-degree earthquake zone. Most of the country is situated on the Anatolian tectonic plate, positioned between the Eurasian, African, and Arabian tectonic plates (Bonev and Beccaletto \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). This tectonic and geological setting has led to the occurrence of numerous destructive earthquakes throughout both historical and instrumental periods in Turkey. The western region of Turkey is of great geological and tectonic significance, making it an area of interest for further investigation. This region is highly susceptible to seismic activity due to its high maximum ground acceleration values related to earthquake hazards. The movement of Anatolia towards the west induces east-west compression and north-south expansion, which activates faults in the Aegean Region. Particularly, the Marmara Region in the western provinces of Turkey is exceptionally prone to earthquakes. The North Anatolian Fault Zone (NAFZ), tracing along the Marmara Sea, is a crucial active fault line with the potential to generate major earthquakes (Kalafat and G\u0026ouml;rg\u0026uuml;n, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Notably, the western part of Turkey represents not only the country's most densely populated region but also its industrial heartland. This area comprises major cities and industrial centers with dense populations, holding significant economic importance. Cities such as Istanbul, Izmir, Bursa, and Ankara are pivotal trade hubs, experiencing robust commercial, tourism, and industrial activities. However, it's imperative to analyze these commercial areas concerning earthquakes, as seismic events can profoundly impact commercial activities. A large-scale earthquake has the potential to damage infrastructure, destroy buildings, and cause significant losses, thereby negatively affecting trade and the economy (Ocal, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eMajor cities such as Istanbul, Bursa, and Izmir, along with the surrounding provinces, face a significant risk of experiencing large earthquakes. These areas are located in close proximity to the North Anatolian Fault Zone (NAFZ) and other active fault lines in the Aegean region. Istanbul is highly vulnerable to a major earthquake due to its location near the Marmara Sea and its position on the NAFZ. The Marmara Region was struck by a catastrophic earthquake on August 17, 1999, measuring 7.4 in magnitude, tragically leading to the loss of more than 17,000 lives (McClusky et al. \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Erdik \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). Cities such as Istanbul, G\u0026ouml;lc\u0026uuml;k, and Sakarya experienced significant damage, with numerous buildings collapsing or sustaining severe damage. The confirmed number of fatalities was recorded at 17,480, accompanied by approximately 44,000 injuries. The earthquake caused extensive damage, with nearly 300,000 homes either damaged or completely collapsed, and over 40,000 business establishments impacted. Other cities, including D\u0026uuml;zce, Bolu, Sakarya, and Bursa, are situated on the southern segment of the NAFZ and are at risk of significant seismic activity. On November 12, 1999, a 7.2 magnitude earthquake occurred in D\u0026uuml;zce, located approximately 110 km (70 miles) east of the August 17 earthquake epicenter, resulting in further casualties and damage. Provinces such as Balikesir and Canakkale are also located in earthquake-prone zones. On March 18, 1953, a 7.4 magnitude earthquake struck the Yenice-G\u0026ouml;nen region of Balıkesir, causing an estimated death toll of around 265 people and extensive damage to buildings (Pinar \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e1953\u003c/span\u003e; \u0026Ccedil;ağatay \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Izmir, situated in the Aegean region, faces significant risk due to its proximity to active fault lines. On June 6, 1970, a 7.2 magnitude earthquake struck the Gediz River valley near Izmir, resulting in an estimated death toll of approximately 1,086 people (Bayrak and Bayrak \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). The town of Gediz and nearby regions experienced significant destruction, with widespread damage to buildings. In a more recent event, on October 30, 2020, a powerful earthquake measuring 6.9 on the moment magnitude scale struck near Izmir, off the coast of Samos. This earthquake, one of the largest in the Aegean Region, lasted around 16 seconds and was followed by a series of aftershocks. The earthquake affected the town of Seferihisar, which is located 27 km away from the epicenter, making it the closest area in Turkey to be impacted. The event also triggered a tsunami in the town of Sigacik kwon as ancient Teos (Karadaş and \u0026Ouml;ner \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eEarthquake catalogues are an important tool for earthquake hazard assessment thus they convey information on seismic characteristics of a region. Accordingly, earthquake catalogues are frequently utilized in seismic hazard analysis to model earthquake sources particularly for areal source models. However, delineation of seismic sources is an important issue in seismic source modeling as there exits considerable epistemic uncertainty in defining boundaries of source zones. This issue is mostly handled by combining different source models as different branches in seismic source characterization (SSC) logic tree with variable weights based on expert judgments. Nevertheless, a statistical approach to delineate sources attributed to diffused seismicity may decrease uncertainty related to the boundaries of the seismic sources as well as address inaccuracy of expert judgments.\u003c/p\u003e \u003cp\u003eCluster analysis is a widely utilized research technique in data mining, emphasized by Yuan and Yang (\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Its main objective is to categorize distinct groups where observations or objects within each cluster demonstrate similarities (homogeneity) and differences from those in other clusters (heterogeneity), as highlighted by Novianti et al. (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The k-means algorithm stands as a prominent clustering approach extensively discussed in the literature, as referenced by Sinaga and Yang (\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) and Yuan and Yang (\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). In earthquake data analysis, researchers extensively apply cluster analysis techniques to group earthquakes based on specific characteristics. For example, Novianti et al. (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) used clustering to study earthquake epicenters in Bengkulu province and adjacent areas, utilizing tectonic earthquake data from January 1970 to December 2015. Kamat and Kamath (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) employed k-means clustering to categorize earthquakes in India based on their location and magnitude. Likewise, Rifa et al. (\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) utilized k-medoids and k-means algorithms to classify earthquake data in Indonesia, considering magnitude and depth as criteria. These studies demonstrate how cluster analysis techniques are valuable for comprehending earthquake patterns and characteristics, playing a pivotal role in earthquake prediction, classification, and hazard assessment.\u003c/p\u003e \u003cp\u003eEntropy, a measure of disorder and randomness within a system, has found valuable application in evaluating regularity and patterns in data series. Notably, approximate entropy (ApEn) and sample entropy (SampEn) algorithms are commonly employed to estimate the randomness in a data series without prior knowledge of its source (Pincus, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e1991\u003c/span\u003e; Unal et. al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Recent research has delved into the relationship between entropy and seismicity, especially concerning earthquake prediction. Studies have revealed that changes in the complexity measure associated with entropy in seismicity can demonstrate discernible patterns preceding major earthquakes (Kalimeri et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Seismic events are considered as microstates, and the Tsallis Entropy framework has been utilized to analyze seismic data. The entropic index 'q' within this framework reflects the magnitude-frequency distribution, spatiotemporal properties of earthquake swarms, asperities, and the presence of regional hydrothermal features (Balasis et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). This approach, in conjunction with long-range temporal correlations, has proven effective in describing real seismic data in regions such as Japan (Sigalotti et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Additionally, temporal alterations in the entropic index 'q' have been observed to gradually increase and then sharply rise prior to a major earthquake (Balasis et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAfter seismic microzonation of earthquakes and determination of regional volatility with entropy approaches, predicting the future forecasts for each region plays a very important role for seismic hazard assessment studies. At this stage, long-short term memory (LSTM is an effective method for estimating earthquake magnitudes due to its ability to comprehend the complex dynamics of time series data arranged chronologically. The memory cells in LSTM can capture long-term dependencies and learn hidden relationships that can be used to predict future earthquake magnitudes. Wang et al. (\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), Berhich et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) and Cekim et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) attempted to predict earthquakes magnitudes with high accuracy using LSTM.\u003c/p\u003e \u003cp\u003eThe main goal of this study is to cluster earthquakes based on their epicentral location using the k-means algorithm. A secondary objective is to evaluate the regularity and predictability of the resulting clusters. To achieve this, we conduct a comparative analysis by calculating approximate and sample entropy measures. It's noteworthy that the western part of Turkey has not been extensively examined regarding earthquake volatility using entropy-based approaches. Lastly, LSTM method is conducted to predict magnitude of earthquakes in each zone.Through the application of these methods, our aim is to deepen our understanding of seismic characteristics and patterns in this region. This paper are organized as follows: Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e provides a detailed description of the study area and the data utilized in this research. Section 3 outlines the methodology employed for the study. The research findings are presented in Section 4. Finally, Section 5 concludes the paper by summarizing the key findings and their implications.\u003c/p\u003e"},{"header":"2. Study Area","content":"\u003cp\u003eTurkey, situated in Western Asia and part of Eurasia, is positioned within the Alpine-Himalayan belt, globally recognized as a highly earthquake-prone region (Okay et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e1991\u003c/span\u003e). The country's geological structure and geodynamic location give rise to a multitude of active faults (Şeng\u0026ouml;r and Yılmaz, 1981; Janssen et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). A particularly active and tectonically significant area in Turkey is the Aegean Region, depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Situated at one end of the Gediz graben system and influenced by the Western Anatolian Expansion Regime, this region has witnessed numerous seismic events throughout its history (Flerit et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Bohnhoff et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Kalafat and G\u0026ouml;rg\u0026uuml;n, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis study focuses on evaluating earthquakes in the Aegean Region with a moment magnitude of 3.0 (Mw) or higher, encompassing the period from January 1970 to September 2021. The Aegean Region has a complicated tectonic structure marked by numerous independent fault lines. According to Şeng\u0026ouml;r (1979a, b), there are four main neotectonic provinces in Turkey, namely the North Anatolian province, the East Anatolian contraction province, the Central Anatolian 'Ova' province and the West Anatolian extensional province, each of which has specific tectonic properties. To begin, we conducted an analysis to assess the active faults in the region, considering their tectonic and geological characteristics. Active fault data within Turkey's land boundaries were sourced from the Activ ault Map of Turkey (Emre et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). By using these datasets with predefined data standards, we created a comprehensive compilation of linear seismic sources. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the raw earthquake catalog events spanning from 1970 to 2021 in the region\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe primary objective of this study is to compile a comprehensive earthquake catalog for the designated study area. This catalog was meticulously crafted by reviewing three earthquake catalogs that collectively cover the study area. The fundamental source utilized is the Disaster and Emergency Management Presidency, Earthquake Department DDA catalog (AFAD-DDA). Additionally, two other reputable earthquake catalogs were considered: The Kandilli Observatory Earthquake Catalogue (KOERI) and the Tan (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) earthquake catalog. The study area encapsulates a total of 202,080 earthquakes recorded from 1900 to 2021, meticulously documented in the AFAD-DDA catalog. However, this catalog does not exhibit homogeneity concerning earthquake magnitude, encompassing the smallest recorded magnitude of M\u003csub\u003el\u003c/sub\u003e = 0.5. On the other hand, the KOERI catalog highlights 13,950 earthquakes recorded within the study area from 1900 to 2021. While this catalog is also not homogeneous in magnitude, it includes earthquakes of magnitude M 3.5 and above. Moreover, the Tan (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) catalog, another critical source considered for the study catalog, encompasses earthquakes recorded between 1905 and 2018. Within this catalog, out of the total 337,429 earthquakes recorded, an impressive 252,594 were situated within the study area.\u003c/p\u003e \u003cp\u003eThe primary objective was a comparative analysis to identify common earthquakes in the AFAD-DDA, KOERI, and Tan (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) catalogs, focusing on earthquake parameters within the AFAD-DDA catalog. Specific criteria, including a time difference of \u0026le;\u0026thinsp;3 minutes and position differences (longitude and latitude)\u0026thinsp;\u0026le;\u0026thinsp;0.5 degrees, were applied to compare earthquake parameters. The analysis, based on 153,533 earthquakes, revealed a robust correlation between the AFAD-DDA and Tan (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) catalogs, particularly for magnitudes of 3.0 and above. This affirmed the reliability of the AFAD-DDA catalog, indicating any observed disparities with the KOERI catalog could be attributed to the latter. The merged catalogs underwent refinement to correct parameters for matching earthquakes and identify potential omissions in the AFAD-DDA catalog. Each earthquake was uniquely numbered, listed chronologically, and duplicates were removed. Parameter corrections were applied to matching earthquakes, and any absent from the AFAD-DDA catalog were included, cross-verified with ISC and ISC_EHB catalogs. To standardize magnitude, original magnitudes were converted to the Mw scale using conversion equations from Kadirioğlu and Kartal (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), Tan (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), and Scordilis (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), selected for their derivation from earthquake catalogs and frequent use in the region.\u003c/p\u003e \u003cp\u003eThe Gardner and Knopoff (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1974\u003c/span\u003e) declustering analysis was employed to remove foreshocks and aftershocks from the catalog. This widely used method, which involves a standard time-space window approach, was applied using the ZMAP program. Following the declustering process, the catalog was refined to comprise 16,503 earthquakes, with a total of 5,284 identified clusters and 30,107 associated earthquakes removed. To visually represent the epicentral distribution and Kernel density of the earthquakes in the declustered earthquake catalog, maps were generated using ArcGIS and are showcased in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, respectively. These steps were pivotal in ensuring the compilation of a reliable and declustered earthquake catalog for the study.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. Methodology","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1. K-means clustering algorithm\u003c/h2\u003e \u003cp\u003eThe k-means clustering algorithm stands as a popular technique in data mining, particularly for clustering large datasets (Na et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Its fundamental objective is to group observations in a manner that minimizes the difference within each cluster while maximizing the difference between clusters (Sinaga and Yang, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Diverse methods have been devised for clustering data based on specific criteria. These encompass partitional methods like k-medoids, k-means, and fuzzy c-means, density-based methods such as OPTICS, DBSCAN, and DBCLASD, hierarchical methods including BIRCH, CURE, and ROCK, model-based approaches like EM, COBWEBSC, and LASSIT, and grid-based methods like STING, CLIQUE, and OptiGrid. These methods constitute the primary clustering approaches available in the literature (Rehioui et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Fahad et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eNon-hierarchical and partitional clustering, like k-means, segments data via partitioning (Govender and Sivakumar, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). It's a widely adopted unsupervised technique that generates clustering results without a predetermined outcome (Dubey and Choubey, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Zeebaree et al., \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). In k-means, we start by randomly assigning k cluster centers (desired clusters). The algorithm iterates, assigning each data point to the nearest cluster center using Euclidean distance. Cluster centers are updated by calculating the mean of the data points within each cluster. This continues until convergence, determined by a predefined stopping criterion. K-means is valued for its simplicity and efficiency, crucial for large datasets. However, initial cluster center selection and the need to predefine the number of clusters (k) can affect its performance. The assumption of spherical, equal-sized clusters might not always match the data. Still, k-means is vital for pattern discovery, especially when cluster count is known or estimable, owing to its simplicity and scalability, widely used in data mining, pattern recognition, and image analysis. The k-means clustering algorithm is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn k-means clustering algorithm, first of all, '\u003cem\u003ek\u003c/em\u003e' cluster number is determined and clusters are created. Then, each data is assigned to a cluster. Cluster center points \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({(C}_{i})\\)\u003c/span\u003e\u003c/span\u003eare obtained by calculating the average values for all data in the relevant cluster as follows:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${C}_{i}=\\frac{1}{N}{\\sum }_{j=1}^{N}{X}_{j}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe k-means clustering algorithm uses distance metrics like Euclidean, Manhattan, Canberra, Correlation, or Minkowski to calculate center-to-data distances. Euclidean distance, commonly employed, gauges similarity through squared coordinate differences. Smaller Euclidean distance signifies similarity, while larger implies dissimilarity. Metric choice depends on data and clustering task (Ghazal et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Syakur et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Sony et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Euclidean distance is widely used due to its simplicity and intuitive interpretation, especially with numerical data. However, for categorical or ordinal variables, Hamming or Jaccard distance might be more suitable. Different distance metrics, including Euclidean, play a crucial role in determining data point similarity and cluster assignment in k-means. Choosing the right metric helps identify patterns and group similar data points effectively. The Euclidean distance (\u003cem\u003ed\u003c/em\u003e) between the points \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({(x}_{1},{y}_{1})\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({(x}_{2},{y}_{2})\\)\u003c/span\u003e\u003c/span\u003e in 2-dimensional space is given by\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$d=\\sqrt{{({x}_{2}-{x}_{1})}^{2}+{({y}_{2}-{y}_{1})}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAfter computing the distances, the data points are reassigned to the most appropriate cluster based on the distance between the data point and the centroid of each cluster. This iterative process continues until no further changes in cluster assignments occur or a maximum number of iterations is reached (Kumar et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Dubey and Choubey, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Determining the optimal number of clusters is a critical aspect of the k-means clustering algorithm for a given dataset (Shahapure and Nicholas, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Two common methods used to decide the optimal number of clusters are the Elbow criterion and the Silhouette method.\u003c/p\u003e \u003cp\u003eThe Elbow criterion assesses the sum of squared errors (SSE) for various cluster counts (k). By plotting SSE against k, the \"elbow\" point, indicating a significant decrease in SSE, helps determine the optimal number of clusters (Nainggolan et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Humaira and Rasyidah, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). On the other hand, the Silhouette score evaluates the cohesion and separation of resulting clusters. A score close to 1 signifies correct clustering, while near \u0026minus;\u0026thinsp;1 implies incorrect clustering. Higher Silhouette scores indicate the appropriateness of the k-means model for the dataset (Yuan and Yang, \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Ogbuabor and Ugwoke, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Both the Elbow criterion and the Silhouette method provide valuable insights into determining the suitable number of clusters for a given dataset. The choice between the two methods depends on the specific characteristics of the dataset and the objectives of the clustering analysis.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Entropy Measures\u003c/h2\u003e \u003cp\u003eEntropy, originating from thermodynamics, quantifies system disorder or randomness. Introduced by Clausius in 1864, it measures unusable thermal energy in a system. Beyond thermodynamics, entropy finds applications in fields like information theory and data analysis. Claude Shannon extended it in 1948 to measure information content in signals, representing uncertainty or randomness. Higher entropy means more disorder or unpredictability. Entropy varies with the system's state; ordered systems have entropy zero. On a universal scale, entropy tends to increase, reducing available energy for work. It's widely used in predictive modeling and analyzing complex systems. Common entropy metrics include Shannon, Approximate, Sample, Tsallis, and Renyi entropy (Renyi, 1961; Tsallis, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e1998\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eShannon entropy, a measure of the uncertainty or diversity of a probability distribution, is often used to analyse the distribution of samples in a data set and to measure the amount of information in the data set. Therefore, Shannon entropy measures how uncertain or regular the distribution of a data set is and provides information about its predictability. The mathematical function for calculating the Shannon entropy of a set of non-negative random variables X with distribution function F(x) and probability density function f(x) is as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$H\\left(X\\right)=-\\underset{0}{\\overset{\\infty }{\\int }}f\\left(x\\right)logf\\left(x\\right)dx$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eTsallis entropy, a generalized form of Shannon entropy in information theory, is defined by the parameter α. It offers a flexible diversity measure, allowing more precise measurements than Shannon entropy. It is a generalization of Shannon entropy, offering versatility in entropy calculations capturing both negative and positive values based on the chosen α, enhancing its versatility. The Tsallis entropy can be computed as\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$${H}_{\\alpha }\\left(X\\right)=\\frac{1}{1-\\alpha }\\underset{0}{\\overset{\\infty }{\\int }}{f}^{\\alpha }\\left(x\\right)dx -1$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere all \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha \\in {D}_{\\alpha }=\\left(\\text{0,1}\\right)\\cup (1,\\infty )\\)\u003c/span\u003e\u003c/span\u003e and it is clear that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(H\\left(X\\right)=\\underset{\\alpha \\to 1}{\\text{lim}}{H}_{\\alpha }\\left(X\\right)\\)\u003c/span\u003e\u003c/span\u003e. This is why it is reduced to the Shannon entropy.\u003c/p\u003e \u003cp\u003eR\u0026eacute;nyi entropy, a flexible alternative to the Shannon entropy, measures data set information using parameter α. It's a generalization of Shannon entropy, offering versatility in entropy calculations. The R\u0026eacute;nyi entropy of the random variable X can be given as\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$${H}_{\\alpha }\\left(X\\right)=\\frac{1}{1-\\alpha }log\\underset{0}{\\overset{\\infty }{\\int }}{f}^{\\alpha }\\left(x\\right)dx$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha \u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha \\ne 1\\)\u003c/span\u003e\u003c/span\u003e. It can also be seen that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(H\\left(X\\right)=\\underset{\\alpha \\to 1}{\\text{lim}}{H}_{\\alpha }\\left(X\\right)\\)\u003c/span\u003e\u003c/span\u003e again, as in the Tsallis entropy.\u003c/p\u003e \u003cp\u003eApproximate entropy (ApEn) and sample entropy (SampEn) are mathematical algorithms specifically designed to quantify the repeatability or predictability within a time series dataset. These entropy measures aim to estimate the level of randomness or irregularity in a dataset without prior knowledge about the underlying data generation process. ApEn, developed by Pincus (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e1991\u003c/span\u003e), assesses the complexity and regularity of real-life time series data without the need for coarse-graining techniques. SampEn, introduced by Richman and Moorman (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2000\u003c/span\u003e), improves upon the limitations of ApEn by mitigating the influence of time series length on the analysis results, thereby reducing errors. The ApEn algorithm is an entropy-based method used to assess the complexity and predictability of earthquake time series data. It quantifies the irregularity or complexity of a time series by evaluating the probability that similar patterns within the data will persist as the pattern length increases. The calculation involves determining the logarithm of the conditional probability that two sequences of a specified length, with a maximum tolerance level, will remain similar within a defined range. A lower ApEn value indicates a more regular and predictable time series, while a higher ApEn value indicates greater complexity and irregularity. The ApEn can be obtained as follows:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$ApEn\\left(x,m,r\\right)=\\frac{1}{N-m+1}\\left[\\sum _{i=1}^{N-m+1}log\\left(\\frac{\\left|{j}_{i}\\right|}{N-m+1}\\right)\\right]-\\frac{1}{N-m}\\left[\\sum _{i=1}^{N-m}log\\left(\\frac{\\left|{k}_{i}\\right|}{N-m}\\right)\\right],$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${j}_{i}=\\left\\{\\zeta \\left|‖{y}_{i}-{y}_{\\zeta }‖\\right.\\le r\\wedge \\zeta \\in \u0026lang;1,N-m+1\u0026rang;\\right\\},$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$${k}_{i}=\\left\\{\\zeta \\left|‖{z}_{i}-{z}_{\\zeta }‖\\right.\\le r\\wedge \\zeta \\in \u0026lang;1,N-m\u0026rang;\\right\\}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$${y}_{i}=\\left[{x}_{i},{x}_{i+1},\\dots ,{x}_{i+m-1}\\right], {z}_{i}=\\left[{x}_{i},{x}_{i+1},\\dots ,{x}_{i+m}\\right], N=\\left|x\\right|.$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eEq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) searches for similar subsequences \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({y}_{i}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({z}_{i}\\)\u003c/span\u003e\u003c/span\u003e of length \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(m\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(m+1\\)\u003c/span\u003e\u003c/span\u003e. Assuming that the evaluation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(‖{y}_{i}-{y}_{\\zeta }‖\\le r\\)\u003c/span\u003e\u003c/span\u003e is a basic operation, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N-m+1\\)\u003c/span\u003e\u003c/span\u003e operations are required to compute each \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|{j}_{i}\\right|\\)\u003c/span\u003e\u003c/span\u003e. The total number of operations would then be \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(2{N}^{2} + N(6 - 4m) + 2{m}^{2} - 6m + 7\\)\u003c/span\u003e\u003c/span\u003e, so the time complexity of the approximate entropy is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Theta }\\left({N}^{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eSampEn, an enhancement over ApEn, overcomes the limitations associated with dataset length. It evaluates the regularity and complexity of a time series by assessing the probability of similar patterns in the data remaining similar, while considering the length of the time series. By accounting for dataset length, SampEn provides a more accurate estimation of complexity without the bias introduced by dataset length. Like ApEn, a lower SampEn value indicates a more regular and predictable time series, while a higher SampEn value signifies increased complexity and irregularity. The SampEn is obtained as\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$SampEn\\left(x,m,r\\right)=log\\left(\\frac{\\sum _{i=1}^{N-m+1}\\left|{b}_{i}\\right|}{\\sum _{i=1}^{N-m}\\left|{a}_{i}\\right|}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e.\u003c/p\u003e \u003cp\u003eHere, we have\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$${b}_{i}=\\left\\{\\zeta \\left|‖{y}_{i}-{y}_{\\zeta }‖\\right.\\le r\\wedge \\zeta \\in \u0026lang;1,N-m+1\\setminus i\u0026rang;\\right\\},$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$${a}_{i}=\\left\\{\\zeta \\left|‖{z}_{i}-{z}_{\\zeta }‖\\right.\\le r\\wedge \\zeta \\in \u0026lang;1,N-m\\setminus i\u0026rang;\\right\\}$$\u003c/div\u003e\u003c/div\u003e,\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$${y}_{i}=\\left[{x}_{i},{x}_{i+1},\\dots ,{x}_{i+m-1}\\right], {z}_{i}=\\left[{x}_{i},{x}_{i+1},\\dots ,{x}_{i+m}\\right], N=\\left|x\\right|.$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn terms of ApEn, the sets \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({b}_{i}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{i}\\)\u003c/span\u003e\u003c/span\u003e are different from the sets \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({j}_{i}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({k}_{i}\\)\u003c/span\u003e\u003c/span\u003e. They do not include the index \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i\\)\u003c/span\u003e\u003c/span\u003e, so the computation of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|{b}_{i}\\right|\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|{a}_{i}\\right|\\)\u003c/span\u003e\u003c/span\u003e only requires \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N-m\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N-m-1\\)\u003c/span\u003e\u003c/span\u003eoperations. It also introduces the possibility that all \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|{a}_{i}\\right|\\)\u003c/span\u003e\u003c/span\u003e can sum to zero. Then the total number of operations is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(2{N}^{2}+N(2-4m)+2{m}^{2}-2m+1\\)\u003c/span\u003e\u003c/span\u003e and the time complexity is again \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Theta }\\left({N}^{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3. LSTM (Long Short-Term Memory) Model\u003c/h2\u003e \u003cp\u003eRecurrent Neural Network (RNN) effectively deals with long-term dependencies but faces issues like gradient fading (Cao et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). To tackle this, Hochreiter and Schmidhuber (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1997\u003c/span\u003e) introduced LSTM, a variant of RNN, which became widely used in time series forecasting (Cho et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Gers and Schmidhuber, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). LSTM overcomes gradient vanishing using memory cells and control gates, outperforming classical RNNs (Livieris et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). It excels in addressing time series forecasting challenges (Chimmula and Zhang, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eLSTM cells consist of three primary structures: the input gate, the memory gate and the output gate. The cell state, represented by a horizontal line, carries information throughout the network (Yadav et al., \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The input gate determines the relevance of new input, the forget gate manages information retention, and the output gate organizes the transmitted information (Yamak et al., \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Livieris et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The LSTM algorithm is highly efficient for time series modelling due to its ability to capture long-term dependencies, store relevant information in memory cells, and regulate the flow of information through gates. Its general structure is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eInput Gate\u003c/strong\u003e \u003cp\u003eIt is the stage of determining what new information will be stored in the cell state. It consists of two basic components, the sigmoid layer and the \u003cem\u003etanh\u003c/em\u003e layer. The sigmoid layer decides which information will be stored in the cell state. The \u003cem\u003etanh\u003c/em\u003e layer creates a vector of new candidate values that can be added to the cell state. The outputs of the sigmoid layer and \u003cem\u003etanh\u003c/em\u003e layer are calculated, respectively, as follows\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equ8\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$${i}_{t}=\\sigma \\left({W}_{{i}_{h}}\\left[{h}_{t-1}\\right]+{W}_{{i}_{x}}\\left[{X}_{t}\\right]+{b}_{i}\\right)$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e,\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\stackrel{\\sim}{{c}_{t}}=tanh\\left({W}_{{c}_{h}}\\left[{h}_{t-1}\\right]+{W}_{{c}_{x}}\\left[{X}_{t}\\right]+{b}_{c}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe outputs of the sigmoid layer and the \u003cem\u003etanh\u003c/em\u003e layer are then combined to calculate new information to be added to the cell state:\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$${c}_{t}={f}_{t}\\odot {c}_{t-1}+{i}_{t}*\\stackrel{\\sim}{{c}_{t}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, ⊙ is the element-wise multiplication and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the forget gate output.\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eForget Gate\u003c/strong\u003e \u003cp\u003eIt is the stage to determine the information to be extracted from the cell state. The values and are obtained and a sigmoid layer is used. The output of the forget gate takes a value between 0 and 1. 0 means that the information corresponding to the value should be completely forgotten, while 1 means that the information corresponding to the value should be retained. The output of the forget gate is calculated as follows\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equ11\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$${f}_{t}=\\sigma \\left({W}_{{f}_{h}}\\left[{h}_{t-1}\\right]+{W}_{{f}_{x}}\\left[{X}_{t}\\right]+{b}_{f}\\right)$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe output of the forget gate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{t}\\)\u003c/span\u003e\u003c/span\u003eis then used to modulate the previous memory cell state \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({c}_{t-1}\\)\u003c/span\u003e\u003c/span\u003e. It performs an element-wise multiplication (⊙) with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({c}_{t-1}\\)\u003c/span\u003e\u003c/span\u003eto determine which information to keep and which to forget:\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$${c}_{t}={f}_{t}\\odot {c}_{t-1}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eOutput Gate\u003c/strong\u003e \u003cp\u003eThis stage determines which information will be output and plays a crucial role in deciding which part of the LSTM memory contributes to the final output. Similar to the input gate, it employs a sigmoid layer followed by a \u003cem\u003etanh\u003c/em\u003e layer. This layer determines the degree of contribution, which is then multiplied element-wise by the output of the sigmoid layer using a non-linear \u003cem\u003etanh\u003c/em\u003e function. The operations in the process are calculated as follows\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equ13\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$${o}_{t}=\\sigma \\left({W}_{{o}_{h}}\\left[{h}_{t-1}\\right]+{W}_{{o}_{x}}\\left[{X}_{t}\\right]+{b}_{o}\\right)$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e,\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ14\" name=\"EquationSource\"\u003e\n$${h}_{t}={o}_{t}\\odot \\text{t}\\text{a}\\text{n}\\text{h}\\left({c}_{t}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003eHere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({i}_{t}\\)\u003c/span\u003e\u003c/span\u003e represents the vector of the input gate, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{t}\\)\u003c/span\u003e\u003c/span\u003e represents the vector of the forget gate, o\u003csub\u003et\u003c/sub\u003e represents the output gate, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{\\sim}{{c}_{t}}\\)\u003c/span\u003e\u003c/span\u003e is the vector of the candidate values added to the new cell state, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({c}_{t}\\)\u003c/span\u003e\u003c/span\u003e represents the vector of the memory cell. The weight matrices are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({W}_{i}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({W}_{f}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({W}_{o}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({W}_{c}\\)\u003c/span\u003e\u003c/span\u003e. The bias vectors are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({b}_{i}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({b}_{f}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({b}_{o}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({b}_{c}\\)\u003c/span\u003e\u003c/span\u003e. In Eq.\u0026nbsp;(\u003cspan refid=\"Equ13\" class=\"InternalRef\"\u003e13\u003c/span\u003e), the sigmoid function designated by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sigma\\)\u003c/span\u003e\u003c/span\u003e and finally, the output matrix represented by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({h}_{t}\\)\u003c/span\u003e\u003c/span\u003e. The final output\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ h}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the result of element-wise multiplication between the output gate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({o}_{t}\\)\u003c/span\u003e\u003c/span\u003eand the hyperbolic tangent of the current memory cell state \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({(c}_{t})\\)\u003c/span\u003e\u003c/span\u003e. This output represents the information that the LSTM model decides to pass on to the subsequent time step or use for prediction. LSTM gives effective results in earthquake magnitude estimation. For this reason, it is frequently applied to forecast future earthquake magnitudes by analyzing past data (Lakshmi and Tiwari, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Berhich et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Sadhukhan et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhang and Wang, \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Results","content":"\u003cdiv\u003e\n \u003cp\u003eThe descriptive statistics obtained from earthquake magnitude and depth data, covering the period between January 1970 and September 2021, are presented in Table \u003cspan\u003e1\u003c/span\u003e. Q\u003csub\u003e1\u003c/sub\u003e, Q\u003csub\u003e2\u003c/sub\u003e, and Q\u003csub\u003e3\u003c/sub\u003e denote the first, second, and third quartiles correspondingly. The histogram graphs in Fig. \u003cspan\u003e7\u003c/span\u003ea and b also illustrate earthquake magnitude and depth data, respectively. Analyzing the data from Table \u003cspan\u003e1\u003c/span\u003e and the visual representation in Fig. \u003cspan\u003e7\u003c/span\u003e reveals essential characteristics of earthquakes in the Aegean Graben System.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 1\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eThe descriptive statistics for the Depth (km) and Magnitude (Mw) of earthquakes that occurred between January 1970 and September 2021\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDepth (km)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMagnitude (Mw)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDepth (km)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMagnitude (Mw)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eMin.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eMax.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e183.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.60\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eSt. Deviation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e21.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.54\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eMedian\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eSkewness\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.54\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eMean\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e16.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eKurtosis\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e20.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e16.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\n \u003cp\u003eThe minimum magnitude recorded stands at 3.0, representing the smallest earthquake magnitude within this dataset. Conversely, the maximum magnitude observed is 7.6, indicating the highest earthquake magnitude documented in the Aegean Graben System. The first quartile at 6.81 km reveals that 25% of earthquakes have depths below or equal to this value. The median, set at 10 km, marks the midpoint where 50% of earthquakes fall below or equal to this depth. Moving further, the third quartile is at 16.32 km, indicating that 75% of earthquakes have depths less than or equal to this value. The average depth stands at 16.06 km, giving a central tendency estimate and portraying a typical depth for earthquakes in the dataset. Additionally, the standard deviation of 21.25 km signifies the spread or variability around the average, implying a wider range of depth values when higher. The skewness value of 3.84 indicates a right-skewed distribution, suggesting a longer tail on the right side. Lastly, the kurtosis value of 20.79 denotes a highly peaked distribution with heavy tails, providing insights into the distribution\u0026apos;s shape.\u003c/p\u003e\n \u003cp\u003eThe statistics given in Table \u003cspan\u003e1\u003c/span\u003e also shed light on earthquake magnitude distribution. The first quartile at 3.10 indicates 25% below this, median at 3.30 shows 50% below, and third quartile at 3.70 means 75% below. The average magnitude, 3.48, gives a central tendency measure. A standard deviation of 0.54 signifies variability around the average, higher values implying greater dispersion. Skewness (1.54) indicates right-skewed distribution with a longer tail on the right, and kurtosis (5.38) implies a highly peaked distribution with heavy tails.\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eFigure \u003cspan\u003e8\u003c/span\u003e presents the box plots for the magnitude (km) of earthquakes between years 1970 and 2021. When examining this graph, two distinct patterns in earthquake magnitudes between 1970 and 2021 are noteworthy. It is observed that from 1970 to 1990, the annual earthquake magnitudes were higher, and after 1990, earthquake magnitudes decreased compared to the previous years. The decline observed between 1990 and 2021 may imply a shift or decrease in stress distribution over that timeframe. However, it\u0026apos;s essential to emphasize the significance of precise and thorough earthquake data collection. The lack of a clear trend between 1970 and 1990 may be due to limitations in data sources or observation systems during this period. However, advancements in technology and the expansion of monitoring networks in later years likely led to the acquisition of more accurate and reliable data.\u003c/p\u003e\n\u003cp\u003eAfter exploratory data analysis, a k-means clustering analysis is applied to analyze earthquakes between January 1970 and September 2021 using earthquake magnitude, latitude, and longitude as input variables from the declustered catalog. The objective is to uncover distinct clusters within the dataset. The Silhouette score and the Elbow criterion are used to determine the ideal number of clusters for the k-means method. These aid in selecting the most appropriate number of clusters that effectively capture the inherent patterns in the data. The Silhouette score assesses clustering quality by examining the compactness of data points within clusters and the separation between different clusters. Higher Silhouette scores indicate well-defined and separated clusters. Additionally, the Elbow criterion is employed to pinpoint the number of clusters that explain the most significant portion of variance in the data. This involves plotting the percentage of variance explained against the number of clusters. The \u0026quot;Elbow\u0026quot; point on the plot signifies the optimal number of clusters, where the additional gain in explained variance becomes minimal.\u003c/p\u003e\n\u003cp\u003eFigure 9 illustrates the outcomes of both the Silhouette score and the Elbow criterion, assisting in the determination of the optimal number of clusters. The Silhouette score plot provides insights into the clustering quality for various numbers of clusters, while the Elbow criterion plot demonstrates the explained variance as a function of the number of clusters. By examining these plots, one can determine the number of clusters that maximizes the Silhouette score or identifies the point where the explained variance levels off significantly (indicating diminishing improvements in clustering). This chosen number of clusters will be utilized for conducting the k-means clustering analysis on the earthquake dataset.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 9.\u003c/strong\u003e Graphs for Silhouette score and Elbow criterion for earthquake between years 1970 and 2021.\u003c/p\u003e\n\u003cp\u003eUpon analyzing Fig.\u0026nbsp;9.a, it\u0026apos;s clear that the model with three clusters achieves the highest Silhouette score, indicating distinct and well-separated clusters. The two-cluster model follows with the second-highest Silhouette score, succeeded by the models with four and five clusters. This suggests the dataset can be effectively grouped into three or four distinct clusters based on earthquake magnitude, latitude, and longitude. Figure\u0026nbsp;9.b, illustrating the elbow criterion, demonstrates the most significant decrease in within-cluster sum of squares at three clusters. Moreover, there\u0026apos;s a notable decrease from three to five clusters, with diminishing decreases for higher cluster numbers. The alignment of the Silhouette score and the elbow criterion strongly suggests the optimal cluster number is likely three or four. Both criteria consistently point to these numbers, affirming they represent the underlying patterns in the data. This convergence boosts confidence in selecting either three or four clusters for the k-means clustering analysis of the earthquake dataset.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan\u003e10\u003c/span\u003e shows clustering results from the k-means algorithm. Each cluster is represented by a unique color, allowing for easy analysis of earthquake spatial distribution based on latitude and longitude. The x-axis represents longitude, and the y-axis represents latitude. This plot provides insights into how earthquakes are distributed and clustered across the study area. Figure \u003cspan\u003e10\u003c/span\u003e further reveals distinct spatial patterns and earthquake groupings within the selected clusters.\u003c/p\u003e\n\u003cp\u003eMany earthquakes in the Aegean Region concentrate in the sea due to islands and the indented coastline. Through k-means clustering, earthquake magnitudes were effectively grouped into three clusters, revealing distinct patterns and enhancing our understanding of seismic behavior in the region. In Table \u003cspan\u003e2\u003c/span\u003e, the characteristics of each cluster, derived from the k-means clustering with an optimal cluster number of 3, are presented. Figure \u003cspan\u003e10\u003c/span\u003e.b visually validates the presence of these three clusters, aligning with the optimal cluster number identified through the average Silhouette width value. A deeper look into Table \u003cspan\u003e2\u003c/span\u003e provides additional insights. The first cluster (blue in Fig. \u003cspan\u003e10\u003c/span\u003e.b) comprises 4352 observations with an average magnitude of approximately Mw\u0026thinsp;=\u0026thinsp;3.4. The second cluster encompasses 5382 earthquakes, while the third cluster includes 6111 earthquakes. Analysis of Table \u003cspan\u003e2\u003c/span\u003e shows that the mean magnitudes for the second and third clusters are around Mw\u0026thinsp;=\u0026thinsp;3.4 and Mw\u0026thinsp;=\u0026thinsp;3.6, respectively.\u003c/p\u003e\n\u003cdiv\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 2\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eCharacteristics of each cluster when the optimal number is 3 via k-means clustering\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCluster\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMagnitude Mean\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLongitude Mean\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLatitude Mean\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNumber of Events\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVariance\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e38.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4352\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.281\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e27.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e39.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5382\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.209\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e27.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e36.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6111\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.336\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eIn Fig. \u003cspan\u003e10\u003c/span\u003e.b, Cluster 3 displays earthquakes with magnitudes ranging from Mw\u0026thinsp;=\u0026thinsp;3.0 to Mw\u0026thinsp;=\u0026thinsp;6.9 and depths up to 183.8 km. Notably, the destructive Izmir earthquake of October 30, 2020, falls within this cluster, marked by its shallow depth and severe impact in the Aegean and Marmara regions, especially Izmir province. In Cluster 2, earthquakes are predominantly land-based, with magnitudes spanning from Mw\u0026thinsp;=\u0026thinsp;3.0 to Mw\u0026thinsp;=\u0026thinsp;6.5 and maximum depth recorded at 78 km. Many of these quakes occurred on the mainland. Cluster 1 showcases earthquakes occurring on both land and islands. With 4352 earthquakes and an average magnitude of Mw\u0026thinsp;=\u0026thinsp;3.4, this cluster has the fewest observations but extends to depths of 159.2 km.\u003c/p\u003e\n\u003cp\u003eIn Table \u003cspan\u003e3\u003c/span\u003e, the calculated ApEn and SampEn values are also provided for each cluster of earthquakes. These entropy values reflect the complexity or irregularity of the time series patterns within each cluster. The ApEn and SampEn values offer insights into the predictability and regularity of the seismic activity within the analyzed clusters.\u003c/p\u003e\n\u003cdiv\u003e\u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 3\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eEntropy measures of earthquake magnitudes for each cluster with k-means clustering\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCluster 1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCluster 2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCluster 3\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eApEn\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9584647\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9754377\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.276853\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eSampEn\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.7440741\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.766529\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.355065\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eAnalyzing the entropy values presented in Table \u003cspan\u003e3\u003c/span\u003e, we can deduce distinct patterns within the three clusters. Notably, Cluster 1 displays a higher degree of regularity and uniformity than the other clusters. This suggests a consistent and predictable pattern in seismic activity for this cluster. Conversely, Cluster 3 exhibits lower predictability with higher entropy values, indicating a less regular and more unpredictable seismic pattern. These observations shed light on the diverse characteristics of earthquake clusters in the Aegean Region. Cluster 1 showcases a homogenous seismic activity pattern, emphasizing its predictability. Conversely, Cluster 3 presents a more intricate and unpredictable pattern, highlighting the variability and complexity its seismic events.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan\u003e11\u003c/span\u003e illustrates monthly average earthquake magnitudes for each cluster, aiding in the visualization of temporal variations and trends. Connecting these insights from the entropy analysis to the temporal variations illustrated in Fig. \u003cspan\u003e11\u003c/span\u003e, we can discern a compelling correlation. Cluster 2, demonstrating higher regularity in seismic activity, aligns with a smoother and more consistent trend in earthquake magnitudes over the months. This reinforces the notion of predictability within this cluster, as the seismic events follow a uniform pattern. Conversely, in Cluster 3 where seismic activity is less predictable, the monthly average earthquake magnitudes depict a more erratic pattern. The higher entropy values observed in Cluster 3 might indeed be reflected in these fluctuations, showcasing a dynamic and less homogeneous seismic activity scenario. These plots offer insights into seismic activity dynamics, aiding in the identification of patterns or notable changes over time. The smoothed monthly averages provide a clear overview of magnitude behavior.\u003c/p\u003e\n\u003cp\u003eIn Fig. \u003cspan\u003e11\u003c/span\u003e, the time series plots have been visually examined and they show noticeable trends. This observation is further supported in Fig. \u003cspan\u003e12\u003c/span\u003e by analyzing the autocorrelation function (ACF) and partial autocorrelation function (PACF) plots for each cluster. The first differences of the series in each cluster are calculated to address this issue. This differencing process effectively removes the trend component and transforms the series into a stationary form. Examination of the resulting differenced series confirms that the trends have been successfully removed from all three clusters.\u003c/p\u003e\n\u003cp\u003eWe also perform the LSTM method to consider memory mechanisms to capture and learn complex relationships of earthquakes. In the application of the LSTM method to k-means-clustered three sub-catalogs, a series of steps are followed to build and train the model. First, the data is prepared by dividing it into training (70%) and testing (30%) sets. Subsequently, the data is normalized using Min-Max normalization to make sure that the data falls within a certain range. Moving on to the model architecture, the LSTM model is employed in the second step. The Tanh activation function is utilized, and the parameter \u0026quot;return_sequences\u0026thinsp;=\u0026thinsp;True\u0026quot; is set to maintain the output sequence, which is crucial for capturing temporal dependencies. The third step involves the training process, where an optimization algorithm, stochastic gradient descent, is utilized. This algorithm helps to determine the optimal batch size and the number of epochs needed for effective training. The loss function chosen for this training phase is the mean squared error, a common choice for regression tasks. In the final step, the LSTM model is trained using the specified parameters and the prepared training data. Once trained, the model can be employed to make predictions, forecasts, and even estimate confidence intervals for future time periods based on the patterns and information captured during the training phase. The values of batch size and epoch number values mentioned in Step 3 used for the clusters are given in Table \u003cspan\u003e4\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv\u003e\u0026nbsp;\u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 4\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eThe LSTM parameters values for all clusters\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCluster 1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCluster 2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCluster 3\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eBatch size\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e128\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e32\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eEpoch number\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eFigure 13 displays the number of iterations for each cluster alongside its corresponding loss function value. This value represents the error between the predicted and actual values calculated using the Mean Squared Error (MSE) criterion. The objective is to achieve the best possible predictions with minimal error, in other words, with minimum loss. It is worth noting that Cluster 1 approaches this value with a higher number of iterations. On the contrary, Cluster 3 achieves the greatest loss function value by employing the highest number of iterations, whereas Cluster 2 attains a lower value after 750 iterations.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 13\u003c/strong\u003e. Loss vs iterations graph for all clusters\u003c/p\u003e\n\u003cp\u003eThe appropriateness of these figures for training and testing data is assessed via the mean square error (RMSE) criterion. In addition, the RMSE values presented in Table \u003cspan\u003e5\u003c/span\u003e corroborate the parameter sizes established in Table \u003cspan\u003e4\u003c/span\u003e. Correspondingly, the parameters in Table \u003cspan\u003e4\u003c/span\u003e with the lowest RMSE values among the parameters are deemed the most suitable. When the above LSTM steps are applied, the predicted values for each cluster are first shown in Fig. \u003cspan\u003e14\u003c/span\u003e. Later, Fig.\u0026nbsp;15 shows the forecast and confidence limits of the average earthquake magnitude obtained up to March 2028 for the clusters.\u003c/p\u003e\n\u003cdiv\u003e\u0026nbsp;\u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 5\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eThe RMSE values of all clusters\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eThe RMSE values\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCluster 1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCluster 2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCluster 3\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eTrain data\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.27\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eTest data\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.59\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eFigure 15 illustrates a clear comparison of the actual series and the forecast series. The fit appears to be satisfactory for all clusters. It is challenging to forecast the sudden changes in the three clusters that occurred in the average magnitudes of earthquakes between 1970 and 1990, which marked the beginning of the period. It is observed that the average earthquake magnitudes of the second cluster after 1990 are close to the predictions. This supports the findings presented in Table \u003cspan\u003e5\u003c/span\u003e. In this regard, it appears that the mean earthquake magnitudes and predicted values in the test dataset of the third cluster are significantly distinct from the other clusters.\u003c/p\u003e\n\u003cp\u003eBased on the findings, we anticipate distinctive average earthquake magnitudes within each cluster until the year 2028. Cluster 1 is expected to maintain lower-than-average magnitudes, indicating a relatively subdued seismic activity pattern. In contrast, Cluster 2 is foreseen to exhibit significantly higher-than-average magnitudes, highlighting a heightened level of seismic activity characterized by substantial events. Cluster 3, falling somewhere in between, is projected to sustain an average magnitude trend, underscoring a balanced seismic activity pattern. These projections offer valuable insights into the expected seismic behavior within the respective clusters, aiding in proactive measures for seismic risk assessment and preparedness. In general, earthquake magnitudes that decreased after the 2000s are expected to continue after the 2020s, with different seismic movements depending on the region covered by each cluster. This is due to various seismic movements that rely on the region covered by each cluster. Future estimations of earthquake magnitude averages have been attempted whilst considering the impacts of geological structures of each cluster, determined by region.\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eEarthquakes are seismic activities that can cause significant loss and destruction. Turkey, being located in a highly seismic region hosted by dense active faults from west to east, experiences frequent and intense earthquakes. Cluster analysis is a powerful tool for advancing our understanding of earthquakes and improving our ability to manage associated risks. By analyzing the resulting clusters, we can gain valuable insights into magnitude ranges, spatial distribution, and potential relationships between earthquake events in the region. This information is instrumental for studying seismic hazards, assessing risks, and implementing effective mitigation strategies in the Aegean Region. Our study aims to contribute to a deeper understanding of earthquake dynamics in Turkey. We conducted a comprehensive analysis of earthquake classification and detection of volatilities concerning depth and size. This knowledge is crucial for assessing seismic hazards, enhancing disaster preparedness, and implementing effective mitigation strategies. The use of entropy-based measures, including approximate entropy and sample entropy provides significant insights into the regularity, complexity, and patterns present in seismic data. These methods enhance our understanding of seismic behavior and potentially aid in earthquake forecasting and hazard assessment. Sample entropy, specifically, is utilized to quantify the fluctuation degree of earthquake magnitudes. By grouping seismic events using k-means, researchers can uncover patterns and relationships within the data, leading to improved earthquake analysis and a better understanding of seismic activity.\u003c/p\u003e \u003cp\u003eThe LSTM method, with its ability to capture ordered relationships in earthquake magnitude estimation, adapt through parameter adjustments, and effectively handle complex and multidimensional data, stands out. This approach allows for accurate predictions and contributes to earthquake risk management. In this study, we utilized the LSTM method to calculate future earthquake magnitude predictions for the clusters obtained in the last stage. As a result, the region in the 2nd cluster is anticipated to experience more severe earthquakes in the coming years. Understanding the tectonic and geological characteristics of the region, combined with observed seismicity patterns, provides valuable insights into earthquake processes in Turkey. This knowledge is critical for seismic hazard assessment, earthquake preparedness, and the implementation of effective mitigation strategies to minimize the devastating impacts of future earthquakes.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe research presented in this study received funding from The Scientific and Technical Research Council of T\u0026uuml;rkiye (T\u0026Uuml;BİTAK) under project number 121F208. We would like to express our gratitude to Assoc. Prof. Dr. Senem Tekin for her contribution in preparing the dataset. We are also thankful to Prof. Dr. Tolga \u0026Ccedil;an for his valuable guidance and advice throughout the project.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eConflict of Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eBalasis, G., Daglis, I. A., Papadimitriou, C., Anastasiadis, A., Sandberg, I., \u0026amp; Eftaxias, K. (2011). Quantifying dynamical complexity of magnetic storms and solar flares via nonextensive Tsallis entropy. Entropy, 13(10), 1865-1881.\u003c/li\u003e\n \u003cli\u003eBalasis, G., Daglis, I. A., Papadimitriou, C., Kalimeri, M., Anastasiadis, A., \u0026amp; Eftaxias, K. (2008). Dynamical complexity in Dst time series using non‐extensive Tsallis entropy. Geophysical Research Letters, 35(14).\u003c/li\u003e\n \u003cli\u003eBayrak, Y., \u0026amp; Bayrak, E. (2012). 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IEEE Transactions on Geoscience and Remote Sensing.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"earthquake, k-means clustering, sample entropy, approximate entropy, long-short term memory","lastPublishedDoi":"10.21203/rs.3.rs-3979686/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3979686/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWestern Anatolia stands out as one of the globally active seismic regions. The paleoseismic history of numerous significant faults in this area, including information about recurrence intervals of damaging earthquakes, magnitude, displacement, and slip rates, remains inadequately understood. The extensive crustal extension at the regional level has given rise to significant horst-graben systems delineated by kilometer-scale normal faults, particularly in carbonate formations, where vertical crustal displacements have taken place. We categorize earthquakes with a k-means clustering algorithm in Western Anatolia from 1900 to 2021 based on specific characteristics or patterns present in the data. Additionally, we explore the volatility in depth and size within each cluster using approximate and sample entropy methods. These entropy measures offer valuable insights into the complexity and irregularity of earthquake patterns in different zones. The findings indicate that to understand seismic activity in the Aegean region comprehensively, it needs to be analyzed by dividing it into three regions using the k-means clustering algorithm. Entropy procedures are implemented to validate that the identified regions accurately depict the seismic patterns. The long-short-term memory (LSTM) method obtains separate earthquake magnitude predictions for each of the three regions. When these values are evaluated with the root mean squared error (RMSE) criterion for the three regions with the actual values, the train data gives strong results with 0.30 and the test data with 0.49 on average. The outcomes demonstrate that the future forecast for each region exhibits unique trends, predicting larger earthquakes in the second segment.\u003c/p\u003e","manuscriptTitle":"Seismic Microzonation and Future Forecasting of Earthquakes in Western Anatolia through K-Means Clustering Analysis with Magnitude Volatility Detection by Entropy Approaches","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-27 13:53:13","doi":"10.21203/rs.3.rs-3979686/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d8f57341-8efb-4738-8e6e-ead963c4c8e0","owner":[],"postedDate":"March 27th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-05-12T15:45:15+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-27 13:53:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3979686","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3979686","identity":"rs-3979686","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}