5:15 PM - 6:45 PM
[SCG50-P07] Spectral clustering-based association analysis of tremor detected stations: application to S-net
Keywords:Spectral clustering, Tectonic tremor, S-net, Japan Trench
Introduction
Tectonic tremors, a kind of slow earthquakes, have been observed near the megathrust seismogenic zone (Obara & Kato, 2016). Since tremor is associated with aseismic slip, comprehensive tremor detection is crucial for monitoring slip phenomena around the seismogenic zone.
The envelope correlation method (Obara, 2002) has been applied to detect tremors. However, this method struggles to distinguish between earthquake and tremor, whereas the machine learning methods can classify them based on characteristics such as dominant frequency and duration. Sagae et al. (2023, SSJ) developed a CNN model (ETN-detector) using spectrograms from all the S-net stations, successfully classifying signals into earthquake, tremor, and noise. However, single-station data cannot fully prevent misclassification. For instance, regional earthquake signals could be misclassified as tremors due to high-frequency attenuation. Association based on detection results from multiple stations reduces misclassification and clearly identifies tremor signals. Therefore, in this study, we newly developed a tremor association method based on spectral clustering (von Luxburg, 2007) and examined the characteristics of groups of stations that detected tremors.
Method
Spectral clustering is a graph-based clustering technique. A graph is a data structure consisting of nodes and edges, suitable for exploring connections among data. It is expressed by the Laplacian matrix L = D – A, where A is the adjacency matrix, and D is the degree matrix. A is symmetric with the non-diagonal component Aij representing the weight of the edge connecting the i-th and j-th nodes. If there is no edge between two nodes, Aij is zero. D is diagonal, and Dii is the sum of the weights of the edges connected to the i-th node. Given an eigenvector whose i-th component xi is the feature value of the i-th node, the eigenvalue of L is represented by λ = Σi,j Aij (xi – xj)2. Small eigenvalues indicate that the features xi and xj are more similar when the edge weights Aij are large. Spectral clustering can cluster nodes based on the eigenvectors.
Data processing
We constructed a k-nearest neighbor graph (k = 10), considering the locations of S-net stations as nodes. The ETN-detector outputs tremor probability based on three-component spectrograms. To construct the graph considering the tremor probability pi at each station, we assigned edge weights as the product of the probabilities between two stations. The adjacency matrix A, whose non-diagonal components are pipj, represents the graph. Finally, the Laplacian matrix L is constructed from A.
The eigenvalue decomposition of L is performed. Using the Gaussian mixture model (Bishop, 2006), we partitioned the stations into clusters based on the eigenvector corresponding to the smallest eigenvalues and extracted clusters including three or more stations.
Result & Discussion
We studied the station clusters for tremors listed in Nishikawa et al. (2023). For all the extracted clusters, the spatial spread of the cluster was evaluated by the standard deviation of distance from the centroid of the stations. Focusing on the clusters with large standard deviations (≧ 100 km), we found that signals associated with regional earthquakes were contained in the time windows from which the clusters were extracted. Moreover, we applied our method to continuous data and confirmed that regional earthquake signals can be efficiently removed by setting a threshold based on the standard deviation of the cluster.
Spectral clustering can partition clusters using the eigenvector corresponding to the second smallest eigenvalue. It allows the partitioning of clusters associated with adjacent tremors. We will discuss the features of the partitioned cluster and its effect on the hypocenter location.
Acknowledgment: This research was supported by JSPS KAKENHI Grant Number JP21H05205 in Grant-in-Aid for Transformative Research Areas (A) “Science of Slow-to-Fast Earthquakes”.
Tectonic tremors, a kind of slow earthquakes, have been observed near the megathrust seismogenic zone (Obara & Kato, 2016). Since tremor is associated with aseismic slip, comprehensive tremor detection is crucial for monitoring slip phenomena around the seismogenic zone.
The envelope correlation method (Obara, 2002) has been applied to detect tremors. However, this method struggles to distinguish between earthquake and tremor, whereas the machine learning methods can classify them based on characteristics such as dominant frequency and duration. Sagae et al. (2023, SSJ) developed a CNN model (ETN-detector) using spectrograms from all the S-net stations, successfully classifying signals into earthquake, tremor, and noise. However, single-station data cannot fully prevent misclassification. For instance, regional earthquake signals could be misclassified as tremors due to high-frequency attenuation. Association based on detection results from multiple stations reduces misclassification and clearly identifies tremor signals. Therefore, in this study, we newly developed a tremor association method based on spectral clustering (von Luxburg, 2007) and examined the characteristics of groups of stations that detected tremors.
Method
Spectral clustering is a graph-based clustering technique. A graph is a data structure consisting of nodes and edges, suitable for exploring connections among data. It is expressed by the Laplacian matrix L = D – A, where A is the adjacency matrix, and D is the degree matrix. A is symmetric with the non-diagonal component Aij representing the weight of the edge connecting the i-th and j-th nodes. If there is no edge between two nodes, Aij is zero. D is diagonal, and Dii is the sum of the weights of the edges connected to the i-th node. Given an eigenvector whose i-th component xi is the feature value of the i-th node, the eigenvalue of L is represented by λ = Σi,j Aij (xi – xj)2. Small eigenvalues indicate that the features xi and xj are more similar when the edge weights Aij are large. Spectral clustering can cluster nodes based on the eigenvectors.
Data processing
We constructed a k-nearest neighbor graph (k = 10), considering the locations of S-net stations as nodes. The ETN-detector outputs tremor probability based on three-component spectrograms. To construct the graph considering the tremor probability pi at each station, we assigned edge weights as the product of the probabilities between two stations. The adjacency matrix A, whose non-diagonal components are pipj, represents the graph. Finally, the Laplacian matrix L is constructed from A.
The eigenvalue decomposition of L is performed. Using the Gaussian mixture model (Bishop, 2006), we partitioned the stations into clusters based on the eigenvector corresponding to the smallest eigenvalues and extracted clusters including three or more stations.
Result & Discussion
We studied the station clusters for tremors listed in Nishikawa et al. (2023). For all the extracted clusters, the spatial spread of the cluster was evaluated by the standard deviation of distance from the centroid of the stations. Focusing on the clusters with large standard deviations (≧ 100 km), we found that signals associated with regional earthquakes were contained in the time windows from which the clusters were extracted. Moreover, we applied our method to continuous data and confirmed that regional earthquake signals can be efficiently removed by setting a threshold based on the standard deviation of the cluster.
Spectral clustering can partition clusters using the eigenvector corresponding to the second smallest eigenvalue. It allows the partitioning of clusters associated with adjacent tremors. We will discuss the features of the partitioned cluster and its effect on the hypocenter location.
Acknowledgment: This research was supported by JSPS KAKENHI Grant Number JP21H05205 in Grant-in-Aid for Transformative Research Areas (A) “Science of Slow-to-Fast Earthquakes”.