1:45 PM - 3:15 PM
[SCG55-P12] Estimation of fault planes by two-step clustering on hypocenter distribution
Keywords:Fault plane estimation, 3D hypocenter distribution, Unsupervised learning, Local structure, Online clustering
Hypocenter distributions have been used as indicators of fault geometries at depth. The fault geometries have been estimated by subjective visual inspections, e.g., using cross sections. The objective estimation will be useful for better understanding of subsurface fault structures and development of automated determination.
Piegari et al. (2022) have used an unsupervised machine learning clustering method to identify the three-dimensional characteristics of a fault plane from hypocenters. In a large data set due to the collection and accumulation of hypocenter distributions, multiple fault planes are connected as a dense hypocenter distribution. Therefore, it is necessary to adjust the number of hypocenters and their distribution range to be the clustering method's input.
Previously, we proposed a method to solve the global linkage of hypocenter distributions by two-step clustering methods (Sato et al., 2022, SSJ). First, we capture the structure of the dense hypocenter distribution by using normal vectors, then partition the plane structure by a clustering algorithm based on the angles of normal vectors. Next, we divide the hypocenter distribution of each cluster into subclusters using the coordinates of normal vectors. In this method, the agglomerative clustering algorithm is used to cluster the normal vectors, which introduces a problem of increased computational cost (amount of memory required and processing time) when using large-scale catalogs. Therefore, we combined our method with Birch (Zhang et al., 1997), an online clustering method, to create initial clusters using the normal vectors of the hypocenter distribution. After that, the hypocenter distribution is clustered based on the hypocenter coordinates by using HDBSCAN (McInnes et al., 2017) to form clusters per fault plane.
In this study, we aimed to validate the method with a large dataset by detecting each fault plane from earthquake catalogs created by extracting hypocenters near the fault plane based on the known fault plane model and Gaussian distribution.
We test the proposed method against the earthquake catalogs extracted from the Southern California catalog of Hauksson et al. (2012). The SCEC Community Fault Model (CFM)(Nicholson et al., 2014) is used as the reference fault model for the excerpting process. In the excerpting process, a histogram is created for each fault using the distance perpendicular to the plane of the fault model. The histograms are then extracted by changing the standard deviation of the Gaussian distribution, σ is set to 1000, 5000, and 10000 m.
The results of applying the proposed method to the earthquake catalogs are shown in the figure. The top part of the figure shows the detected fault planes using the earthquake catalogs separately. The bottom part of the figure shows the angle error comparison between the detected fault plane and the fault model. The results in the top part of the figure show that most of the detected fault planes were almost vertical when σ is 1000 m. However, detection of nearly horizontal fault planes increased as σ increased. In the bottom part of the figure, the dip angle error is almost always less than 30 degrees at σ is 1000 m, while the dip angle error tends to increase as σ increases. Moreover, the strike angle error is a similar change was observed regardless of the increase in standard deviation.
The results confirm that the dip angle decreases with increasing σ. This method uses principal component analysis (PCA) on the divided clusters to calculate strike and dip. Therefore, it is considered that when the spread of the epicenter distribution to the surroundings is larger than the depth direction, the result of the PCA shows a change toward the horizontal.
In the SCEC CFM, there is a range where several fault planes exist in parallel. In addition, there are fault planes with sparse hypocenter distributions. The hypocenters on the surrounding fault planes is also excerpted, and the hypocenter distribution across several faults is generated. This is thought to cause errors in the strike direction.
In the method previously presented by the authors, fault planes were detected and checked against the focal mechanism solution, and only fault planes within a set threshold range were extracted. This method effectively extracts a small range of angular errors in strike and dip in the lower part of the figure. However, in the case of adjacent fault planes, which was clarified in this verification, a future study is needed regarding separating the hypocenter distribution.
Acknowledgments
This study was supported by MEXT Project for Seismology TowArd Research innovation with data of Earthquake (STAR-E). (Grant No. JPJ010217)
Piegari et al. (2022) have used an unsupervised machine learning clustering method to identify the three-dimensional characteristics of a fault plane from hypocenters. In a large data set due to the collection and accumulation of hypocenter distributions, multiple fault planes are connected as a dense hypocenter distribution. Therefore, it is necessary to adjust the number of hypocenters and their distribution range to be the clustering method's input.
Previously, we proposed a method to solve the global linkage of hypocenter distributions by two-step clustering methods (Sato et al., 2022, SSJ). First, we capture the structure of the dense hypocenter distribution by using normal vectors, then partition the plane structure by a clustering algorithm based on the angles of normal vectors. Next, we divide the hypocenter distribution of each cluster into subclusters using the coordinates of normal vectors. In this method, the agglomerative clustering algorithm is used to cluster the normal vectors, which introduces a problem of increased computational cost (amount of memory required and processing time) when using large-scale catalogs. Therefore, we combined our method with Birch (Zhang et al., 1997), an online clustering method, to create initial clusters using the normal vectors of the hypocenter distribution. After that, the hypocenter distribution is clustered based on the hypocenter coordinates by using HDBSCAN (McInnes et al., 2017) to form clusters per fault plane.
In this study, we aimed to validate the method with a large dataset by detecting each fault plane from earthquake catalogs created by extracting hypocenters near the fault plane based on the known fault plane model and Gaussian distribution.
We test the proposed method against the earthquake catalogs extracted from the Southern California catalog of Hauksson et al. (2012). The SCEC Community Fault Model (CFM)(Nicholson et al., 2014) is used as the reference fault model for the excerpting process. In the excerpting process, a histogram is created for each fault using the distance perpendicular to the plane of the fault model. The histograms are then extracted by changing the standard deviation of the Gaussian distribution, σ is set to 1000, 5000, and 10000 m.
The results of applying the proposed method to the earthquake catalogs are shown in the figure. The top part of the figure shows the detected fault planes using the earthquake catalogs separately. The bottom part of the figure shows the angle error comparison between the detected fault plane and the fault model. The results in the top part of the figure show that most of the detected fault planes were almost vertical when σ is 1000 m. However, detection of nearly horizontal fault planes increased as σ increased. In the bottom part of the figure, the dip angle error is almost always less than 30 degrees at σ is 1000 m, while the dip angle error tends to increase as σ increases. Moreover, the strike angle error is a similar change was observed regardless of the increase in standard deviation.
The results confirm that the dip angle decreases with increasing σ. This method uses principal component analysis (PCA) on the divided clusters to calculate strike and dip. Therefore, it is considered that when the spread of the epicenter distribution to the surroundings is larger than the depth direction, the result of the PCA shows a change toward the horizontal.
In the SCEC CFM, there is a range where several fault planes exist in parallel. In addition, there are fault planes with sparse hypocenter distributions. The hypocenters on the surrounding fault planes is also excerpted, and the hypocenter distribution across several faults is generated. This is thought to cause errors in the strike direction.
In the method previously presented by the authors, fault planes were detected and checked against the focal mechanism solution, and only fault planes within a set threshold range were extracted. This method effectively extracts a small range of angular errors in strike and dip in the lower part of the figure. However, in the case of adjacent fault planes, which was clarified in this verification, a future study is needed regarding separating the hypocenter distribution.
Acknowledgments
This study was supported by MEXT Project for Seismology TowArd Research innovation with data of Earthquake (STAR-E). (Grant No. JPJ010217)