5:15 PM - 6:30 PM
[SCG50-P06] Hierarchical clustering of reduced stress tensors based on angular stress distance
Keywords:paleostress analysis, hierarchical clustering, angular stress distance, Tanabe Group
To reveal the crustal stress state is essential to elucidate mechanism and driving force of tectonics. In the field of geology, mesoscale structures such as faults, mineral veins and dikes are used to detect paleostresses through stress tensor inversion techniques. The techniques usually determine so-called reduced stress tensors which carry three principal stress axes and a stress ratio. Since the crustal stress state changes temporally and spatially, plural different stresses can be recorded in a set of mesoscale structures. Sometimes we meet a difficulty in inferring the tectonic origins of stresses because of a large number of and a wide variety of stress tensors detected from a study area. In such case we need a statistical approach to find out the characteristics of a group of stress tensors. In order to meet such requirement, this study proposes to utilize the hierarchical clustering method.
The hierarchical clustering method needs to define the differences between elements. In this study, angular stress distance (Yamaji and Sato, 2006) is used as the measure of difference between two reduced stress tensors. Once the tensors are grouped to form a cluster, we also need to define the distances between clusters. There are several methods to define the distances between clusters. Among them the group average method was found to be optimal through a Monte Carlo calculation to compare the methods with evaluations of the cophenetic correlation coefficients (Sokal and Rohlf, 1962).
We applied the hierarchical clustering method to stresses detected from the mesoscale structures in the Tanabe Group, SW Japan. The Tanabe Group is the middle Miocene paleoforearc basin fill, exposed in the southwest of the Kii Peninsula. A total of 1148 clastic dikes and 303 calcite veins have been analyzed by the mixed Bingham distribution method (Yamaji and Sato, 2011), and 327 faults have been analyzed by the Hough transform method (Sato, 2006). As the result of analyses, 21 stresses have been detected. The hierarchical clustering with group average method gave five clusters of stresses. In this clustering analysis, two clusters were distinguished when their angular stress distance is larger than 59.26° (Yamaji and Sato, 2019). Two of the clusters consist solely of the stresses detected in the southern sites. Plural different clusters detected in the same area suggest a temporal stress change. Another cluster comprises the stresses detected in the northern and the central sites. These three clusters appear to reflect a spatial change of the paleostress. Another cluster is composed of the stresses detected from clastic dikes. Clastic dikes observed in the Tanabe Group are considered to have intruded at the time during or soon after deposition (Miyata et al., 2009; Nakaya and Hamada, 2009). This cluster, therefore, shows the stress at the time of middle Miocene. The other cluster include only two stresses, and angular stress distance between them is near 59.26° of the threshold value. This cluster may not reflect the tectonic stress. In this way, hierarchical clustering of the detected stresses has indicated a spatio-temporal change of paleostress.
References
Miyata, Y., Miyake, K. and Tanaka, K., 2009, The Journal of the Geological Society of Japan, 115, 470-482.
Nakaya, S. and Hamada, Y., 2009, Journal of Geography, 118, 472-491.
Sato, K., 2006, Tectonophysics, 421, 319-330.
Sokal, R.R. and Rohlf, F.J., 1962, Taxon, 11, 33-40.
Yamaji, A. and Sato, K., 2006, Geophysical Journal International, 167, 933-942.
Yamaji, A. and Sato, K., 2011, Journal of Structural Geology, 33,1148-1157.
Yamaji, A. and Sato, K., 2019, Journal of Structural Geology, 125, 296-310.
The hierarchical clustering method needs to define the differences between elements. In this study, angular stress distance (Yamaji and Sato, 2006) is used as the measure of difference between two reduced stress tensors. Once the tensors are grouped to form a cluster, we also need to define the distances between clusters. There are several methods to define the distances between clusters. Among them the group average method was found to be optimal through a Monte Carlo calculation to compare the methods with evaluations of the cophenetic correlation coefficients (Sokal and Rohlf, 1962).
We applied the hierarchical clustering method to stresses detected from the mesoscale structures in the Tanabe Group, SW Japan. The Tanabe Group is the middle Miocene paleoforearc basin fill, exposed in the southwest of the Kii Peninsula. A total of 1148 clastic dikes and 303 calcite veins have been analyzed by the mixed Bingham distribution method (Yamaji and Sato, 2011), and 327 faults have been analyzed by the Hough transform method (Sato, 2006). As the result of analyses, 21 stresses have been detected. The hierarchical clustering with group average method gave five clusters of stresses. In this clustering analysis, two clusters were distinguished when their angular stress distance is larger than 59.26° (Yamaji and Sato, 2019). Two of the clusters consist solely of the stresses detected in the southern sites. Plural different clusters detected in the same area suggest a temporal stress change. Another cluster comprises the stresses detected in the northern and the central sites. These three clusters appear to reflect a spatial change of the paleostress. Another cluster is composed of the stresses detected from clastic dikes. Clastic dikes observed in the Tanabe Group are considered to have intruded at the time during or soon after deposition (Miyata et al., 2009; Nakaya and Hamada, 2009). This cluster, therefore, shows the stress at the time of middle Miocene. The other cluster include only two stresses, and angular stress distance between them is near 59.26° of the threshold value. This cluster may not reflect the tectonic stress. In this way, hierarchical clustering of the detected stresses has indicated a spatio-temporal change of paleostress.
References
Miyata, Y., Miyake, K. and Tanaka, K., 2009, The Journal of the Geological Society of Japan, 115, 470-482.
Nakaya, S. and Hamada, Y., 2009, Journal of Geography, 118, 472-491.
Sato, K., 2006, Tectonophysics, 421, 319-330.
Sokal, R.R. and Rohlf, F.J., 1962, Taxon, 11, 33-40.
Yamaji, A. and Sato, K., 2006, Geophysical Journal International, 167, 933-942.
Yamaji, A. and Sato, K., 2011, Journal of Structural Geology, 33,1148-1157.
Yamaji, A. and Sato, K., 2019, Journal of Structural Geology, 125, 296-310.