5:15 PM - 6:45 PM
[STT38-P02] Objective clustering of GNSS velocities based on parallel translation and Euler-vector estimation for the identification of crustal blocks
Keywords:GNSS, clustering, differential geometry, crustal brocks
Dense Global Navigation Satellite System (GNSS) observation data have provided clearer pictures of plate motions. For instance, Thatcher (2007, 2009) identified more crustal blocks than previously known using GNSS observation data[k1] . Identifying these crustal blocks is important and has been utilized in earthquake disaster prevention assessments (e.g., Syu et al., 2016). As is widely recognized, the selection of crustal blocks heavily impacts on the results of block fault models (e.g., McCaffrey, 2007; Wallace et al., 2007; Floyd et al., 2010). Recently, objective methods for identifying crustal block structures have been proposed. Simpson et al. (2012), Savage and Simpson (2013a, 2013b), and Takahashi et al. (2018) used hierarchical clustering in the GNSS velocity vector space to identify crustal blocks in the San Francisco Bay, Mojave Desert, and Taiwan, respectively. Savage and Wells (2015), Savage (2018), and Takahashi and Hashimoto (2022) utilized non-hierarchical clustering with estimating Euler vectors to identify crustal blocks in the Pacific Northwest, Southwest Japan, and New Zealand, respectively. Clustering in the velocity vector space does not necessarily take rigid motions into account. On the contrary, clustering with Euler vectors is challenging to arrange hierarchically, and does not always consider the adjacency of observation sites. This study aims to address these issues by integrating both approaches and proposes a new identification method.
The proposed method utilizes the rotational motion by Euler vectors and the parallel translation of tangent vectors. First, using the GNSS position coordinates of two points and their velocity vectors, we estimate the Euler vector. On the bases of fit of the Euler vector estimation, we define the dissimilarity between the velocity vectors at two points. On the other hand, the differential geometry introduces “parallel translation” that maps a tangent vector at a point to a tangent vector at a different point. This allows us to define the dissimilarity between the velocity vectors of geographically separated points. Here, the concept of "parallel translation" enables us to explain the clustering in the velocity vector space proposed in the previous studies. By using the sum of the two dissimilarities, we propose hierarchical clustering of GNSS velocity vectors that considers both parallel translation and rigid motion.
We checked our method by using the ITRF2008 plate model and the public data provided by Altamimi et al. (2012). Using the proposed hierarchical clustering method, we confirmed that the known plates are reconstructed without any reference other than velocity vectors and positional information. The reconstructed plates can be broadly categorized into North America and a group comprising Eurasia and Australia. Notably, within the latter group, several sub-blocks (Eurasia, India, Australia) were identified, providing an intuitive representation of the similarity in plate motions.
The proposed method utilizes the rotational motion by Euler vectors and the parallel translation of tangent vectors. First, using the GNSS position coordinates of two points and their velocity vectors, we estimate the Euler vector. On the bases of fit of the Euler vector estimation, we define the dissimilarity between the velocity vectors at two points. On the other hand, the differential geometry introduces “parallel translation” that maps a tangent vector at a point to a tangent vector at a different point. This allows us to define the dissimilarity between the velocity vectors of geographically separated points. Here, the concept of "parallel translation" enables us to explain the clustering in the velocity vector space proposed in the previous studies. By using the sum of the two dissimilarities, we propose hierarchical clustering of GNSS velocity vectors that considers both parallel translation and rigid motion.
We checked our method by using the ITRF2008 plate model and the public data provided by Altamimi et al. (2012). Using the proposed hierarchical clustering method, we confirmed that the known plates are reconstructed without any reference other than velocity vectors and positional information. The reconstructed plates can be broadly categorized into North America and a group comprising Eurasia and Australia. Notably, within the latter group, several sub-blocks (Eurasia, India, Australia) were identified, providing an intuitive representation of the similarity in plate motions.