2:30 PM - 2:45 PM
[STT40-03] Estimation of Horizontal Velocity Fields from Euler Vector Inversion Using Gaussian Processes
Estimation of continuous horizontal velocity and strain-rate fields from discrete geodetic data is fundamental to understand crustal deformation. For this purpose, various interpolation methods have been proposed. Many methods interpolate 2-D velocity vectors in a relatively small area under a flat Earth approximation (Shen et al. 1996; Sandwell & Wessel 2016; Okazaki et al. 2021). Several methods properly take into account a spherical Earth: interpolation of 2-D velocity on a sphere (Tape et al. 2009); modeling of angular velocity (Euler vector) to obtain velocity fields (Ward 1998; Kreemer et al. 2018).
Following the last approach, this study formulates an inversion problem of angular velocity from velocity data. The inversion problem is solved by a vector-valued Gaussian process. To apply a Gaussian process, the covariance function of velocity is derived from that of angular velocity. Because a 3-D angular velocity is modeled from a 2-D horizontal velocity, the 3N×3N gram matrix of N data has rank 2N . This rank deficiency is a characteristic of the Euler vector inversion.
This method is applied to GNSS data in Japan during 2006–2009 (Okazaki et al. 2021). The results show a reasonable velocity field with small residuals. Angular velocity rapidly changes around Shikoku and the Bungo channel, which would correspond to a strong coupling between the Eurasian and Philippine sea plates. The estimated strain-rate fields show a large-scale variation, while lack a small-scale variation at volcanos found in Okazaki et al. (2021). Additionally, the estimated strain rate is higher along Fukui–Nagoya, which may be a plate boundary between the Eurasia and North American plates, than along Fukui-Kobe, which is a portion of the Niigata–Kobe tectonic zone. These results imply that the Euler vector inversion method mainly extracts crustal deformation caused by plate interactions.
Following the last approach, this study formulates an inversion problem of angular velocity from velocity data. The inversion problem is solved by a vector-valued Gaussian process. To apply a Gaussian process, the covariance function of velocity is derived from that of angular velocity. Because a 3-D angular velocity is modeled from a 2-D horizontal velocity, the 3N×3N gram matrix of N data has rank 2N . This rank deficiency is a characteristic of the Euler vector inversion.
This method is applied to GNSS data in Japan during 2006–2009 (Okazaki et al. 2021). The results show a reasonable velocity field with small residuals. Angular velocity rapidly changes around Shikoku and the Bungo channel, which would correspond to a strong coupling between the Eurasian and Philippine sea plates. The estimated strain-rate fields show a large-scale variation, while lack a small-scale variation at volcanos found in Okazaki et al. (2021). Additionally, the estimated strain rate is higher along Fukui–Nagoya, which may be a plate boundary between the Eurasia and North American plates, than along Fukui-Kobe, which is a portion of the Niigata–Kobe tectonic zone. These results imply that the Euler vector inversion method mainly extracts crustal deformation caused by plate interactions.