5:15 PM - 6:45 PM
[SCG48-P04] Evaluation of vertical motion off Tohoku considering uncertainty in GNSS-Acoustic positioning
Keywords:GNSS-Acoustic observation, Tohoku-oki, Up-down crustal deformation, Postseismic deformation
GNSS-Acoustic (GNSS-A) observation is a seafloor geodetic technique, and accuracy of its vertical motion for each campaign is typically ~5–10 cm (e.g., Sato et al., 2013), which is worse than that of horizontal motions. Since the horizontal motions are more evident than the vertical motion in general, the vertical component has not been well employed in the previous GNSS-A studies. However, significant vertical displacements due to co- and post-seismic deformations of a huge interplate earthquake have been detected by GNSS-A observations (e.g., the 2011 Tohoku earthquake; Kido et al., 2011; Watanabe et al., 2021); thus, it would be important to appropriately evaluate uncertainty of such vertical motions to discuss mechanisms of the earthquake.
The major error factors of the vertical displacement are following: 1) deterioration of the positioning precision due to geometric insufficiency of sea-surface ranging points, 2) systematic modeling error depending on complexity of an underwater sound speed structure (SSS), 3) Systematic bias of a sea-surface transducer position, and 4) kinematic GNSS positioning error. Estimation error due to the factor 1 (Error-1) is considered to be shown in the model covariance matrix. In contrast, Errors-2–4 are difficult to be assessed because they are systematic modeling biases. This study firstly evaluated Error-2; then, we assumed Errors-3–4 can be expressed by multiples of Error 1 and optimized the multiplier. Finally, we evaluated uncertainty of vertical array displacement rates considering these all factors and discussed vertical deformation off Tohoku after the 2011 Tohoku earthquake.
To calculate travel times in the acoustic ranging, initial sound speed profile (SSP) is required; thus, a measured SSP or a model SSP obtained from JCOPE2M (Miyazawa et al., 2017; 2091) have been employed. Regarding Error-2, we assessed positioning errors due to uncertainty of the initial SSP. We employed actual SSP data of XBT, XCTD and CTD measurements at G01–G25 sites off Tohoku and Nemuro since Sep. 2012 and then obtained a residual dataset between the actual SSPs during each campaign (~0.5–1 day) and another residual dataset between the actual SSPs and the model SSPs of JCOPE2M. We contrived an algorithm to produce a bunch of initial SSPs based on each residual dataset and evaluated the vertical estimation errors by a Monte Carlo method. Note that a static GNSS-A positioning method in the SeaGap software (Tomita & Kido, 2023) was performed to estimate a vertical array displacement. As a result, we found that the estimation error due to temporal fluctuation of SSS was ~2 cm, and that using JCOPE2M was ~6 cm.
Next, we assumed that the estimation error at each campaign was sum of a multiple of Error-1 and Error-2 and optimized the multiplier by a MCMC method that the estimation error was comparable with the dispersion of the vertical displacements from a weighted regression line. We then obtained the optimal value of 6.4 as the multiplier for G01–G20.
Error-3 is a bias peculiar to each sea-surface platform; therefore, it is not necessarily shown in the dispersion of the vertical array displacements from a weighted regression line. To maximally consider the influence of Error-3, we randomly added a bias peculiar to each sea-surface platform and evaluated the uncertainty of a vertical array displacement rate by a Monte Carlo method.
The vertical displacement rates at G01–G20 off Tohoku generally show uplift near the trench and subsidence on the upper plate apart from the trench. This tendency is consistent with viscoelastic relaxation model considering interplate locking (Wang et al., 2018; Luo et al., 2021). However, significant vertical displacement rates beyond the uncertainty were found only at three sites (G01, G04, and G14). In the presentation, we would like to discuss the vertical deformation off Tohoku in detail considering the uncertainty.
The major error factors of the vertical displacement are following: 1) deterioration of the positioning precision due to geometric insufficiency of sea-surface ranging points, 2) systematic modeling error depending on complexity of an underwater sound speed structure (SSS), 3) Systematic bias of a sea-surface transducer position, and 4) kinematic GNSS positioning error. Estimation error due to the factor 1 (Error-1) is considered to be shown in the model covariance matrix. In contrast, Errors-2–4 are difficult to be assessed because they are systematic modeling biases. This study firstly evaluated Error-2; then, we assumed Errors-3–4 can be expressed by multiples of Error 1 and optimized the multiplier. Finally, we evaluated uncertainty of vertical array displacement rates considering these all factors and discussed vertical deformation off Tohoku after the 2011 Tohoku earthquake.
To calculate travel times in the acoustic ranging, initial sound speed profile (SSP) is required; thus, a measured SSP or a model SSP obtained from JCOPE2M (Miyazawa et al., 2017; 2091) have been employed. Regarding Error-2, we assessed positioning errors due to uncertainty of the initial SSP. We employed actual SSP data of XBT, XCTD and CTD measurements at G01–G25 sites off Tohoku and Nemuro since Sep. 2012 and then obtained a residual dataset between the actual SSPs during each campaign (~0.5–1 day) and another residual dataset between the actual SSPs and the model SSPs of JCOPE2M. We contrived an algorithm to produce a bunch of initial SSPs based on each residual dataset and evaluated the vertical estimation errors by a Monte Carlo method. Note that a static GNSS-A positioning method in the SeaGap software (Tomita & Kido, 2023) was performed to estimate a vertical array displacement. As a result, we found that the estimation error due to temporal fluctuation of SSS was ~2 cm, and that using JCOPE2M was ~6 cm.
Next, we assumed that the estimation error at each campaign was sum of a multiple of Error-1 and Error-2 and optimized the multiplier by a MCMC method that the estimation error was comparable with the dispersion of the vertical displacements from a weighted regression line. We then obtained the optimal value of 6.4 as the multiplier for G01–G20.
Error-3 is a bias peculiar to each sea-surface platform; therefore, it is not necessarily shown in the dispersion of the vertical array displacements from a weighted regression line. To maximally consider the influence of Error-3, we randomly added a bias peculiar to each sea-surface platform and evaluated the uncertainty of a vertical array displacement rate by a Monte Carlo method.
The vertical displacement rates at G01–G20 off Tohoku generally show uplift near the trench and subsidence on the upper plate apart from the trench. This tendency is consistent with viscoelastic relaxation model considering interplate locking (Wang et al., 2018; Luo et al., 2021). However, significant vertical displacement rates beyond the uncertainty were found only at three sites (G01, G04, and G14). In the presentation, we would like to discuss the vertical deformation off Tohoku in detail considering the uncertainty.