Abstract
Present day crustal displacement rates can be accurately observed at stations of global navigation satellite system (GNSS), and crustal deformation has been investigated by estimating strain-rate fields from discrete GNSS data. For this purpose, a modified least-square inversion method was proposed by Shen et al. (J Geophys Res 101:27957–27980, 1996). This method offers a simple formulation for simultaneously estimating smooth velocity and strain-rate fields from GNSS data, and it has contributed to clarify crustal deformation fields in many regions all over the world. However, we notice three theoretical points to be examined when we apply the method: mathematical inconsistency between estimated velocity and strain-rate fields, difficulty in objectively determining the optimal value of a hyperparameter that controls smoothness, and inappropriate estimation of uncertainty. In this study, we propose a method of basis function expansion with Akaike’s Bayesian information criterion (ABIC), which overcomes the above difficulties. Application of the two methods to GNSS data in Japan reveals that the inconsistency in the method of Shen et al. is generally insignificant, but could be clear in regions with sparser observation stations such as in islet areas. The method of basis function expansion with ABIC shows a significantly better performance than the method of Shen et al. in terms of the trade-off curve between the residual of fitting and the roughness of velocity field. The estimated strain-rate field with the basis function expansion clearly exhibits a low strain-rate zone in the forearc from the southern Tohoku district to central Japan. We also find that the Ou Backbone Range has several contractive spots around active volcanoes and that these locations well correspond to the subsidence areas detected by InSAR after the 2011 Tohoku-oki earthquake. Thus, the method of basis function expansion with ABIC would serve as an effective tool for estimating strain-rate fields from GNSS data.
Highlights
Earth’s crust is deformed due to relative motions of tectonic plates
Classical methods divide a region into a triangulated network to estimate a mean strain rate within each cell using triangulation survey data (Frank 1966; Prescott 1976) as well as trilateration survey and global navigation satellite system (GNSS) data (Feigl et al 1990)
In this study, we propose a method of basis function expansion to estimate a velocity field from spatially discrete geodetic data, in which a velocity field is expressed by a linear combination of basis functions
Summary
Earth’s crust is deformed due to relative motions of tectonic plates. In particular, we observe significant crustal deformation in plate convergence zones. Classical methods divide a region into a triangulated network to estimate a mean strain rate within each cell using triangulation survey data (Frank 1966; Prescott 1976) as well as trilateration survey and GNSS data (Feigl et al 1990). Continuous interpolation methods were developed (e.g., Haines and Holt 1993; Shen et al 1996) These methods impose a certain degree of smoothness on strain-rate fields to stabilize the estimation from discrete velocity data without knowledge on major faults or block motions. They are still in progress using advanced mathematical tools. Tape et al (2009) applied spherical wavelets to estimate velocity and strain-rate fields, which enables to separate crustal deformation into different length scales. Sandwell and Wessel (2016) developed an interpolation method of discrete 2-D vector data on the basis of Green’s functions of an elastic body, which ensures the coupling of the two components
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