Consistent estimation of strain-rate fields from GNSS velocity data using basis function expansion with ABIC

Abstract Present day crustal displacement rates can be accurately observed at stations of global navigation satellite system (GNSS), and deformation has been investigated by estimating strain-rate fields from discrete GNSS data. For this purpose, a modified least-square inversion method was proposed Shen et al. (J Geophys Res 101:27957–27980, 1996). This offers simple formulation for simultaneously smooth velocity data, it contributed to clarify in many regions all over the world. However, we notice three theoretical points examined when apply method: mathematical inconsistency between estimated fields, difficulty objectively determining optimal value hyperparameter that controls smoothness, inappropriate estimation uncertainty. In study, propose basis function expansion with Akaike’s Bayesian information criterion (ABIC), which overcomes above difficulties. Application two methods data Japan reveals is generally insignificant, but could clear sparser observation such as islet areas. The ABIC shows significantly better performance than terms trade-off curve residual fitting roughness field. field clearly exhibits low zone forearc southern Tohoku district central Japan. We also find Ou Backbone Range several contractive spots around active volcanoes these locations well correspond subsidence areas detected InSAR after 2011 Tohoku-oki earthquake. Thus, would serve an effective tool