A novel GNSS imaging method through velocity uncertainty based on Gaussian process regression and its evaluation

Global Navigation Satellite System (GNSS) imaging method (GIM) has been successfully applied to global regions to investigate vertical land motion (VLM) of the Earth's surface. GNSS images derived from conventional GIM method may present fragmented patches and encounter problems caused by excessive smoothing of velocity peaks, leading to difficulty in short-wavelength deformation detection and improper geophysical interpretation. Therefore, we propose a novel GNSS imaging method based on Gaussian process regression with velocity uncertainty considered (GPR-VU). Gaussian processing regression is introduced to describe the spatial relationship between neighboring site pairs as a priori weights and then reweight velocities by known station uncertainties, converting the discrete velocity field to a continuous one. The GPR-VU method is applied to reconstruct VLM images in the southwestern United States and the eastern Qinghai-Xizang Plateau, China, using the GNSS position time series in vertical direction. Compared to the traditional GIM method, the root-mean-square (RMS) and overall accuracy of the confusion matrix of the GPR-VU method increase by 5.0 % and 14.0 % from the 1° × 1° checkerboard test in the southwestern United States. Similarly, the RMS and overall accuracy increase by 33.7 % and 15.8 % from the 6° × 6° checkerboard test in the eastern Qinghai-Xizang Plateau. These checkerboard tests validate the capability to effectively capture the spatiotemporal variations characteristics of VLM and show that this algorithm outperforms the sparsely distributed network in the Qinghai-Xizang Plateau. The images from the GPR-VU method using real data in both regions show significant subsidence around Lassen Volcanic in northern California within a 30 km radius, slight uplift in the northern Sichuan Basin, and subsidence in its central and southern sections. These results further qualitatively illustrate consistency with previous findings. The GPR-VU method outperforms in diminishing the effect by fragmented patches, excessive smoothing of velocity peaks, and detecting potential short-wavelength deformations.