The Global Positioning System (GPS) derived bedrock displacements respond to multiple geophysical effects, ranging from surface elastic loads to tectonic sources or viscoelastic uplifts stemming from Earth’s viscous mantle. In this study, the GPS‐inferred vertical crustal velocities are rigorously estimated in mainland China. We integrate the GPS vertical velocity field with Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On (GFO) data, adopting an empirical Spatial Structure Function (SSF), to image tectonic deformation in mainland China with respect to the International Terrestrial Reference Frame (ITRF) 2014. We present four profiles across China, which indicate that our new robust results are superior to kriging. Furthermore, we use the GRACE/GFO products to account for elastic deformation due to surface mass changes to isolate tectonic deformation signals at GPS sites within mainland China from 2002 to 2019. By integrating GPS and GRACE/GFO measurements, our results reveal the long‐term spatial patterns of vertical tectonic motion in different blocks in mainland China. We conclude that significant steep velocity gradients occur at tectonic block boundaries that are attributable to locking and elastic strain accumulation on active block boundary faults.

The inner core translational mode (₁S₁), known as the Slichter triplet, can provide important information particularly on the Earth's inner core and its dynamics. A time domain spectral analysis method, the optimal sequence estimation (OSE), is devised and applied to search for the Slichter modes. Applications of the OSE and the multistation experiment (MSE) technique for detection of the singlets of ₃S₁ and ₂S₁ show that both OSE and MSE can isolate their singlets, but OSE provides a higher signal‐to‐noise ratio. OSE also can completely isolate the modes ₀S₂ and ₁S₂. Using two superconducting gravimeter data sets from nine Global Geodynamic Project stations before and after the 2004 Sumatra earthquake, we search for the possible Slichter triplet via OSE and provide a simple validation using the product spectrum. We set two preliminary criteria in order to identify possible signals; results show three signals as candidates for the Slichter triplet, more likely in the data after the 2004 Sumatra earthquake. While choosing the most reasonable criteria needs further studies, we emphasize here the effectiveness of the OSE in searching for the Slichter modes rather than claiming actual detections.

The present‐day deformation of the Tianshan Mountain range is largely resulting from the collision between India and the Eurasian plate, but the mechanism causing its uplift remains controversial. In this study, we present the contemporary tectonic and geodynamic processes resulting in the growth of the Tianshan Mountain range as revealed by integrating Global Positioning System (GPS) and Gravity Recovery and Climate Experiment (GRACE) measurements during 2010–2016. The average ground uplift rate is 0.72 ± 0.12 mm/year, of which 0.39 mm/year is attributed to elastic effects of glacier melting. The residual average tectonic uplift rate of 0.33 ± 0.12 mm/year closely matches the crustal thickening rate (0.33 ± 0.03 mm/year), indicating that horizontal compression plays an essential role in Tianshan orogeny. We also find the Lake Issyk‐Kul region is converging and subsiding, which can be explained by a regional crust folding model. The interaction of adjacent rigid blocks in the Tianshan and surrounding areas is also manifested by the crustal shortening derived from GPS horizontal velocities. This study provides new geodetic results and a new model in current orogenic movement in the Tianshan Mountain range and highlights its complexity.

The AR‐z spectrum devised in Ding and Chao (2015a) for analyzing harmonic signals (an extension of the frequency domain autoregressive AR algorithm developed by Chao and Gilbert (1980) based on Prony's method) proves to have significantly higher sensitivity and spectral resolution than the Fourier and maximum‐entropy spectra, especially when the signal‐to‐noise ratio is low. As such, it can be prone to random fluctuations in the form of spurious variances of the noise spectrum. Here we develop a stabilized AR‐z spectrum taking advantage of a Monte Carlo noise‐assisted bootstrap scheme, and demonstrate its effectiveness in obtaining more robust spectral estimates for single record. We apply the stabilized AR‐z spectrum, and compare it with the Fourier and maximum‐entropy spectra, to a number of global geophysical observables of the Earth, including the elastic free oscillations, length of day variation (ΔLOD), dynamic oblateness (ΔJ₂), polar motion, Earth's nutation, and global mean sea level variation. We report the findings about hitherto unresolved fine structures, including those for the Mf and Mm tidal clusters in the ΔLOD, ΔJ₂, polar motion and the Earth's nutation, and the modal splittings of the Earth's free oscillations. Furthermore, a number of long‐period signals of certain nominal periodicities are detected (or confirmed) in the stabilized AR‐z spectra, including the 6‐year signals in ΔLOD, the 18.6‐year signals expected in ΔLOD and ΔJ₂, and certain quasiperiodic interannual to decadal periodicities whose origins have yet to be identified. Overall, the stabilized AR‐z spectrum demonstrates a momentous performance in the quest for numerical harmonic analysis methods.