This study investigates the transient deformation signals associated with the Ludian M6.8 earthquake, which occurred on June 22, 2014, in southwestern China, using Global Navigation Satellite System (GNSS) data. Within the framework of the Kalman filter, the study employs a First-Order Gauss-Markov (FOGM) model to construct and isolate transient deformation signals, extracting the FOGM time series. Principal Component Analysis (PCA) is then applied to decompose the extracted time series and analyze the spatiotemporal evolution of the top two Principal Components (PCs) of the East-West (EW) and North-South (NS) components, revealing their correlation with the Ludian earthquake. Furthermore, a quantitative analysis of the spatial response characteristics of the second Principal Component (PC2) of the EW component and the first Principal Component (PC1) of the NS component is conducted to characterize the spatial evolution pattern of transient deformation. Finally, the spatial distribution of transient deformation signals is compared with the known co-seismic rupture characteristics, providing further evidence that the extracted signals represent real post-seismic deformation rather than noise. The key findings of this study are as follows: 1. The PC2 of the EW component and the PC1 of the NS component primarily represent post-seismic transient deformation signals associated with the Ludian earthquake. The post-seismic deformation evolution exhibits two distinct phases: a sustained deformation phase from the earthquake occurrence to early 2016 and a recovery phase starting from early 2016, reflecting the time-dependent characteristics of the post-seismic relaxation process. 2. In addition to the well-known linear trend and periodic components, the GNSS displacement time series may also contain non-linear periodic components, suggesting that GNSS data are influenced by a combination of crustal dynamics, surface environmental changes, and anthropogenic factors. 3. The integration of Kalman filtering and PCA-based dimensionality reduction analysis effectively isolates transient deformation signals and nonlinear periodic signals from complex background noise, enhancing the interpretability of GNSS data. This approach provides a highly efficient data processing method for analyzing earthquake-induced deformation.

Transient deformation, such as post-seismic slip, slow slip and pre-seismic slip events, is a limited low-frequency deformation that can last for hours to months, in contrast to a sudden slip on a fault caused by earthquakes. Continuous Global Positioning System (CGPS), one of the most common geodetic techniques for continuously monitoring crustal deformation, is capable of capturing transient deformation signals. A critical point in characterizing transient deformation signals is the development of extracting and deciphering transient deformation signals from a huge and messy data set of position time series. Principal Component Analysis (PCA), one of the data-driven methods, has been employed to derive transient deformation signals from position time series combing with Kalman filtering. Independent Component Analysis (ICA) performs well in recovering and separating the sources of observed data, however, it is rarely used in extracting transient deformation signals. We aim to decompose the transient deformation signals from the daily GPS observation deployed in Akutan Island from 2007 to 2015 with the ICA method and obtain the spatiotemporal responses to the source signals of transient deformation. Our results indicate that ICA method can also characterize effectively transient deformation signals spatially and temporally. Additionally, the independent relationship between sources obtained by ICA allows for flexibility in linearly combining different sources.