GNSS time series analysis of the crustal movement network of China: Detecting the optimal order of the polynomial term and its effect on the deterministic model

GNSS time series analysis provides an effective method for research on the earth's surface deformation, and it can be divided into two parts, deterministic models and stochastic models. The former part can be achieved by several parameters, such as polynomial terms, periodic terms, offsets, and post-seismic models. The latter contains some stochastic noises, which can be affected by detecting the former parameters. If there are not enough parameters assumed, modeling errors will occur and adversely affect the analysis results. In this study, we propose a processing strategy in which the commonly-used 1-order of the polynomial term can be replaced with different orders for better fitting GNSS time series of the Crustal Movement Network of China (CMONOC) stations. Initially, we use the Bayesian Information Criterion (BIC) to identify the best order within the range of 1–4 during the fitting process using the white noise plus power-law noise (WN + PL) model. Then, we compare the 1-order and the optimal order on the effect of deterministic models in GNSS time series, including the velocity and its uncertainty, amplitudes, and initial phases of the annual signals. The results indicate that the first-order polynomial in the GNSS time series is not the primary factor. The root mean square (RMS) reduction rates of almost all station components are positive, which means the new fitting of optimal-order polynomial helps to reduce the RMS of residual series. Most stations maintain the velocity difference (VD) within ±1 mm/yr, with percentages of 85.6%, 81.9% and 63.4% in the North, East, and Up components, respectively. As for annual signals, the numbers of amplitude difference (AD) remained at ±0.2 mm are 242, 239, and 200 in three components, accounting for 99.6%, 98.4%, and 82.3%, respectively. This finding reminds us that the detection of the optimal-order polynomial is necessary when we aim to acquire an accurate understanding of the crustal movement features.