A new approach considering temporal correlations for GPS campaign time series

GPS campaign-mode surveys are periodically collected measurements and their time series has a considerable percentage of data gaps unlike continuous time series. Studying error characteristics of a time series is imperative to compute reliable parameter uncertainties. The power-law process can best describe the background noise for a GPS continuous time series and may be introduced into the analysis through well-known methods. However, the power-law process cannot be applied successfully over GPS campaign time series due to the constraints mentioned above. Here we demonstrate a new approach enabling one to project the stochastic properties of campaign time series into the stochastic domain of the permanent stations of International GNSS Service (IGS) network. The stochastic domain, the combination of white noise (WN) and flicker noise (FN), was obtained from the power spectrum of a continuous time series consisting of truncated daily RINEX observations. We implemented it in the Python3 environment as an open-source package called GPS/GNSS campaign time series analysis (GCTS v1.0). The analysis showed that the velocity uncertainties may be, on average, underestimated by a factor of 2 when assuming the WN-only noise model using campaign data from the UNAVCO data archive collected in San Bernardino and its vicinity. Moreover, to reveal the progress of the new approach, we modelled buried screw dislocations of the San Jacinto, the San Andreas, and parallel faults in their vicinity in elastic half-space. When using the new approach with the combination of WN and FN instead of the WN-only model, we achieved a significant improvement of 15% on average in the chi-square value. Our outcomes showed that the noise process should be considered even for campaign time series. The proposed approach facilitates the analysis of GPS campaign time series even if they include considerable data gaps.