FIG Working Week 2019 (FIG2019), Amsterdam, Netherlands, 10 May 2020, pp.1-14
The overall trend rate, i.e. one-dimensional velocity in a GNSS time-series of a local coordinate component is one of the most important parameters for investigating deformed bodies, such as tectonic regions, landslides, mining fields and engineering buildings. The standard deviation (v) of this trend has been studied in many papers to figure out how precise trend rate can be determined. This standard deviation depends on i) the length of time-series (time-span), ii) the observation frequency, iii) the noise structure in the GNSS data, and iv) the type of the regression model if the time-span is shorter than about 2.5 years. Most of these studies, however, consider that only the white noise exists in the data. It has been reported that a GNSS time-series includes not only flicker noise with an amplitude which is 1.5 and 4.0 times bigger than the white noise, but also random walk noise whose amplitude changes depending on the monument type and local effects, as well as some other power-law noises occurring due to the different geophysical processes. Existence of these colored noises means that the time-series is temporally correlated. Hence, omitting them in the analysis of the GNSS time-series leads to very optimistic standard deviation for the trend rate and so, incorrect statistical decisions. This contribution aims to discuss the minimum detectable overall trend rate (MDTR) with the 80% power of the test for one coordinate component in GNSS time-series. While the time-span is longer than one year for daily GNSS data, the MDTR can be given as about 2.8v from the power function of the non-central 2-distribution. This MDTR is studied in GNSS time-series consisting of trend + annual and semi-annual signals for different noise models (different flicker noise and random walk noise models as functions of observing session duration dependent-RMS repeatability), different time-spans between 1 year to 10 years as well as daily and monthly observation frequencies. According to the numerical results, if the flicker noise is dominant over the white noise, it is expected to have about 3-4 times bigger MDTR whereas random walk noise affects badly the trend rate more than the flicker noise does. The MDTR from the 24-hours-daily GNSS time-series with the common noise structure may be less than 1 mm/year if the time-span is longer than three years. This rate increases if the colored noises increase as well. The longer observing session results in smaller MDTR in any noise models as expected. Interestingly, daily and monthly GNSS data provides similar MDTRs if the time-span is more than about 4 years.