Evaluation of Temporally Correlated Noise in Global Navigation Satellite System Time Series: Geodetic Monument Performance

Estimates of background noise of Global Positioning System-derived timeseries of positions for 740 sites in the western United States are examined. These data consist of daily epochs of three components of displacements that are at least 9.75years long within the interval between 2000 and 2018. We find that these timeseries have significant temporal correlations that could be represented as a combination of white, flicker, random-walk, and band-pass filtered noise. From this noise model, two other metrics are computed: the root-mean-square of seasonal noise, that is, the integrated power spectrum between 0.5 and 2cycles per year, and the standard error in position rate for a 10-year-long timeseries. These two metrics are used to evaluate potential correlations with different geographic regions and with different methods of construction of monuments used to attach the Global Positioning System antenna to the Earth's surface. The sites with the lowest noise, both in terms of rate error and seasonal root-mean-square, are located in semiarid regions east of the rain shadow provided by the Cascade and Sierra Nevada mountain ranges. In addition, according to statistical rank tests, monuments known as drilled-braced monuments perform 30%to 50% better than other monument types (buildings, boreholes, piers, etc.) in terms of having smaller rate errors and lower seasonal noise. Plain Language Summary Global Positioning System receivers are distributed across the western United States and measure displacement rates quantifying the motions from plate tectonics, earthquake faulting, and volcanoes. The quality of these measurements is, in part, determined by how well the receiver's antenna is fastened to the Earth's surface through its monument. The motion of the monument not only responds to the tectonic motions but it also is subject to random motions from the environment adjacent to the monument. The ideal monument would be coupled into the Earth's surface well below the environmentally unstable surface layer. Monument construction techniques range from the inexpensive, $100 installation to the $10,000 installation for a drilled-braced monument (DBM), exceeding the cost of the receiver. To help answer whether the more expensive DBM performs better than other monuments, we used a statistical method that measures the amount of temporally correlated noise, which we attribute to be localized, random motions of the monument. With statistical ranking from 740 sites, we determined, with >99.9% confidence, that measurements from sites with DBMs are more precise than from other sites. However, comparisons of the rate errors indicate that DBMs perform only 30% to 50% better than the other monument types.