SCEC Award Number 16125 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title Network Based Estimates of Noise in Southern California GPS Time Series
Investigator(s)
Name Organization
Paul Segall Stanford University
Other Participants Ksenia Dmitrieva
SCEC Priorities 1d, 1e, 5b SCEC Groups SDOT, Transient Detection, Geodesy
Report Due Date 03/15/2017 Date Report Submitted 07/11/2017
Project Abstract
 Understanding errors in GPS time series is crucial for several SCEC efforts,
including the Community Geodetic Model (CGM), as well as slip-rate estimates based on geodetic measurements.
GPS error estimates are typically based on maximum likelihood estimation (MLE) of individual detrended
time series and thus; a) ignore spatial coherence in the data, and b) assume all trends are true signal.
Dmitrieva et al [2015] developed a Network Noise Estimator
that analyzes all data from a regional network simultaneously, and enforces that the data be the
sum of spatially coherent signal and various noise components. Dmitrieva et al [2016] examined the
effect of detrending on noise estimates. The commonly adopted model of random walk (RW),
flicker noise (FN), and white noise (WN) is the most severely affected by de-trending, with estimates of low amplitude RW most
severely biased.

We analyzed data from 58 stations on stable North America using the Network Noise Estimator to determine robust and conservative estimates of random walk (RW), flicker noise (FN), and white noise (WN). Our analysis suggests that the most stable deep drilled braced monuments have velocity uncertainties of 0.15-0.25 mm/yr given 10 years of data, considerably higher than previous estimates. Due to time limitations we were unable to extend the analysis to southern California stations.
Intellectual Merit We analyzed data from 58 stations on stable North America using the NNE, under the assumption that
the motions there consist of glacial isostatic adjustment (GIA) signals and noise. Subtracting a published model for GIA velocities, but otherwise considering trends to be part of the noise, we find that the braced stations have RW on the order of 0.5 mm/yr$^{0.5}$ and 2 mm/yr$^{0.5}$ (horizontal and vertical), and FN on the order of 2-2.5 mm/yr$^{0.25}$ and 7-9 mm/yr$^{0.25}$ (horizontal and vertical). Standard detrending reduces the RW by a factor of two.
For 10 years of daily position data we find that in the horizontal component the most stable braced stations have velocity uncertainties of 0.15-0.25 mm/yr. Detrending reduces this to slightly over 0.1 mm/yr.
For the vertical component the deep braced monuments have velocity uncertainties of 0.5-0.8 mm/yr, and the shallow drilled stations 0.9-1.3 mm/yr.

Broader Impacts This project supported the intellectual development of a female Ph.D student.
Exemplary Figure Figure 3:
Horizontal velocity uncertainties for 10 years of daily data. Solid colored circles show the uncertainties estimated based on the NNE, lighter shading indicates one standard deviation range. Plus signs indicate velocity uncertainty calculated using noise estimates for de-trended data. Deep-drilled braced: orange, shallow-drilled braced: green, shallow foundation: blue, building wall: purple, building wall: red.
Credits: Dmitrieva and Segall