Network-based estimation of time-dependent noise in GPS position time series

Some estimates of GPS velocity uncertainties are very low, $$<$$<0.1 mm/year with 10 years of data. Yet, residual velocities relative to rigid plate models in nominally stable plate interiors can be an order of magnitude larger. This discrepancy could be caused by underestimating low-frequency time-dependent noise in position time series, such as random walk. We show that traditional estimators, based on individual time series, are insensitive to low-amplitude random walk, yet such noise significantly increases GPS velocity uncertainties. Here, we develop a method for determining representative noise parameters in GPS position time series, by analyzing an entire network simultaneously, which we refer to as the network noise estimator (NNE). We analyze data from the aseismic central-eastern USA, assuming that residual motions relative to North America, corrected for glacial isostatic adjustment (GIA), represent noise. The position time series are decomposed into signal (plate rotation and GIA) and noise components. NNE simultaneously processes multiple stations with a Kalman filter and solves for average noise components for the network by maximum likelihood estimation. Synthetic tests show that NNE correctly estimates even low-level random walk, thus providing better estimates of velocity uncertainties than conventional, single station methods. To test NNE on actual data, we analyze a heterogeneous 15 station GPS network from the central-eastern USA, assuming the noise is a sum of random walk, flicker and white noise. For the horizontal time series, NNE finds higher average random walk than the standard individual station-based method, leading to velocity uncertainties a factor of 2 higher than traditional methods.

[1]  T. Dixon,et al.  Noise in GPS coordinate time series , 1999 .

[2]  John Langbein,et al.  Noise in two‐color electronic distance meter measurements revisited , 2004 .

[3]  Yehuda Bock,et al.  Southern California permanent GPS geodetic array: Error analysis of daily position estimates and site velocities , 1997 .

[4]  J. Zumberge,et al.  Precise point positioning for the efficient and robust analysis of GPS data from large networks , 1997 .

[5]  S. Williams.  The effect of coloured noise on the uncertainties of rates estimated from geodetic time series , 2003 .

[6]  Jan M. Johansson,et al.  An improved and extended GPS-derived 3D velocity field of the glacial isostatic adjustment (GIA) in Fennoscandia , 2007 .

[7]  Giuseppe Puglisi,et al.  Dynamics of the eastern flank of Mt. Etna volcano (Italy) investigated by a dense GPS network , 2006 .

[8]  Wei-cai Lü,et al.  Application of GPS technology to build a mine-subsidence observation station , 2008 .

[9]  James L. Davis,et al.  GPS APPLICATIONS FOR GEODYNAMICS AND EARTHQUAKE STUDIES , 1997 .

[10]  D. Agnew,et al.  Monument motion and measurements of crustal velocities , 1995 .

[11]  John Langbein,et al.  Estimating rate uncertainty with maximum likelihood: differences between power-law and flicker–random-walk models , 2012, Journal of Geodesy.

[12]  Greg Welch,et al.  Welch & Bishop , An Introduction to the Kalman Filter 2 1 The Discrete Kalman Filter In 1960 , 1994 .

[13]  Matt A. King,et al.  Long GPS coordinate time series: Multipath and geometry effects , 2009 .

[14]  M. Bouin,et al.  Geocentric sea-level trend estimates from GPS analyses at relevant tide gauges world-wide , 2007 .

[15]  S. Stein,et al.  Crustal shortening in the Andes: Why do GPS rates differ from geological rates? , 2000 .

[16]  Z. Altamimi,et al.  ITRF2008: an improved solution of the international terrestrial reference frame , 2011 .

[17]  Weiping Jiang,et al.  Effects on noise properties of GPS time series caused by higher-order ionospheric corrections , 2014 .

[18]  M. Bouin,et al.  Correlated errors in GPS position time series: Implications for velocity estimates , 2011 .

[19]  A. Amiri-Simkooei,et al.  Noise in multivariate GPS position time-series , 2009 .

[20]  J. Nocquet,et al.  Deformation of the North American plate interior from a decade of continuous GPS measurements , 2006 .

[21]  Jan P. Weiss,et al.  Single receiver phase ambiguity resolution with GPS data , 2010 .

[22]  J. Kirchner.  Aliasing in 1/f(alpha) noise spectra: origins, consequences, and remedies. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  P. Teunissen,et al.  Assessment of noise in GPS coordinate time series : Methodology and results , 2007 .

[24]  Yehuda Bock,et al.  Error analysis of continuous GPS position time series , 2004 .

[25]  U. Hugentobler,et al.  Estimation of velocity uncertainties from GPS time series: Examples from the analysis of the South African TrigNet network , 2011 .

[26]  D. Agnew,et al.  The time-domain behavior of power-law noises. [of many geophysical phenomena] , 1992 .

[27]  Paul Segall,et al.  Time dependent inversion of geodetic data , 1997 .

[28]  Matt A. King,et al.  Detecting offsets in GPS time series: First results from the detection of offsets in GPS experiment , 2013 .

[29]  Peter Steigenberger,et al.  Improved Constraints on Models of Glacial Isostatic Adjustment: A Review of the Contribution of Ground-Based Geodetic Observations , 2010 .

[30]  Simon D. P. Williams,et al.  Offsets in Global Positioning System time series , 2003 .

[31]  J. A. Davis,et al.  A Kalman Filter Clock Algorithm for Use in the Presence of Flicker Frequency Modulation Noise , 2003 .

[32]  Jürgen Kusche,et al.  Surface mass redistribution inversion from global GPS deformation and Gravity Recovery and Climate Experiment (GRACE) gravity data , 2005 .

[33]  John Langbein,et al.  Noise in GPS displacement measurements from Southern California and Southern Nevada , 2008 .

[34]  Alessandro Maria Michetti,et al.  Fault scarps and deformation rates in Lazio–Abruzzo, Central Italy: Comparison between geological fault slip-rate and GPS data , 2005 .

[35]  S. Stein,et al.  Time-Variable Deformation in the New Madrid Seismic Zone , 2009, Science.

[36]  C. Demets,et al.  High-resolution estimates of Nubia–North America plate motion: 20 Ma to present , 2014 .

[37]  M. Tamisiea,et al.  Combination of geodetic observations and models for glacial isostatic adjustment fields in Fennoscandia , 2010 .

[38]  John Langbein,et al.  Correlated errors in geodetic time series: Implications for time‐dependent deformation , 1997 .

[39]  F. Wyatt.  Displacement of surface monuments: Vertical motion , 1989 .

[40]  Paolo Baldi,et al.  Crustal velocity and strain-rate fields in Italy and surrounding regions: new results from the analysis of permanent and non-permanent GPS networks , 2005 .

[41]  Matt A. King,et al.  Apparent stability of GPS monumentation from short‐baseline time series , 2009 .

[42]  C. Demets,et al.  Crustal velocity field of Mexico from continuous GPS measurements, 1993 to June 2001: Implications for the neotectonics of Mexico , 2003 .

[43]  Robert B. Smith,et al.  Crustal deformation of the Yellowstone–Snake River Plain volcano-tectonic system: Campaign and continuous GPS observations, 1987–2004 , 2007 .

[44]  A H Dodson,et al.  Using continuous GPS and absolute gravity to separate vertical land movements and changes in sea-level at tide-gauges in the UK , 2006, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[45]  Wayne Thatcher,et al.  GPS Constraints on the Kinematics of Continental Deformation , 2003 .

[46]  R. Bennett,et al.  Contemporary strain rates in the northern Basin and Range province from GPS data , 2003 .

[47]  X. Collilieux,et al.  Mitigating the effects of vertical land motion in tide gauge records using a state-of-the-art GPS velocity field , 2012 .

[48]  A. Frankel,et al.  Significant Motions between GPS Sites in the New Madrid Region: Implications for Seismic Hazard , 2012 .

[49]  Andrew Harvey,et al.  Time Series Models. , 1983 .

[50]  Paul A. Rosen,et al.  Co-seismic slip from the 1995 July 30 Mw= 8.1 Antofagasta, Chile, earthquake as constrained by InSAR and GPS observations , 2002 .

[51]  Paul Segall,et al.  Spatiotemporal evolution of a transient slip event on the San Andreas fault near Parkfield, California , 2005 .

[52]  F. Loddo,et al.  GPS-based monitoring of land subsidence in the Po Plain (Northern Italy) , 2009 .

[53]  J. Ray,et al.  Anomalous harmonics in the spectra of GPS position estimates , 2008 .

[54]  Stathis C. Stiros,et al.  Subsidence and evolution of the Thessaloniki plain, Greece, based on historical leveling and GPS data , 2007 .

[55]  Alireza Amiri-Simkooei,et al.  On the nature of GPS draconitic year periodic pattern in multivariate position time series , 2013 .

[56]  W. Augath.  Crustal Deformation , 2003 .