MIDAS robust trend estimator for accurate GPS station velocities without step detection

Abstract

Automatic estimation of velocities from GPS coordinate time series is becoming required to cope with the exponentially increasing flood of available data, but problems detectable to the human eye are often overlooked. This motivates us to find an automatic and accurate estimator of trend that is resistant to common problems such as step discontinuities, outliers, seasonality, skewness, and heteroscedasticity. Developed here, Median Interannual Difference Adjusted for Skewness (MIDAS) is a variant of the Theil‐Sen median trend estimator, for which the ordinary version is the median of slopes vij = (xj–xi)/(tj–ti) computed between all data pairs i > j. For normally distributed data, Theil‐Sen and least squares trend estimates are statistically identical, but unlike least squares, Theil‐Sen is resistant to undetected data problems. To mitigate both seasonality and step discontinuities, MIDAS selects data pairs separated by 1 year. This condition is relaxed for time series with gaps so that all data are used. Slopes from data pairs spanning a step function produce one‐sided outliers that can bias the median. To reduce bias, MIDAS removes outliers and recomputes the median. MIDAS also computes a robust and realistic estimate of trend uncertainty. Statistical tests using GPS data in the rigid North American plate interior show ±0.23 mm/yr root‐mean‐square (RMS) accuracy in horizontal velocity. In blind tests using synthetic data, MIDAS velocities have an RMS accuracy of ±0.33 mm/yr horizontal, ±1.1 mm/yr up, with a 5th percentile range smaller than all 20 automatic estimators tested. Considering its general nature, MIDAS has the potential for broader application in the geosciences.

A 10-Year Comparison of Water Levels Measured with a Geodetic GPS Receiver versus a Conventional Tide Gauge

“…The station is included in the recent compilation by Blewitt et al (2016), who report a vertical rate of 10.25 6 0.68 mm yr 21 in the International Global Navigation Satellite Systems (GNSS) Service (IGS)-developed IGS08 terrestrial reference frame.…”

Time-dependent deformation of Uturuncu volcano, Bolivia, constrained by GPS and InSAR measurements and implications for source models

“…Coordinates are relative to the IGS08 reference frame, which is a GPS-only realization of ITRF2008 (Altamimi et al, 2011). Further details on processing technique can be found in Blewitt et al (2016). Time series for UTUR and COLO are presented in Figure 6 with best-fit rates reported in Table 3.…”

Thermomechanical modeling of the Altiplano-Puna deformation anomaly: Multiparameter insights into magma mush reorganization

“…Reoccupation of a nearby leveling line using the global positioning system (GPS) shows that the ground deformation has been active since at least 1965 at rates comparable to the satellite-derived defor ma tion (del Potro et al, 2013b), but continuous GPS data collected near the center of deformation that span 2010-2015 (Appendix Fig. A1 in Appendix 1) indicate that uplift has slowed to a rate of ~0.24 ± 0.19 cm/yr (Blewitt et al, 2016).…”

“…Andesitic and basaltic andesitic enclaves in Uturuncu lavas and in silicic ignimbrites of the APVC (Michelfelder et al, 2014) are interpreted as aliquots of the least evolved resident magmas in the APMB entrained into the volumetrically dominant, silica-rich dacite magmas (Sparks et al, 2008). The mafic magmas have less radiogenic strontium and more radiogenic neodymium isotopes than associated dacites (Michelfelder et al, 2014) and are thought to be Size and geometry of anomalous structures Schilling et al (2006); Comeau et al (2015Comeau et al ( , 2016 Gravimetry A pproximately 12-24 km wide, vertically elongated (8-12 km high), low-density structures rooted at the top of the APMB at ~15 km below sea level Surface velocity and spatiotemporal evolution of deformation Fialko and Pearse (2012); Henderson and Pritchard (2013);del Potro et al (2013a); Blewitt et al (2016) Geomorphology Absence of sustained residual long-term deformation Null result for residual ground deformation at time, t > 100 yr Perkins et al (2016) Note: See text for details on numerical model. APMB-Altiplano-Puna magma body.…”