Geodesy & Crustal Deformation Geology 6690/7690 Geodesy & Crustal Deformation 18 Sep 2017 GPS Positioning: Signals • Receivers distinguish satellite transmissions from the microwave background by cross-correlating antenna reception with known PRN codes of the SV’s • Tectonic-Grade Applications track phase  on carrier signals (L1, L2, eventually L5 & L4?) and use the doppler to determine range over time • Errors in estimates of satellite position, satellite clocks (& other common-mode errors) are removed by differencing two or more receivers to each satellite • Double-differencing (two satellites, two receivers) is used to ensure an integer ambiguity (= range at the first phase observation, when using doppler). Read for Fri 22 Sep: Luttrell et al (GRL 2013) © A.R. Lowry 2017

Atmosphere I. The Ionosphere: x’s are double-differenced positions using two frequencies; circles positioned using L1 only... Differenced over < 5 km.

GPS Error Sources (and Mitigation) Atmosphere I. The Ionosphere: Uppermost layers of the atmosphere (30–50 km altitude) are ionized by solar radiation Has dispersive effect on microwave Refractive index n = c/v depends on frequency f as: n = 1 + c2/f 2 + c3/f 3 + c4/f 4 + … To first order can correct this by a linear combination of phase at two different frequencies: FLC = FL1 – f2 FL2/f1 Is responsible for most (~1 m) error in WAAS- corrected single- frequency positions… Ideally use dual-freq… Potential for greater improvement using an additional frequency ( higher order correction!)

GPS Error Sources (and Mitigation) Atmosphere I. The Ionosphere: One person’s noise is another person’s signal… GAIM (developed here on campus) uses GPS measurements of Total Electron Content to model space weather in real-time.

GPS Error Sources (and Mitigation) Atmosphere II. The Troposphere:

GPS Error Sources (and Mitigation) Atmosphere II. The Troposphere: Index of refraction depends on pressure, temperature, water vapor in the atmosphere: increases apparent range by 2 to 100+ m Excess phase path for a single day of GPS measurement Generally correct via a single- parameter elevation mapping function (e.g., wet Neill) but > 1 m errors remain at low elevation angle after correction.

GPS Error Sources (and Mitigation) Atmosphere II. The Troposphere: CAYA (Elev 26 m) rel MDO1 POSW (Elev 3940 m) rel MDO1

But again, one person’s noise is another’s signal. This courtesy of SUOMINET…

GPS Error Sources (and Mitigation) Atmosphere II. The Troposphere: Scattering: Worth being aware of for met applications, but little we can do (until we have more signals)!

Example: Total baseline length for two sites in the RGR… What’s this?

Modeled response of an elastic Earth to a 200-km radius disk of water, 1-m in height… At the mm’s level, hydrologic mass becomes a large signal.

Example: Total baseline length for two sites in the Rio Grande Rift network. Note the scatter & uncertainties are very small; effects of elastic response to hydrologic mass loading are clear; however both scatter and departure from a seasonal loading model increase during the summer months. This was anticipated and mentioned in our proposal!

GPS Error Sources (and Mitigation) Multipath results from the microwave energy that reflects off of the ground or other nearby objects and thus arrives with a slightly different path. This energy constructively/destructively interferes with amplitude, and changes the phase by up to half a cycle…

GPS Error Sources (and Mitigation) Soil Moisture Since reflecting surfaces don’t change much, multipath can be reduced with an elevation/ azimuth-dependent correction. But can also use for sensing! Larson et al., GRL 2008 Snow Depth Larson et al., GRL 2009 Vegetation Small et al., GRL 2010

GPS Error Sources (and Mitigation) Also, Reference Frame Parameters: We estimate the satellite positions and other orbital parameters by tracking from the ground… But this only works if the locations of tracking sites are in some sense “known”. The reference frame includes transformations from the Earth-based frame to space-based, e.g., • Earth rotation parameters: axis of rotation, length-of-day • Tidal and loading effects: Earth tide, ocean tidal loading, mass of fluid envelopes • Other assumptions regarding the motions of ground tracking sites…