Geodesy & Crustal Deformation Geology 6690/7690 Geodesy & Crustal Deformation 20 Sep 2017 GPS Position Error (& Mitigation) • Largest error source in differenced, post-processed, phase+code positions is atmospheric mis-modeling • Ionosphere TEC is dispersive and removed by linear combination of two or more carrier frequencies… Used for space weather/ionosphere studies • Tropospheric error includes (1) pressure-temperature- water vapor, & (2) scattering (dispersive) • Multipath is signal that reflects off the ground or other objects. Can be corrected (mostly) with an averaged phase map, but amplitude/phase can also be used to sense local soil moisture, snow depth or vegetation index • Reference Frame describes how we relate Earth-fixed to satellite motion: Can be trickiest part of GPS tectonics! Read for Mon 25 Sep: Wahr §3.1-3.2 (67-75) © A.R. Lowry 2017

Borehole Strainmeters Strainmeters are several orders of magnitude more sensitive than GPS, so they pick up everything... But they are also very challenging data sets to use and understand, because the directions of strain are rotated/ perturbed by local elastic and anelastic (fracture) heterogeneities in a way that is 3D-wavenumber dependent. The successful studies have used them for time-related (not direction-related) purposes... (Station AVN2, Oklahoma) Read for Fri 22 Sep: Luttrell et al (GRL 2013)

Secular Velocities... • “Geologic” Plate Velocity Models use “geologic data” including ocean ridge opening rates derived from dated seafloor magnetic anomalies; relative plate motion directions inferred from transform faults; earthquake slip vectors… • Effectively average over the past 3 million years (because of the need for magnetic anomaly rate constraints)… • NNR versions of these compared to in this paper include NNR-NUVEL-1A by DeMets et al. (1990; 1994); NNR-MORVEL56 by Argus et al. (2011) Courtesy USGS Courtesy USGS

Plate Velocity Modeling using Euler Poles: Assumes rigid “blocks” (or “plates”) move independently relative to one another across the Earth’s surface. Sella et al. (2002) & Altimimi et al. (2012) both use this. Each block will have an Euler Pole: For the p’th block, means the block rotates at angular velocity p around the pole at latitude p, longitude p. Then the velocity at any point on the block is given by: Assumes? How small a “plate” can we reasonably expect? Altamimi et al. (2012) adds an “origin rate bias” term: which is purely a reference frame issue related to inadequacy of sampling & our knowledge of mass flux.

Altamimi et al. (2012) is first and foremost about defining a plate velocity Reference Frame for GPS velocities. Note: • X, Y, Z refers to the Earth-centered, Earth-fixed GPS coordinate system. We use coordinate transformations to convert these to more familiar lat, lon, height above an ellipsoid… • “Origin rate bias” is translation rate of the X, Y, Z = 0 origin of the coordinate frame • They also find a global rotation-rate about the X-axis that describes the difference between their and other NNR frames These are all rooted in issues of inadequate sampling of the global velocity field.

The good news is their estimate of translation rate is not significant at 95% confidence (and can be thought of more as just an expression of uncertainty in motions introduced by the sampling geometry!)

Modeling GPS Velocities: Velocities (i.e., the secular changes or “trends” in position, dxi/dt) are important observables for several different applications: • Critical first-order term needed to define the GPS reference frame (positions are referenced to these!) • Critical first-order term for assessing interseismic strain rates (strain is the spatial derivative of displacement!) • Necessary baseline for evaluating temporal changes in behavior!

Example time series including correction for an antenna Sella et al., JGR 2002 Example time series including correction for an antenna change at the site.