1. 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 § (67-75)
© A.R. Lowry 2017

2. 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)

3. 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

4. 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.

5. 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.

6. 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!)

7. 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!

8. 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.