1. 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

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

3. 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!)

4. 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.

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

6. 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.

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

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

9. 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)!

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

11. 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.

12. 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!

13. 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…

14. 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

15. 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…