Global Positioning System-GPS
Satellite Laser Ranging-SLR
In Satellite Laser Ranging (SLR) a global network of stations measure
the instantaneous round trip time of flight of pulses of light to satellites
equipped with special reflectors. This provides instantaneous range
measurements of horizontal and vertical station motions on a global
scale in a geocentric reference frame of mm/yr level precision. The
height of the geoid has been determined to less than ten cm at long
wavelengths less than 1500 km. Thirty-second mean gravity anomalies
from the EGM96 model show the fine detail.
Very Long Baseline Interferometry-VLBI
VLBI (Very Long Baseline Interferometry) is a geometric technique: it
measures the time difference between the arrival at two Earth-based
antennas of a radio wavefront emitted by a distant quasar. VLBI
determines the relative positions of the antennas to a few
millimeters precision.
Interpretation of Space Geodesy Data
VLBI consists of a pair of receivers, at different locations on the
Earth, looking at the same quasar. When two receivers are oriented
facing a quasar, receiver A will receive a code before receiver B.
Using the time delay, the distance between the two stations can be
determined. Now, at a later time, when station A is again oriented
with respect to the quasar as before, if B has moved so that it is
closer to A the delay time between the reception of a code will be
less than before. But, if the distance between receivers A and B
has remained fixed but the Earth has expanded in the mean time,
this, due to curvature reduction, would also reduce the delay
time between the two receivers.
SLR consists of beaming lasers toward satellites and provides
independent but similar measurements to VLBI, with the same
ambiguity as to whether there has been surface horizontal
movement, or Earth expansion.
Surface Movement or Earth Expansion?
S
A
R
S
S΄
D
B
A
R
d
A
B΄
B
B
R΄
(a)
(b)
(B. Mundy)
(c)
R: the radius, R, of the unexpanded earth, the same in (a) and (b);
S: the arc length, S, between stations A and B, the same in (a) and (c),;
D: the long time delay D could be the same in (a) and (b) in a constant size Earth
if there is no arc length shortening, that is no horizontal converging of plates.
d: the short time delay d could be the same in (b) and (c), as a result of the
reduction of distance AB by BB΄, that is reduction of arc length to S΄, in a constant
size Earth, due to converging plates on the small radius R 1, or to the reduction
of curvature, on a bigger Earth, with radius R΄ 2R.
Earth Expansion and Space Geodesy
Subsidence rate : expansion rate  1 : 6.1
A
S21,44
S11,57
h10.293
h20.129
C1,2 1,41
R2=2R1
θ241.40
Convergence rate : expansion rate  1 : 7.7
A
~525 km
A
B
θ1=900 R =1
1
B
B
R1  3200 km
R2  6400 km
200 m.y.a. – 0 m.y.a.
The cord length C1=2R1sin(θ1/2)1.414R1, of a central angle, θ1=900 in a R1=1
circle, is equal to the cord length C2 that corresponds to θ2 41.40 in a R2=2R1
circle. On the other hand, in R1=1, and θ1=900 the arc length, S1 rad(900)R1
1.57R1 and the segment height, h1=R1-[R12-(C/2)2]1/2 0.293R1, while for θ2 
41.40 and R2 = 2R1, S2rad(41.40)2R1 1.44R1, and h2  0.129R1. Thus in an Earth
in which its radius has doubled the last 200 m.y., that is an average radius
increase of ~1.6 cm/yr, the central continental points will appear to subside,
by ~2.6 mm per year, while stations A and B, that are ~4500 km apart, will
appear to converge by ~2.1 mm / yr, both to small to be accurately detected.
The Local Exaggeration of Space Geodesy Data
A-B, D-E, A-E: Lengthening, Primary Global Extension
B-C, C-D, B-D: Shortening, Secondary Surface Compression
A-D, B-E: No Apparent Change
Exaggeration, beyond the few mm/yr, of divergence or convergence between
two stations, usually associated with décollement, depends on the position of the
stations relative to local extensional or compressional surface features. Also
episodic events such as earthquakes, can result to high uplift rates. In the 17
Aug 1999, Izmit 7.4 earthquake, a co-seismic uplift of ~75 cm has been measured
between two radar acquisitions on 13 Aug & 17 Sep 1999.
VLBI Vertical Data
http://lupus.gsfc.nasa.gov/plots/maps/jpg/
In an expanding Earth the vertical
motions do not measure radius
increase, but the effect of reduced
curvature, which means apparent
subsidence rates in the range of
mm/yr. Indeed the nine (9) out of ten
(10) values of vertical motions in
western U.S.A. are negative, and
the average absolute value is ~2.9 
2.5 mm/yr. The negative vertical
motions are attributed to the
symmetric-chaotic deposition of
excess mass, and describe the
spheroidal surface, while the
positive vertical motions are
manifestation of the asymmetricconcentrated emplacement of
excess mass, which is responsible
for the positive geoidal anomalies.
VLBI Horizontal Data 1
http://lupus.gsfc.nasa.gov/plots/maps/jpg/
As it can be seen horizontal velocities vary from ~10 mm/yr to a max
of ~70 mm/yr showing Hawaii moving towards Asia. Hawaii moving
towards Asia is a typical example of exaggerated local control. Since
Hawaii is located on an extensional and domed feature, then a station
facing another station will move toward it faster than ‘normal’.
VLBI Horizontal Data 2
http://lupus.gsfc.nasa.gov/plots/maps/jpg/
Space geodesy data although still ambiguous, due to accuracy
problems (errors are in the order of few mm, at least) and to local
exaggeration of relative motions,
a) signify local small scale movements,
b) differ significantly from the supposed plate motions, and
c) are consistent with size increase of the Earth.