3. 11/10 11/12/2004 12.201/12.501 3
History and Types
• Geodesy: Science of measuring size and shape of the
Earth (and temporal changes added in last 20 years)
• Split into two fields:
– Physical Geodesy: Study of Earth Potential fields (mainly
gravity field)
•Historically used surface gravity measurements: Boundary value
problems (Greens Theorem etc): Given derivative of field on a
surface, find the value of the field outside and on surface.
•Space based methods for long wavelength (>300 km). Ground
based tracking of satellites (LAGEOS), radar altimetry (TOPEX,
JASON), satellite-to-satellite tracking (GRACE), gradiometers
(GOCE),
– Positional Geodesy: Determine of positions; land boundaries,
maps and deformations. Lectures hear will cover latter topic.
4. 11/10 11/12/2004 12.201/12.501 4
History and Types
• Although physical and positional geodesy are often
treated separately, they are dependent on each other
especially with development of space base geodetic
methods:
– When earth orbiting objects are used as measurement targets,
the gravity field is needed to integrate equations of motion of
object.
– To use orbit perturbations to determine gravity field, the
“perturbations” are measured from ground positions which
need to be known at some point.
– Modern methods solve these two problems simultaneously
although even today this is not always done correctly. (First
and second degree harmonic terms in gravity field).
5. 11/10 11/12/2004 12.201/12.501 5
Geodetic coordinate systems
• Modern spaced based geodetic measurements allow
determination of geometric coordinates (basically
Cartesian coordinates in a global frame)
– Origin of coordinates: nominally center of mass location (small
movements with respect to center of figure (a few centimeters)
– Orientation of axes: Z near maximum moment of inertia, X
through Greenwich, Y completes systems
–Mathematically compute direction of normal to ellipsoid
(geodetic latitude and longitude)
• However, prior to space based methods, coordinates
based gravity field:
– Direction of gravity vector define astronomical latitude and
longitude. Height measured above an equipotential surface
(geoid).
7. 11/10 11/12/2004 12.201/12.501 7
Positional Geodesy Methods
• Triangulation: Dates from 1600’s and the work of Snell.
Uses angle measurements and 1-2 short, directly
measured distance (usually ~1km). Other distances
are deduced then from trigonometry.
– Angles can be measured to ~1 arc sec = 5x10-6 rads.
– Accuracy of this geodetic method is ~10-5 proportional error
–Main geodetic method until the 1940s
• Trilateration: Direct distance measurement using
electromagnetic distance measurement (EDM).
– Techniques developed after WW II and followed from the
RADAR development.
– Most methods used phase measurements at different
frequencies rather than time-of-flight measurements.
8. 11/10 11/12/2004 12.201/12.501 8
Example of methods: South Africa
The Meridian Arc of
Abbe de Lacaille
Measured in 1751 to
help determine
shape of Earth.
9. 11/10 11/12/2004 12.201/12.501 9
Later measurements
1840-1846
Typical sites distances are 20-
50 km.
Points are located on tops of
mountains typically
The baseline measurement
was in Cape Town.
11. 11/10 11/12/2004 12.201/12.501 11
Densification
In tectonically
active area, these
old survey results
can be used to
get strain
accumulation
estimates with up
to 150 year time
spans.
12. 11/10 11/12/2004 12.201/12.501 12
Space based measurements
• The advent of the Earth orbiting satellites starting in
1955, and the development of radio astronomy
(Jansky, 1932) started to bring about a revolution in
geodetic accuracy.
• Activity started after WWII using technology developed
during the war and in response to cold war.
• New methods removed the need for line-of-sight
Jansky 22 Mhz steerable
radio telescope (1932)
Modern radio telescope
13. 11/10 11/12/2004 12.201/12.501 13
Principles of new methods
• Satellites allowed measurement to objects well above
the surface of the earth which could be seen from
locations that could not see earth other.
• The electronic distance measurement methods could
be used make distance measurements rather than
angle measurements. (As in astronomical positioning)
• Radio techniques allowed relative distance
measurements using quasars
• Satellite orbits perturbed by gravity field (and other
non-conservative forces such as drag) and so physical
and positional geodesy at the same time.
14. 11/10 11/12/2004 12.201/12.501 14
Space Geodetic Techniques
• Satellite Laser Ranging (SLR): Uses pulsed laser system to
measure time of flight travel from ground telescope to orbiting
satellite equipped with corner cube reflectors.
• First deployed in late 1960s; Lunar system deployed by Apollo
and Russian programs (LLR).
• Currently about 38 reporting stations (11/04).
• International Laser Ranging service (ILRS):
http://ilrs.gsfc.nasa.gov/
LAGEOS I: Launched 1976, 5958 km altitude, 109
deg Inclination, 411 kg
LAGEOS II: Launched 1992, 5616-1950 km
altitude, 52 deg Inclination, 400 km
60 cm diameter spheres
16. 11/10 11/12/2004 12.201/12.501 16
Space geodetic methods
• Very long baseline interferometry (VLBI): Uses radio signals from
extragalatic radio sources to measure difference in arrival times at
widely separated radio telescope.
• First measurements in 1969: First detection on plate motion
between Europe and North America in 1986.
• 38 VLBI sites currently International VLBU service (IVS)
http://ivscc.gsfc.nasa.gov/
Pietown Radio telescope (25 m
diameter) (right)
Effelsberg radio telescope in
Germany (100 m diameter) (left)
18. 11/10 11/12/2004 12.201/12.501 18
VLBI and SLR operations
• SLR sites tend to operate independently with priorities at each site as to
which satellites to track. There are about 30 satellites with corner cube
reflectors. SLR stations need human operators and track for 8-24 hours
per day 5-7 days per week.
• VLBI measurements need to be coordinated because multiple
telescopes need to look at the same radio object at the same time.
Sessions are scheduled for 24 hours durations with measurements
every few minutes. Regular measurements programs in EOP sessions
twice per week, daily intensive sessions (1-hr), plus other sessions.
• There are mobile VLBI and SLR systems, but these are moved with
trucks, and so tend to be repositioned infrequently. (In the 1980s mobile
VLBI and SLR systems made measurements in tectonically active
regions, but GPS replaced these types of measurements in the 1990s).
• SLR is useful for satellite tracking, and low order gravity field changes
• VLBI provides 1-day averaged station positions and inertial reference
frame
20. 11/10 11/12/2004 12.201/12.501 20
GPS Original Design
• Started development in the late 1960s as
NAVY/USAF project to replace Doppler positioning
system
• Aim: Real-time positioning to < 10 meters, capable of
being used on fast moving vehicles.
• Limit civilian (“non-authorized”) users to 100 meter
positioning.
21. 11/10 11/12/2004 12.201/12.501 21
GPS Design
• Innovations:
–Use multiple satellites (originally 21, now ~28)
–All satellites transmit at same frequency
–Signals encoded with unique “bi-phase, quadrature
code” generated by pseudo-random sequence
(designated by PRN, PR number): Spread-spectrum
transmission.
–Dual frequency band transmission:
•L1 ~1.5 GHz, L2 ~1.25 GHz
23. 11/10 11/12/2004 12.201/12.501 23
Measurements
• Measurements:
– Time difference between signal transmission from satellite and
its arrival at ground station (called “pseudo-range”, precise to
0.1–10 m)
– Carrier phase difference between transmitter and receiver
(precise to a few millimeters)
–Doppler shift of received signal
• All measurements relative to “clocks” in ground
receiver and satellites (potentially poses problems).
24. 11/10 11/12/2004 12.201/12.501 24
Positioning
• For pseudo-range to be used for “point-positioning” we
need:
– Knowledge of errors in satellite clocks
– Knowledge of positions of satellites
• This information is transmitted by satellite in
“broadcast ephemeris”
• “Differential” positioning (DGPS) eliminates need for
accurate satellite clock knowledge by differencing the
satellite between GPS receivers (needs multiple
ground receivers).
25. 11/10 11/12/2004 12.201/12.501 25
Satellite constellation
• Since multiple satellites need to be seen at same time
(four or more):
– Many satellites (original 21 but now 28)
– High altitude so that large portion of Earth can be seen
(20,000 km altitude —MEO)
26. 11/10 11/12/2004 12.201/12.501 26
Current constellation
• Relative sizes
correct (inertial
space view)
• “Fuzzy” lines not
due to orbit
perturbations, but
due to satellites
being in 6-planes at
55o inclination.
28. 11/10 11/12/2004 12.201/12.501 28
Pseudo-range accuracy
• Original intent was to position using pseudo-range:
Accuracy better than planned
• C/A code (open to all users) 10 cm-10 meters
• P(Y) code (restricted access since 1992) 5 cm-5
meters
• Value depends on quality of receiver electronics and
antenna environment (little dependence on code
bandwidth).
29. 11/10 11/12/2004 12.201/12.501 29
GPS Antennas (for precise positioning)
• Rings are
called choke-
rings (used to
suppress
multi-path)
Nearly all antennas are patch antennas (conducting
patch mounted in insulating ceramic).
30. 11/10 11/12/2004 12.201/12.501 30
Positioning accuracy
• Best position accuracy with pseudo-range is about 20
cm (differential) and about 5 meters point positioning.
Differential positioning requires communication with
another receiver. Point positioning is “stand-alone”
• Wide-area-augmentation systems (WAAS) and CDMA
cell-phone modems are becoming common differential
systems.
• For Earth science applications we want better
accuracy
• For this we use “carrier phase” where “range”
measurement noise is a few millimeters (strictly range
change or range differences between sites)
31. 11/10 11/12/2004 12.201/12.501 31
Carrier phase positioning
• To use carrier phase, need to make differential measurements
between ground receivers.
• Simultaneous measurements allow phase errors in clocks to be
removed i.e. the clock phase error is the same for two ground
receivers observing a satellite at the same time (interferometric
measurement).
• The precision of the phase measurements is a few millimeters.
To take advantage of this precision, measurements at 2
frequencies L1 and L2 are needed. Access to L2 codes in
restricted (anti-spoofing or AS) but techniques have been
developed to allow civilian tracking of L2. These methods make
civilian receivers more sensitive to radio frequency interference
(RFI)
• Next generation of GPS satellites (Block IIF) will have civilian
codes on L2. Following generation (Block III) will have another
civilian frequency (L5).
32. 11/10 11/12/2004 12.201/12.501 32
Phase positioning
• Use of carrier phase measurements allows positioning
with millimeter level accuracy and sub-millimeter if
measurements are averaged for 24-hours.
• Examples:
– The International GPS Service (IGS) tracking network. Loose
international collaboration that now supports several hundred,
globally distributed, high accuracy GPS receivers.
(http://igscb.jpl.nasa.gov)
– Applications in California: Southern California integrated GPS
network (SCIGN http://www.scign.org)
34. 11/10 11/12/2004 12.201/12.501 34
IGS network
• Stations in the IGS network continuously track GPS
satellites and send their data to international data
centers at least once per day. All data are publicly
available.
• A large number of stations transmit data hourly with a
few minutes latency (useful in meteorological
applications of GPS).
• Some stations transmit high-rate data (1-second
sampling) in real-time. (One system allows ±20 cm
global positioning in real-time with CDMA modem
connection).
35. 11/10 11/12/2004 12.201/12.501 35
Uses of IGS data
• Initial aim was to provide data to allow accurate determination of
the GPS satellite orbits: Since IGS started in 1994, orbit accuracy
has improved from the 30 cm to now 2-3 cm
• From these data, global plate motions can be observed in “real-
time” (compared to geologic rates)
• Sites in the IGS network are affected by earthquakes and the
deformations that continue after earthquakes. The understanding
of the physical processes that generate post-seismic deformation
could lead to pre-seismic indicators:
– Stress transfer after earthquakes that made rupture more/less likely
on nearby faults
– Material properties that in the laboratory show pre-seismic signals.
• Meteorological applications that require near real-time results
38. 11/10 11/12/2004 12.201/12.501 38
Motions in California
Red vectors relative to North America;
Blue vectors relative to Pacific
Motion across
the plate
boundary is ~50
mm/yr.
In 100-years this
is 5 meters of
motion which is
released in large
earthquakes
40. 11/10 11/12/2004 12.201/12.501 40
Post-seismic
Estimates
As more
earthquakes are
seen with GPS,
deformations
after earthquakes
are clearer
Here we show
log dependence
to the behavior.
41. 11/10 11/12/2004 12.201/12.501 41
WIDC (74 km
from epicenter)
Coseismic
offset removed
N 51.5±0.8 mm
E 15.7±0.6 mm
U 4.3±1.8 mm
Log amplitude
N 4.5 ± 0.3 mm
E 0.7 ± 0.2 mm
U 3.3 ± 0.7 mm
42. 11/10 11/12/2004 12.201/12.501 42
Deformation in the
Los Angeles Basin
Measurements of
this type tell us how
rapidly strain is
accumulating
Strain will be
released in
earthquakes (often
large)
43. 11/10 11/12/2004 12.201/12.501 43
Repeating slow
earthquakes in Pacific
North West
Example of repeating
“slow” earthquakes (no
rapid rupture)
These events give
insights into material
properties and nature of
time dependence of
deformation
45. 11/10 11/12/2004 12.201/12.501 45
CONCLUSIONS
• GPS, used with millimeter precision, is revealing the
complex nature and temporal spectrum of
deformations in the Earth.
• Programs such as Earthscope plan to exploit this
technology to gain a better understanding about why
earthquakes and volcanic eruptions occur.
• GPS is probably the most successful dual-use (civilian
and military) system developed by the US
• In addition to the scientific applications, many
commercial applications are also being developed.
