Transcript Geodesy - Haystack Observatory

Geodesy
A look at the Earth
What is Geodesy?
- The Merriam Webster Dictionary defines
Geodesy as, "a branch of applied mathematics
concerned with the determination of the size
and shape of the earth and the exact positions
of points on its surface and with the description
of variations of its gravity field."
- so more simply, Geodesy is the study of all
aspects concerning the shape, size, and
movements of the Earth.
History:
- Geodesy dates back to the earliest of
civilizations
● Back then, people were concerned more
with the immediate lands around them,
not the Earth as whole as we see it today
● Later, it expanded to the distances from
the home to the markets and other places
of exchange
● As transportation evolved, so did the need
for more exact measurements of locations.
Therefore Geodesy evolved.
History continued:
- Earliest conceptions about the world held that
is was flat
● First ideas of a spherical Earth didn't
come about until 6th century BC
- What methods of observation led to the Earth
being a sphere?
vs.
Dawn of the sphere:
- The first reasonings for a spherical Earth
relied on astronomical observations (weird that
looking into space teaches us about Earth)
1. Earth's shadow on a lunar eclipse is
curved
2. Polaris (North star) lowers in the sky as
one travels south
3. Pythagoris reasoned that mathematically
a sphere is a more perfect shape, therefore
the gods would have fashioned Earth as
such
As science often does...
- The first attempts to "measure" the size of
Earth began with pure conjecture
1. Plato guessed the circumference to be
between 62,800 km and 74,000 km
2. Archimedes approximated a
circumference of 55,500 km
- Clearly they weren't entirely accurate...
Increasing accuracy:
- First "accurate" measurement of the Earth's
circumference was done by the Greek
Eratosthenes
● "Measured" angle of the Sun at two points
during the summer solstice
o
o
One point the sun was directly overhead (showed
to the bottom of a well)
Other, the sun's angle of elevation measured to
be 1 / 50th of a circle
Eratosthenes cont:
- By "knowing" the
distance between the two
points to be now 1/50th of
the total sphere, he
calculated the
circumference to be
~46,620 km (not bad)
- Actual circumference is a
little over 40,000 km
Others of note:
- Posidonius: calculations of 240,000 stadia
and later 180,000 stadia
● stadia is an ancient distance measurement
- Aryabhata: Indian mathematician who
accurately calculated the Earth's circumference
as 24,835 miles, which was only 0.2% smaller
than the actual value of 24,902 miles. This
approximation remained the most accurate for
over a thousand years.
Others of note:
- Biruni (973-1048): Persian who used many
trigonometry equations (mostly triangulation)
to solve many complex geodesic equations.
Attained a radius value of 6,339.9 km, just shy
of today's values.
● Used the same techniques
to calculate the heights of
mountains and depths of
valleys
"Modern" additions:
- The first modern update comes
from the development of the
meridian arc measurement
● First uses by Jean Picard in
1700 and later by Jacques
Cassini
● Showed that the Earth was
not a perfect sphere but
more of an oblate ellipsoid
of revolution
Video:
So, what next...
How do we get a more accurate picture of the
Earth?
What techniques or technologies would help?
Space!
- That's right! To get a more accurate picture of
the ground below us, we need to look to the sky
above us.
Space Age:
- The first satellite for geodesic research was launched in 1962
● "The U.S. Army developed the SECOR (Sequential Collation of Range)
system and the first SECOR transponder was orbited on ANNA-1B in
1962... The system operated on the principle that an electromagnetic wave
propagated through space undergoes a phase shift proportional to the
distance traveled. A ground station transmitted a phase modulated signal
which was received by the satellite-borne transponder and returned to the
ground. The phase shift experienced by the signal during the round trip
from ground to satellite and back to ground was measured electronically at
the ground station which provided as its output a digitized representation
of range." - http://www.ngs.noaa.gov/PUBS_LIB/Geodesy4Layman/TR80003D.HTM
o So the information they utilized from the radio waves was based on
the phase, or timing of the received signals
Modern Geodesy:
- Modern Geodesic techniques all stem from
those original space efforts:
1. Global Positioning System (GPS) and Global
Navigation Satellite System (GNSS) - same thing but
GPS is the american version
2. Very Long Baseline Interferometry (VLBI)
3. Satellite Ranging System (SLR)
4. Satellite Altimetry (measuring ocean height and
topography)
1.) GPS and GNSS:
- A total of 32 (optimally) satellites are
maintained in orbit at any time
31 operational satellites in orbit as of today (July
2013)
o Allows for a minimum signal from 4 satellites
o
GPS Background
Each GPS spacecraft
●Carries highly accurate
clock
●Transmits its clock and
position
●Signals are transmitted
on 2 (or 3) frequencies
GPS Satellite Signal Structure
Code modulation:
●Identifies SV
●Spread power
●Range
X
GPS
signal
GPS Positioning
GPS Background
What is GPS used to do?
●
First there is the obvious:
●
●
Used to determine exact positioning of objects
and locations on the surface of Earth
Besides the obvious:
●
Determination of the TEC in the ionosphere
●
●
●
TEC = Total Electron Content
Based on differing delays of different frequencies as
they pass through the atmosphere
Important in studying the overall effects of the Sun’s
activities on Earth
Ionospheric Parameters
GPS can be used to measure
Ground-Based Receivers
●
Total Electron Content (TEC)
●
Scintillation Parameters: S4 and σΦ
Space-Based Receivers
●
Electron Density Profiles (EDP)
●
Scintillation Parameters: S4 and σΦ
S4= sqrt ((<I2> - <I>2 )/<I>2), where
I is the intensity of the signal and <> is the ensemble mean.
σΦ = sqrt((<Φ2>-<Φ>2), where Φ is the phase of the signal.
2.) VLBI:
- VLBI, Very Long Baseline Interferometry, was
developed for improved resolution in radio
astronomy
o
o
Resolution of radio (and optical) images increases
as a function of the aperture size
By using multiple radio antennae over long distances
(baselines) effectively increases the size of radio
aperture
VLBI basics:
The same radio is gathered by different antennae and each
signal is matched to a highly accurate atomic clock
VLBI basics:
Each data set is then
synchronized and
correlated together to
achieve a much stronger
measurement of the radio
data gathered
Nowadays, as technology
has improved, larger and
larger amounts of data are
able to be utilized as digital
recording becomes more
and more efficient
Tapes are no longer used, everything is digital now
Geodetic VLBI:
- It was quickly discovered that VLBI could be
used to get clearer picture of Earth as well as
space
● By using the very accurate timing data
between the antennae sites, many of
Earth's motions could be more accurately
tracked.
● What motions in particular do you think
VLBI could effectively track?
VLBI's geodetic contributions:
- Variations in the Earth's
orientation and length of
day
o
o
clearer picture of the
Earth's axial precession,
nutation, and polar
wandering
Earth's spin is actually
slowing down and the day
being lengthened by
~2 ms every century
VLBI's geodetic contributions:
- Maintenance of the terrestrial reference frame
- Measurement of gravitational forces of the
Sun and Moon on the Earth
- Regional deformation and uplift or
subsistence
- And one of its greatest contribution...
● The first direct evidence of plate tectonic
movement!
Plate Tectonics:
- Because of VLBI's high resolution, plate
motion can be measured very precisely
o
millimeter accuracy!
- By tracking time differences of many quasars
using a global system of antennae, the change
in baseline distance between the antennae can
be tracked and measured directly
Video:
3.) SLR:
- SLR stands for Satellite Laser Ranging and
does exactly what it sounds like
● SLR stations emit ultrashort pulses of
light at satellites that are equipped with
special reflectors
● This data gives extremely precise ranging
measurements that can be used in a
variety of ways
o
If you want to know more:
 http://ilrs.gsfc.nasa.gov/docs/slrover.pdf
4.) Satellite Altimetry:
- Measuring the topography (heights) of the
oceans using dual-band altimeters on satellites
o
Topex/Poseidon, Jason-1 and Jason-2
- Very useful in tracking climate change in both
the short term as well as long term
- Objectives:
http://sealevel.jpl.nasa.gov/science/scienceobjectives/
- Good flash presentations:
http://sealevel.jpl.nasa.gov/files/archive/ost/index.html
http://sealevel.jpl.nasa.gov/files/archive/Movie11.html
Is this important?
Global sea level has
risen about 3
millimeters (0.1 inch) a
year since
Topex/Poseidon (on
the left) began its
precise measurement
of sea surface height in
1993 and was followed
by Jason-1 in 2001. In
this graph, the vertical
scale represents
globally averaged sea
level. Seasonal
variations in sea level
have been removed to
show the underlying
trend. Image credit:
University of Colorado
Most important detail in
geodesy:
- Time! For any of these techniques to work, a
standard time reference needs to be used across
the board
o
o
You also need extremely accurate clocks.
Accurate clocks = good correlation of data between
multiple observation points
- Modern UTC:
http://upload.wikimedia.org/wikipedia/comm
ons/a/ad/Standard_time_zones_of_the_worl
d.png