12.201/12.501 Essentials of Geophysics

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12.201/12.501 Essentials of Geophysics

• Geodetic Methods
• Prof. Thomas Herring
• tah_at_mit.edu
• http//www-gpsg.mit.edu/tah

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Topics

• History of geodesy
• Space based methods
• VLBI/SLR
• GPS (Friday).

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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 (gt300
  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.

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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).

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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).

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Geodetic coordinates Latitude
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Positional Geodesy Methods

• Triangulation Dates from 1600s 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.

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Example of methods South Africa
The Meridian Arc of Abbe de Lacaille Measured
in 1751 to help determine shape of Earth.
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Later measurements 1840-1846
Typical sites distances are 20-50 km.Points are
located on tops of mountains typicallyThe
baseline measurement was in Cape Town.
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1920s triangulation network
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Densification
In tectonically active area, these old survey
results can be used to get strain accumulation
estimates with up to 150 year time spans.
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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
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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.

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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 kgLAGEOS II Launched 1992,
5616-1950 km altitude, 52 deg Inclination, 400
km60 cm diameter spheres
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Current SLR network (11/04)
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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)
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Current VLBI Network (11/04)
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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

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Global Positioning System (GPS)
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GPS Original Design

• Started development in the late 1960s as
  NAVY/USAF project to replace Doppler positioning
  system
• Aim Real-time positioning to lt 10 meters,
  capable of being used on fast moving vehicles.
• Limit civilian (non-authorized) users to 100
  meter positioning.

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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

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Latest Block IIR satellite(1,100 kg)
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Measurements

• Measurements
• Time difference between signal transmission from
  satellite and its arrival at ground station
  (called pseudo-range, precise to 0.110 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).

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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).

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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)

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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.
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Ground Track
Paths followed by satellite along surface of
Earth.
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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).

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GPS Antennas (for precise positioning)
Nearly all antennas are patch antennas
(conducting patch mounted in insulating ceramic).
Rings are called choke-rings (used to suppress
multi-path)
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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)

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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).

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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
  )

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IGS Network
Currently over 400 stations in network
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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).

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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

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Orbit Improvement
1993
2004
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Global Plate Motions
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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
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Hector Mine co-seismic
Brown dots are small earthquakes Green lines are
faults
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Post-seismic Estimates
As more earthquakes are seen with GPS,
deformations after earthquakes are clearer Here
we show log dependence to the behavior.
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WIDC (74 km from epicenter)Coseismic offset
removed
N 51.50.8 mmE 15.70.6 mmU 4.31.8 mm
Log amplitude N 4.5 0.3 mmE 0.7 0.2 mmU 3.3
0.7 mm
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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)
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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
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GPS Measured propagating seismic waves
Data from 2002 Denali earthquake
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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.