12.201/12.501 Essentials of Geophysics

12.201/12.501 Essentials of Geophysics

Geodetic MethodsProf. Thomas Herring

[email protected]://www-gpsg.mit.edu/~tah

mailto:[email protected]

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 (>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.

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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

North

Equator

Geoid

gravity direction

Normal to ellipsoid

φgφa

Local equipotenital surfaceEarth's surface

P

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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.

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Example of methods: South Africa

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

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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1920’s 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

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

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

http://ilrs.gsfc.nasa.gov/

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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)



http://ivscc.gsfc.nasa.gov/

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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 < 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 0.1–10 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).

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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)

• Rings are called choke-rings (used to suppress multi-path)

Nearly all antennas are patch antennas (conducting patch mounted in insulating ceramic).

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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)

http://igscb.jpl.nasa.gov/








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 Improvement1993

2004

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Global Plate Motions

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Motions in CaliforniaRed 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 51.5±0.8 mmE 15.7±0.6 mmU 4.3±1.8 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.

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12.201/12.501 Essentials of Geophysics