A Historical A Historical Perspective on Perspective on

GeodesyGeodesy

Kristine M. LarsonDepartment of Aerospace Engineering Sciences

University of Colorado

OutlineOutline

Geodesy: 300 BC to 1970Geodesy: 300 BC to 1970

Space Geodesy: 1970 - Space Geodesy: 1970 -

GPS Geodesy: 1985 -GPS Geodesy: 1985 -

The FutureThe Future

What is Geodesy ?What is Geodesy ?

Geodesy is defined as the science of Geodesy is defined as the science of determining the determining the sizesize, , shapeshape and and gravitygravity fieldfield of the Earth. of the Earth.

If you know the size/shape of the If you know the size/shape of the Earth, you should also be able to Earth, you should also be able to figure out figure out wherewhere you are on the you are on the Earth.Earth.

Why would people care about Why would people care about the size and shape of the the size and shape of the

Earth?Earth?

Intellectual curiousity. Intellectual curiousity. Navigation.Navigation. Land boundaries.Land boundaries.

The Size of the EarthThe Size of the Earth

Pythagoras (~569 BC) and Aristotle Pythagoras (~569 BC) and Aristotle (384 BC) postulated that the Earth (384 BC) postulated that the Earth was a sphere.was a sphere.

Eratosthenes (276 BC) calculated the Eratosthenes (276 BC) calculated the circumference of the Earth incircumference of the Earth in

On the measurement of the EarthOn the measurement of the Earth

Is the Earth a sphere?Is the Earth a sphere?

If so, the If so, the measurement of a measurement of a degree should be the degree should be the same everywhere.same everywhere.

How do you measure How do you measure a degree? In 1615 a degree? In 1615 Willebrord Snell first Willebrord Snell first developed a developed a triangulation networktriangulation network in Holland. in Holland. 1580-1626

In 1617, Snell published In 1617, Snell published Eratosthenes Eratosthenes BatavusBatavus which described his proposal to use which described his proposal to use triangulation to determine the radius of the triangulation to determine the radius of the Earth.Earth.

baseline

V = baseline

AB

3. Use Law of Sines

€

sinαA

=sin β

B=

sinγV

1. Measure baseline V

2. Measure and

4. Now you know A, B, and V.

5. Spherical trig: positions

A

1. A is your new baseline

2. Measure and

3. Etc.

Himalaya SurveyingHimalaya Surveying

The theodolite used in The theodolite used in the Great Survey of the Great Survey of India weighed 1100 India weighed 1100 lbs.lbs.

If no high structures If no high structures were available, they were available, they needed to be built.needed to be built.

MeasurementsMeasurements

Heliotrope=“turn the Heliotrope=“turn the sun.”sun.”

Limited to sunny Limited to sunny days.days.

Night-time Night-time observations made in observations made in late 19th century late 19th century using lamps.using lamps.

Is the Earth a Sphere?Is the Earth a Sphere?

Define the Earth's equatorial radius Define the Earth's equatorial radius Re and polar radius Rp.Re and polar radius Rp.

Re > RpRe > Rp oblate spheroid oblate spheroid (British,Newton)(British,Newton)

Re < Rp Re < Rp prolate spheroid prolate spheroid

(French, Cassini)(French, Cassini)

What did the data say?What did the data say?

Pendulum clocks (T = sqrt(L/g)) from Pendulum clocks (T = sqrt(L/g)) from South America (Jean Richer) ran 2.5 South America (Jean Richer) ran 2.5 minutes/day slower than in Paris.minutes/day slower than in Paris.

Arc measurements in France - Arc measurements in France - Pyrenees to Dunkerque.Pyrenees to Dunkerque.

Cassini himself had observed the Cassini himself had observed the oblateness of Jupiter’s moons, but oblateness of Jupiter’s moons, but said the “Earth was different.”said the “Earth was different.”

What did theory say?What did theory say?

Newton’s Newton’s gravitational gravitational mechanics mechanics predicted the predicted the Earth’s shape Earth’s shape should be oblate.should be oblate.

He predicted a He predicted a difference of difference of 1/230. 1/230.

French Royal Academy of French Royal Academy of SciencesSciences

Expedition to Lapland: Maupertuis, Expedition to Lapland: Maupertuis, 3 academicians, astronomer, and a 3 academicians, astronomer, and a priest. priest.

Expedition to Peru: Bouguer and de Expedition to Peru: Bouguer and de La Condamine, botanist, engineer, La Condamine, botanist, engineer, surgeon, 2 mathematicianssurgeon, 2 mathematicians

LaplandLapland

““great Flies with great Flies with green Heads”green Heads”

Bad weather. Bad weather. Limited sunlight.Limited sunlight. Shipwrecked in the Shipwrecked in the

Baltic on their return.Baltic on their return. Maupertuis brought Maupertuis brought

two native girls back two native girls back to Paris.to Paris.

10 month journey10 month journey Natives didn’t believe Natives didn’t believe

anyone would care.anyone would care. Bad weather.Bad weather. Altitude sickness.Altitude sickness. Surgeon killed in a Surgeon killed in a

riot.riot. Botanist lost his data; Botanist lost his data;

nervous breakdown.nervous breakdown.

PeruPeru

1735-17441735-17441736-17371736-1737

What was the result?What was the result?

Newton predicted a difference in Newton predicted a difference in polar and equatorial radii of 1/230. polar and equatorial radii of 1/230.

By comparing the Lapland data with By comparing the Lapland data with triangulation data from France, flattening triangulation data from France, flattening was determined to be 1/217.was determined to be 1/217.

Modern values are 1/298.Modern values are 1/298. It was later determined that the It was later determined that the

observations were riddled with systematic observations were riddled with systematic errors!errors!

Led geodetic survey Led geodetic survey of the state of of the state of Hanover (1818).Hanover (1818).

Triangulated during Triangulated during the day, analyzed the day, analyzed data at night (using data at night (using the least squares the least squares method he invented method he invented in his spare time).in his spare time).

Gauss also invented Gauss also invented the heliotrope.the heliotrope.

Johann C.F. GaussJohann C.F. Gauss1777-1855

Geodesy in the New WorldGeodesy in the New World

Mason-Dixon LineMason-Dixon Line

Named after British geodesists Named after British geodesists (astronomers) Charles Mason and (astronomers) Charles Mason and Jeremiah Dixon.Jeremiah Dixon.

Measured to settle dispute between Measured to settle dispute between Pennsylvania and Maryland (Delaware)Pennsylvania and Maryland (Delaware)

The court determined:The court determined: the boundary the boundary should be fixed at the latitude 39°43' Northshould be fixed at the latitude 39°43' North

Coast and Geodetic SurveyCoast and Geodetic Survey

Thomas Jefferson Thomas Jefferson founded the Coast founded the Coast Survey in 1807.Survey in 1807.

Renamed the Coast Renamed the Coast and Geodetic Survey and Geodetic Survey in 1878.in 1878.

Least squares used to Least squares used to adjust the adjust the triangulation triangulation networks.networks.

William BowieWilliam Bowie

Head of the C & GS.Head of the C & GS. Co-founder of the American Co-founder of the American

Geophysical Union (AGU)Geophysical Union (AGU) ““A dozen or more A dozen or more

mathematicians were able to mathematicians were able to work simultaneously, and in 15 work simultaneously, and in 15 months the readjustment was months the readjustment was complete.”complete.”

1872-1940

A Geodesist’s NightmareA Geodesist’s Nightmare

H. Reid

Measuring Fault MotionsMeasuring Fault Motionsbefore Space Geodesybefore Space Geodesy

Up through the 1980’s there were Up through the 1980’s there were extensive triangulation and later extensive triangulation and later trilateration networks in regions of trilateration networks in regions of deformation.deformation.

Coast and Geodetic Survey/National Coast and Geodetic Survey/National Geodetic SurveyGeodetic Survey

U.S. Geological SurveyU.S. Geological Survey

Trilateration

USGS Trilateration NetworksOwens Valley

Late 1970’s: NASA Gets Interested

Very Long Baseline Interferometry (VLBI)

Atlantic spreading measured by VLBI over 6 years (1986).

Ref: Tom Herring

Satellite Laser Ranging (SLR)

NASA Crustal Dynamics NASA Crustal Dynamics ProjectProject

They developed very sophisticated They developed very sophisticated hardware.hardware.

They confirmed that the mid-Atlantic ridge They confirmed that the mid-Atlantic ridge was spreading; first measurements of was spreading; first measurements of Basin and Range extension.Basin and Range extension.

NASA got bored with the science.NASA got bored with the science.

Lots of interesting problems remained!

Global Positioning SystemGlobal Positioning System

First launched in First launched in 1978; constellation 1978; constellation complete in 1995.complete in 1995.

Could GPS bridge the Could GPS bridge the gap between EDM gap between EDM and VLBI/SLR?and VLBI/SLR?

Crustal deformation Crustal deformation campaigns began ~20 campaigns began ~20 years ago.years ago.

Southern California Southern California BorderlandsBorderlands

Campaign-style GPSCampaign-style GPS

8 hour averagesof 5 minute observations.

“short” baselines

7 GPS satellites

Continuous GPSContinuous GPS

Global positions; 12-15 satellites; solutions 1/wk

24 hr avg of 5 min observations

Continuous GPS Continuous GPS

Larson and Freymueller, 1995; Larson et al., 1997

How do you relate velocities How do you relate velocities to plate motions?to plate motions?

€

rv =

r ω ×

r r

CurrentlyCurrently

28 satellites; 5 min observations -

24 hour average positions

Why (part 1) ?Why (part 1) ?

Why (part 2)?Why (part 2)?

Tracking network before and now

“global” tracking sites in 1987

Why (part 3)?Why (part 3)?

Why (part 4)?Why (part 4)?GPS benefited enormously from the legacy GPS benefited enormously from the legacy of VLBI and SLR. of VLBI and SLR. Specifically, VLBI had faced and solved Specifically, VLBI had faced and solved many of the significant problems that would many of the significant problems that would impact GPS, particularly modeling the wet impact GPS, particularly modeling the wet troposphere.troposphere.GPS’ definition of the “terrestrial” reference GPS’ definition of the “terrestrial” reference frame continues to benefit from contributions frame continues to benefit from contributions of VLBI and SLR. of VLBI and SLR.

What kind of scientific What kind of scientific problems has GPS geodesy problems has GPS geodesy

addressed?addressed?

Precise Navigation and Timing

GRACE and JASON

Postglacial ReboundPostglacial Rebound

Postglacial Rebound

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Churchill, Manitoba

Michael Heflin, JPL

Source: Larson and van Dam

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Interseismic deformation

Coseismic

deformation

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Postseismic deformation Sources: E. Calais and M. Heflin

Ref: Tom Herring

Cascadia Episodic

Tremor and Slip

Dragert and others, Pacific Geoscience Centre

Volcano MonitoringVolcano Monitoring

Kilauea Volcano

15 minute (filtered) averages of 5 minute observations

Larson et al. (2001).

Greenland Ice SheetGreenland Ice Sheet

Zwally et al., 2002, ScienceSwiss Camp

Full constellation; observations 10 hours every 10 days; Remove assumption that the receiver doesn’t move.

days

Seismology Seismology

Eberhart-Phillips et al., 2003 (Science)

Seismic InstrumentationSeismic Instrumentation

Andria Bilich PhD

Preliminary ResultsPreliminary Results

2003 September 25 Tokachi-Oki (Hokkaido) Earthquake

1 Hz GPS Position Estimates

Kyuhong

Choi PhD

1 Hz GPS Position Estimates

Earthscope: Exploring the Earthscope: Exploring the Structure and Evolution of the Structure and Evolution of the

North AmericanNorth American

What does this have to do What does this have to do with democracy?with democracy?

UNAVCO Members

AcknowledgementsAcknowledgements

NSF NSF NASANASA UNAVCOUNAVCO IGS, JPL, IGS, JPL,

CORSCORS SOPAC, CDDISSOPAC, CDDIS USGS USGS