1. A Historical Perspective on Geodesy
Kristine M. Larson
Department of Aerospace Engineering Sciences
University of Colorado

2. Outline Geodesy: 300 BC to 1970 Space Geodesy: 1970 -
GPS Geodesy:
The Future

3. What is Geodesy ?
Geodesy is defined as the science of determining the size, shape and gravity field of the Earth.
If you know the size/shape of the Earth, you should also be able to figure out where you are on the Earth.

4. Why would people care about the size and shape of the Earth?
Intellectual curiousity.
Navigation.
Land boundaries.

5. The Size of the Earth
Pythagoras (~569 BC) and Aristotle (384 BC) postulated that the Earth was a sphere.
Eratosthenes (276 BC) calculated the circumference of the Earth in
On the measurement of the Earth

7. Is the Earth a sphere?
If so, the measurement of a degree should be the same everywhere.
How do you measure a degree? In 1615 Willebrord Snell first developed a triangulation network in Holland.

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

9. 1. Measure baseline V
2. Measure a, b, and g
3. Use Law of Sines
4. Now you know A, B, and V. B g A
5. Spherical trig: positions a b
V = baseline

10. 1. A is your new baseline
2. Measure a, b, and g
3. Etc. g a A b

11. Himalaya Surveying
The theodolite used in the Great Survey of India weighed 1100 lbs.
If no high structures were available, they needed to be built.

12. Measurements Heliotrope=“turn the sun.” Limited to sunny days.
Night-time observations made in late 19th century using lamps.

13. Is the Earth a Sphere?
Define the Earth's equatorial radius Re and polar radius Rp.
Re > Rp oblate spheroid (British,Newton)
Re < Rp prolate spheroid
(French, Cassini)

14. What did the data say?
Pendulum clocks (T = sqrt(L/g)) from South America (Jean Richer) ran 2.5 minutes/day slower than in Paris.
Arc measurements in France - Pyrenees to Dunkerque.
Cassini himself had observed the oblateness of Jupiter’s moons, but said the “Earth was different.”

15. What did theory say?
Newton’s gravitational mechanics predicted the Earth’s shape should be oblate.
He predicted a difference of 1/230.
Figure stolen from

16. French Royal Academy of Sciences
Expedition to Lapland: Maupertuis, 3 academicians, astronomer, and a priest.
Expedition to Peru: Bouguer and de La Condamine, botanist, engineer, surgeon, 2 mathematicians

17. Lapland Peru 1736-1737 1735-1744 “great Flies with green Heads”
Bad weather.
Limited sunlight.
Shipwrecked in the Baltic on their return.
Maupertuis brought two native girls back to Paris.
10 month journey
Natives didn’t believe anyone would care.
Bad weather.
Altitude sickness.
Surgeon killed in a riot.
Botanist lost his data; nervous breakdown.

18. What was the result?
Newton predicted a difference in polar and equatorial radii of 1/230.
By comparing the Lapland data with triangulation data from France, flattening was determined to be 1/217.
Modern values are 1/298.
It was later determined that the observations were riddled with systematic errors!

19. Johann C.F. Gauss
Led geodetic survey of the state of Hanover (1818).
Triangulated during the day, analyzed data at night (using the least squares method he invented in his spare time).
Gauss also invented the heliotrope.

20. Geodesy in the New World
Known for demarking the boundary between the North and the South.
4 years, 233 miles

21. Mason-Dixon Line
Named after British geodesists (astronomers) Charles Mason and Jeremiah Dixon.
Measured to settle dispute between Pennsylvania and Maryland (Delaware)
The court determined: the boundary should be fixed at the latitude 39°43' North

22. Coast and Geodetic Survey
Thomas Jefferson founded the Coast Survey in 1807.
Renamed the Coast and Geodetic Survey in 1878.
Least squares used to adjust the triangulation networks.

23. William Bowie Head of the C & GS.
Head of the C & GS.
Co-founder of the American Geophysical Union (AGU)
“A dozen or more mathematicians were able to work simultaneously, and in 15 months the readjustment was complete.”

24. A Geodesist’s Nightmare

26. H. Reid

27. Measuring Fault Motions before Space Geodesy
Up through the 1980’s there were extensive triangulation and later trilateration networks in regions of deformation.
Coast and Geodetic Survey/National Geodetic Survey
U.S. Geological Survey

28. Trilateration

29. USGS Trilateration Networks
Owens Valley

30. Late 1970’s: NASA Gets Interested
Big, Complicated, Expensive

31. Very Long Baseline Interferometry (VLBI)

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

33. Ref: Tom Herring

34. Satellite Laser Ranging (SLR)

35. NASA Crustal Dynamics Project
They developed very sophisticated hardware.
They confirmed that the mid-Atlantic ridge was spreading; first measurements of Basin and Range extension.
NASA got bored with the science.

36. Lots of interesting problems remained!

37. Global Positioning System
First launched in 1978; constellation complete in 1995.
Could GPS bridge the gap between EDM and VLBI/SLR?
Crustal deformation campaigns began ~20 years ago.
Much cheaper and more portable; don’t need adults to run the euqipment.

38. Southern California Borderlands

39. Campaign-style GPS 8 hour averages of 5 minute observations.
“short” baselines
7 GPS satellites

40. Continuous GPS Global positions; 12-15 satellites; solutions 1/wk
24 hr avg of 5 min observations

41. Continuous GPS
Larson and Freymueller, 1995; Larson et al., 1997

42. How do you relate velocities to plate motions?

43. Currently 28 satellites; 5 min observations -
24 hour average positions

44. Why (part 1) ?

45. Why (part 2)? Tracking network before and now
“global” tracking sites in 1987

46. Why (part 3)?

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

48. What kind of scientific problems has GPS geodesy addressed?

49. Precise Navigation and Timing
GRACE and JASON

50. Postglacial Rebound

51. Postglacial Rebound Churchill, Manitoba Source: Larson and van Dam
Michael Heflin, JPL

52. Interseismic deformation
Coseismic
deformation
Postseismic deformation
Sources: E. Calais and M. Heflin

53. Ref: Tom Herring

54. Cascadia Episodic Tremor and Slip
Dragert and others, Pacific Geoscience Centre

55. Volcano Monitoring
15 minute (filtered) averages of 5 minute observations
Kilauea Volcano
Larson et al. (2001).

56. Greenland Ice Sheet
Swiss Camp
Zwally et al., 2002, Science

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

58. Seismology
Eberhart-Phillips et al., 2003 (Science)

59. Seismic Instrumentation
Andria Bilich PhD

60. Preliminary Results

61. 2003 September 25 Tokachi-Oki
(Hokkaido) Earthquake

62. 1 Hz GPS Position Estimates
Kyuhong
Choi PhD

63. 1 Hz GPS Position Estimates

64. Earthscope: Exploring the Structure and Evolution of the North American

65. What does this have to do with democracy?
UNAVCO Members

66. Acknowledgements
NSF
NASA
UNAVCO
IGS, JPL, CORS
SOPAC, CDDIS
USGS