1. More observables: gravity and the geoid Isostasy “Perfect” adjustment not realistic… –Rigid crust, dynamic features in mantle mean that density anomalies do exist Ice cube  =.917 g/cm 3 (at 0 C) Water  =1 g/cm 3

2. Brief Isostasy Review/Exercise Ice cube  =.917 g/cm 3 (at 0 C) Water  =1 g/cm 3

3. Airy Pratt Types of Isostasy Each explains crustal elevations differently

4. Geodesy - study of Earth’s shape Today: –Describing the shape of the earth –What governs it? 1.Gravity 2.Mass anomalies 3.Dynamic processes (later) –Coming up- How do we measure the shape of the earth?

5. Levels of detail: –Sphere –Ellipsoid Accounts for 20km difference between poles and equator –? Describing Earth’s shape

6. Levels of detail: –Sphere –Ellipsoid Accounts for 20km difference between poles and equator –Other variations? Describing Earth’s shape

7. Topography, relief –What we are interested in Ellipsoid, spheroid –“best fit” simple shape Geoid –Gravitational equipotential surface (fluid should follow) Describing Earth’s shape

8. Geoid: the actual equipotential surface at sea level

11. Model detail depends on spatial scale, timeframe, observation type.

13. Early Geodesy Initial methods: Distances and angles Distance: –Knotted ropes (stretch!) –Chains (expand!) Angles –Tripods and telescopes Ancient surveyors 1400-1390 B.C.

14. Initial methods: Distances and angles Distance: –Knotted ropes (stretch!) –Chains (expand!) Angles –Tripods and telescopes Ramsden chain, used in 1784 near London Early Geodesy

15. Point A to Point B –Lots of trigonometry!

16. Early Geodesy Goal: just measuring shape/size Survey of India, 1767 –3000 stations –Height of Mt Everest –Dense jungles, diseases Late 1800’s –First measured EQ –Go resurvey, see how much ground moved! Up til 1970’s - not much change From Royal Geol. Survey archives

17. Next steps Plate tectonics more widely accepted Explosion of leveling, triangulation, trilateration Very Long Baseline Interferometry (VLBI) stations “catch” relative plate motions VLBI setup Laser-based total station surveying

18. Scale 10 mm/yr Very Long Baseline Interferometry (VLBI) determinations of plate velocities

19. Next: GPS! Global Positioning System (GPS) –Types of GPS: Hand-held: accuracy ~10-30 m Campaign mode: accuracy ~1-5 cm/yr Continuous mode: accuracy ~1-3 mm/yr

20. More GPS Plate motions measured by GPS Problems: –Only measure deformation at specific points –Need to go there for each measurement –Or…build continuous observation site (expensive!)

21. Density contrasts cause geoid upward deflection But motion of blob in mantle causes deflection in density contrasts at surface and internal boundaries (depending on viscosity) Internal mass effects upon geoid From: Hager, 1984