Physics

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Physics Chemistry of the EarthGravity II
Isostacy

• Jesse Fisher Lawrence

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History of Isostacy

• In the 18th and 19th century surveys of
  mountainous arias showed that the gravity was
  less than expected by the excess mass beneath
  high topography. Why?

Bouguers 1735 survey in Peru (the Andes) used a
pendulum to measure gravity variations. He
measured a 1/1331 variation in the period of a
pendulum.
T Period k physical properties of the pendulum
(length weight distribution) g gravity
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History of Isostacy

• Surveyor General of India (1830-1843), Everest
  surveyed the Himalayas with theodolites. He
  discovered the highest summit on Earth, which was
  named after him. The survey yielded discrepancies
  that he thought were errors, but where not. What
  were they?

These errors were due to excess mass.
Theodolite Survey
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History of Isostacy

• George Biddell Airy in 1855 proposed that the
  surface topography can be compensated by a
  thicker column of material beneath (Like
  icebergs most of the iceberg is beneath the
  water).

Everest
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History of Isostacy

• John Pratt 1854-59 proposed that density changes
  in the crust changes topography.

Everest
Tibetan Plateau
Topography
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Compensation Depth

• At some depth (The Compensation Depth) the
  cumulative load (???g?h?) at one location is
  equal to the load at another location (???g?h??

Pratt Model
Airy Model
?ch1?md1?ch2?md2 ?chn?mdn
?c1h1?c2h2 ?cn-1hn-1?cnhn
Note Plates must have no strength for isostatic
Models to work
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Flexural/Regional Support

• If the plates do have elastic strength, then
  topography can be supported.

Elastic Plate
No Elastic Strength
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Hawaii - Gravity Flexure
Hawaii Gravity -141 to 333 mGals

• Terrain-corrected Bouguer gravity anomaly map
• Highs over the islands
• Low gravity moat around the islands.

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Subduction Zones as Elastic Plates

• The old and cold subducting slab pulls the end of
  the slab down
• Flexural bulge next to trench
• Mariana trench matched well with an elastic
  thickness (thickness of strong region) of 28 km.

• Tonga trench requires plastic deformation above
  some yield strength.

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Isostatic Rebound

• Melting freezing of glaciers is much faster
  than plate response.
• Glaciers 100s to 1000s of years
• Plates 103 to 108 years
• Rate of plate change depends on the rigidity of
  the plate and the viscosity of the mantle.
• Only large ice loads cause flexure.
• Small Loads 100 km diameter
• Sensitive to upper mantle structure
• 0.5-1.0?1020 Pa s
• gt 75 km Elastic Thickness
• Large Loads 1000 km diameter
• Sensitive to deep structure
• 0.5?1020 Pa over 1021 Pa lower mantle

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Isostatic Rebound

• Scandinavia 10,000 years the end of an ice age
• About 2.5 km thick ice sheet melted
• Current peak uplift is 9 mm yr-1

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Viscous Flow Model

• Over longer periods of time resistance to force
  can be modeled as viscous flow (think of
  molasses).

Mountain Building
Erosion Deflection
Crust
Growing Root
Shrinking Root
Mantle
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Thermal Isostacy

• None of the previous model most of the Earths
  surface. Thermal isostacy is a combination of
  both Airy and Pratt isostacy.
• As an oceanic plates age, they
• Cool become more dense -Pratt Model
• Thicken -Airy Model

Old, Cold, Thick Dense
Young, Warm, Thin, Low Density
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• The End