Gravity and Isostasy 2

Rob

ert J

. Li l l

i eR

ober

t J. L

i l li e

Himalayas, I ndia/ Tibet

Very High Mountains During Collision

Parks and Plates©2005 Robert J. Lillie

Ali [email protected]

Department of Earth SciencesKFUPM

Gravity and Isostasy 2

Introduction to GeophysicsIn

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Previous Lecture

Gravity and IsostasyIsostatic EquilibriumTopography of ocean floorTwo forms of isostatic upliftSign of Bouguer Anomaly in Ocean (+) andContinent (-)Examples from Saudi Arabia

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Gravity Measurement

Wednesday, 8.00 AM, May 17?Any area you might suggest?

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see Chapter 2 of Lowrie)Intr

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Gravity and IsostasyIn

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Whole Earth Geophysics ©1999 Robert J. Lillie

Archdeacon Pratt pendulum/plumb-bob survey (1855)

The actual deflection for the Himalayas was less than expected, due to a deficiency of mass beneath the mountains.In

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Expected deflection of a plumb bob (highly exaggerated), due to the attraction of the mass of a mountain range.

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Models of Isostasy Isostatic Equilibrium - Compensation

Airy Pratt

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Airy Model

Airy proposed that crust is thicker beneath mountains andthinner beneath the oceans.

Excess mass under the oceans from a shallower, high densitymantle. Mass deficiency beneath mountains due to crustal root.

Mass Excess

Mass Deficit

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Pratt

Pratt proposed that observation could be explained by lateral changes in density within a uniform thickness crust.

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Pratt compensation: body densities vary.

(lateral density variations prop up orogens)


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Airy compensation: body thicknesses vary.(thick, low-density orogenic roots displace high-

density mantle)

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•In reality, both conditions are at work.

P=ρ g zWhere:

P =pressure at the point within the earth

ρ = average density of the material above the pointG = acceleration due to gravity

(9.8 m/s2)Z =depth

Hydrostatic pressure is the pressure exerted on a point within a body of water. Similarly, pressure at a given depth within the Earth can be viewed as a Lithostatic pressure

Local IsostasyIn

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Fig 8.18 of Lillie

P=ρ g h

Where:P=pressure exerted by crustal blockρ = density of the crustal blockh= thickness of the crustal block

The pressure exerted by a crustal block for the models (Pratt/Airy) can be expressed as:

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Local Isostasy


The pressure must be the same everywhere at the depth of compensation in two models (Pratt/Airy).

The base of each block for the Pratt model is at the exact depth of compensation, as:P= ρ2gh2 =ρ3gh3 =ρ4gh4 = ρ5gh5 ρ2, ρ3, ρ4, ρ5= density of each blockh2, h3, h4, h5= thickness of each blockIn

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Local Isostasy : Pratt Model

P/g= ρ2h2 =ρ3h3 =ρ4h4 = ρ5h5

Dividing out a constant gravitational acceleration (g):

For Pratt model shown above,

ρ5<ρ4<ρ3 <ρ2 <ρ1

Where ρ1 is the density of Earth’s mantle.

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Local Isostasy : Pratt Model

P/g= ρ5h5 =(ρ2h4 + ρ1h’4) = (ρ2h3 + ρ1h’3) =(ρ2h2 + ρ1h’2) =constant

•For Airy isostatic model given above, the pressure exerted at the depth of compensation (divided by g) is:

h’2, h’3, h’4 = thickness of mantle column from the base of each crustal block to the depth of compensation

MantleDensity

CrustalDensity

ρ2 < ρ1

Only the thickest crustal block extends to the depth of compensation.

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Local Isostasy : Airy Model

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The Airy than the Pratt model is generally closer to Isostatic compensation.

• Illustrations for Airy Model as:

a. Regions with oceanic and continental crust

b. Thickened crust weighted down by mountains

According to Airy model, the crustal root beneath elevated regions is appeared to be typically 5 to 8 times the height of the topographic relief.

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CRUSTAL BUOYANCY

Why does continental collision lead to the highest elevations of Earth?

Parks and Plates©2005 Robert J. LillieIn

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CRUSTAL BUOYANCY

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Small Buoyancy



CRUSTAL BUOYANCY

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Small Buoyancy

Large Buoyancy



CRUSTAL BUOYANCY

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CONTINENTAL COLLISION LEADS TO THE HIGHEST TOPOGRAPHY ON EARTH

“Millions of years ago India and an ancient ocean called the Tethys Ocean were sat on a tectonic plate. This plate was moving northwards towards Asia at a rate of 10 centimetres per year. The Tethys oceanic crust was being subducted under the Asian Continent. The ocean got progressively smaller until about 55 milion years ago when India 'hit' Asia. There was no more ocean left to lubricate the subduction and so the plates welled up to form the High Plateau of Tibet and the Himalayan Mountains. The continental crust under Tibet is over 70 kilometres thick. North of Katmandu, the capital of Nepal, is a deep gorge in the Himalayas. the rock here is made of schist and granite with contorted and folded layers of marine sediments which were deposited by the Tethys ocean over 60 million years ago.”

Source: http://www.moorlandschool.co.uk/earth/tectonic.htm

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CONTINENTAL COLLISION LEADS TO THE HIGHEST TOPOGRAPHY ON EARTH

http://www.moorlandschool.co.uk/earth/tectonic.htm

Collisional Mountain Range


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Gravity and Isostasy 2

Technology

Transcript of Gravity and Isostasy 2