Gravity and Isostasy 2

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  • Expected deflection of a plumb bob (highly exaggerated), due to the attraction of the mass of a mountain range.
  • the plumb bob used to define vertical in the astronomical measurements
  • Gravity and Isostasy 2

    1. 1. Ali Oncel [email_address] Department of Earth Sciences KFUPM Gravity and Isostasy 2 Introduction to Geophysics Introduction to Geophysics-KFUPM
    2. 2. Previous Lecture <ul><li>Gravity and Isostasy </li></ul><ul><li>Isostatic Equilibrium </li></ul><ul><li>Topography of ocean floor </li></ul><ul><li>Two forms of isostatic uplift </li></ul><ul><li>Sign of Bouguer Anomaly in Ocean (+) and </li></ul><ul><li>Continent (-) </li></ul><ul><li>Examples from Saudi Arabia </li></ul>Introduction to Geophysics-KFUPM
    3. 3. Gravity Measurement <ul><li>Wednesday, 8.00 AM, May 17? </li></ul><ul><li>Any area you might suggest? </li></ul>Introduction to Geophysics-KFUPM
    4. 4. Introduction to Geophysics-KFUPM see Chapter 2 of Lowrie)
    5. 5. Gravity and Isostasy Introduction to Geophysics-KFUPM Whole Earth Geophysics ©1999 Robert J. Lillie Archdeacon Pratt pendulum/plumb-bob survey (1855)
    6. 6. The actual deflection for the Himalayas was less than expected , due to a deficiency of mass beneath the mountains. Introduction to Geophysics-KFUPM Expected deflection of a plumb bob ( highly exaggerated ), due to the attraction of the mass of a mountain range .
    7. 7. Introduction to Geophysics-KFUPM
    8. 8. Models of Isostasy Isostatic Equilibrium - Compensation Introduction to Geophysics-KFUPM
    9. 9. Airy Model Airy proposed that crust is thicker beneath mountains and thinner beneath the oceans. Excess mass under the oceans from a shallower, high density mantle. Mass deficiency beneath mountains due to crustal root. Mass Excess Mass Deficit Introduction to Geophysics-KFUPM
    10. 10. Pratt Pratt proposed that observation could be explained by lateral changes in density within a uniform thickness crust. Introduction to Geophysics-KFUPM
    11. 11. Introduction to Geophysics-KFUPM <ul><ul><li>Pratt compensation : body densities vary. </li></ul></ul><ul><ul><ul><li>(lateral density variations prop up orogens) </li></ul></ul></ul>Whole Earth Geophysics ©1999 Robert J. Lillie
    12. 12. Introduction to Geophysics-KFUPM <ul><ul><li>Airy compensation : body thicknesses vary. </li></ul></ul><ul><ul><li>(thick, low-density orogenic roots displace high-density mantle) </li></ul></ul>Whole Earth Geophysics ©1999 Robert J. Lillie
    13. 13. Introduction to Geophysics-KFUPM <ul><li>In reality, both conditions are at work. </li></ul>
    14. 14. P= ρ g z Where: P =pressure at the point within the earth ρ = average density of the material above the point G = acceleration due to gravity (9.8 m/s 2 ) 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 Isostasy Introduction to Geophysics-KFUPM Fig 8.18 of Lillie
    15. 15. P= ρ g h Where: P= pressure exerted by crustal block ρ = density of the crustal block h = thickness of the crustal block The pressure exerted by a crustal block for the models (Pratt/Airy) can be expressed as: Introduction to Geophysics-KFUPM Local Isostasy
    16. 16. Whole Earth Geophysics ©1999 Robert J. Lillie 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= ρ 2 gh 2 = ρ 3 gh 3 = ρ 4 gh 4 = ρ 5 gh 5 ρ 2, ρ 3, ρ 4, ρ 5 = density of each block h 2, h 3, h 4, h 5 = thickness of each block Introduction to Geophysics-KFUPM Local Isostasy : Pratt Model
    17. 17. P/g = ρ 2 h 2 = ρ 3 h 3 = ρ 4 h 4 = ρ 5 h 5 Dividing out a constant gravitational acceleration (g): For Pratt model shown above, ρ 5 < ρ 4 < ρ 3 < ρ 2 < ρ 1 Where ρ 1 is the density of Earth’s mantle. Introduction to Geophysics-KFUPM Local Isostasy : Pratt Model
    18. 18. P/g = ρ 5 h 5 =( ρ 2 h 4 + ρ 1 h’ 4 ) = ( ρ 2 h 3 + ρ 1 h’ 3 ) =( ρ 2 h 2 + ρ 1 h’ 2 ) = constant <ul><li>For Airy isostatic model given above, the pressure exerted at the depth of compensation (divided by g) is: </li></ul>h’ 2, h’ 3, h’ 4 = thickness of mantle column from the base of each crustal block to the depth of compensation ρ 2 < ρ 1 Only the thickest crustal block extends to the depth of compensation . Introduction to Geophysics-KFUPM Local Isostasy : Airy Model Mantle Density Crustal Density
    19. 19. Introduction to Geophysics-KFUPM
    20. 20. The Airy than the Pratt model is generally closer to Isostatic compensation. <ul><li>Illustrations for Airy Model as: </li></ul><ul><li>Regions with oceanic and continental crust </li></ul><ul><li>Thickened crust weighted down by mountains </li></ul>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. Introduction to Geophysics-KFUPM
    21. 21. CRUSTAL BUOYANCY Why does continental collision lead to the highest elevations of Earth? Parks and Plates ©2005 Robert J. Lillie Introduction to Geophysics-KFUPM
    22. 22. Parks and Plates ©2005 Robert J. Lillie Why does continental collision lead to the highest elevations of Earth? CRUSTAL BUOYANCY Introduction to Geophysics-KFUPM
    23. 23. Parks and Plates ©2005 Robert J. Lillie Why does continental collision lead to the highest elevations of Earth? CRUSTAL BUOYANCY Introduction to Geophysics-KFUPM
    24. 24. Small Buoyancy Parks and Plates ©2005 Robert J. Lillie Why does continental collision lead to the highest elevations of Earth? CRUSTAL BUOYANCY Introduction to Geophysics-KFUPM
    25. 25. Small Buoyancy Large Buoyancy Parks and Plates ©2005 Robert J. Lillie Why does continental collision lead to the highest elevations of Earth? CRUSTAL BUOYANCY Introduction to Geophysics-KFUPM
    26. 26. Parks and Plates ©2005 Robert J. Lillie 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 Introduction to Geophysics-KFUPM
    27. 27. CONTINENTAL COLLISION LEADS TO THE HIGHEST TOPOGRAPHY ON EARTH Introduction to Geophysics-KFUPM Collisional Mountain Range Parks and Plates © 2005 Robert J. Lillie

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