PHYSICAL PROPERTIES of the EARTHS INTERIOR: DISTRIBUTION

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PHYSICAL PROPERTIES of the EARTHS INTERIOR
DISTRIBUTION ISOSTASY

• Densities of Minerals and Rocks
• Distribution of Density inside the Earth
• Isostasy

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Densities of Minerals and Rocks

• Density of most abundant rock forming minerals
  2.2-3.5 g/cm3 
• Density of ore minerals 4.0-8.0 g/cm3 (Schön,
  1998)

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(Schön, 1998)

• Sedimentary rocks
• Density mineral comp pores fractures
  filling material
• Density versus depth gt nonlinear

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• Density of pore (and rock) fluids
• The density (?) of liquids and gases is
  controlled by chemical
• composition, pressure (P) and temperature (T).
• P ? ? ?
• T ? ? ?
• Examples
• Fresh water 1 g/cm3
• Salt water 1.146 g/cm3
• Oil 0.85 g/cm3

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(Schön, 1998)

• Metamorphic rocks
• Density mineral comp. density of initial rock
  material degree of
• metamorphism thermodynamic condition and
  processes
• Range of density gt small, Density ? from
  acidic to basic

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(Schön, 1998)

• Magmatic rocks
• qtz ? gt density ?
• density ? gt from acidic to
  basic rocks

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(Schön, 1998)

• P ? gt Fractures cracks are closed. gt Density
  ?

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(Bott, 1982)

• Nafe-Drake Curve Water-saturated sediments
  sedimentary rocks
• Birch (1961) density gt ?a(m) bVp a,b
  constants Vp P-wave vel.
• Phase change Partial melting ?
• Anderson (1967) VpA(m) ?? A(m) constant, ?
  experimental constant

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(Bott, 1982)

• Coarse grained igneous rocks and eclogites
• Compressional wave velocities and densities in
  rocks

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(Plummer McGeary, 1991)

• Distribution of Density inside the Earth
• Average density of rocks in the Earth5.5 g/cm3

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Lateral Density Variations in the Mantle

• (Bott, 1982)

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• Substantial lateral density variations of
  relatively short wave length
• in the upper most mantle beneath ocean ridges and
  continental uplifts
• Longer wave length features of deeper origin
  which give rise to
• the satellite derived global gravity anomalies.
• gt 2500 km mantle and core-mantle level
• Density anomalies within the mantle are caused by
  chemical inhomogeneity or lateral temperature
  variation ( convection flow)
• gt Depth of phase transition 400 650 km !

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(Watts, 2001)

• Isostasy
• B ?block b ?fluid
• b/B ?block/ ?fluid

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• Archimedes principle
• The weight of a block that floats in a liquid is
  equal to the volume of liquid
• that is displaced.
• Pressure at the base of a column of rock beneath
  a mountain
• PIForce/Unit Areag x (Mass/Unit Area)
• ISOSTASY is a balance or equilibrium between
  adjacent blocks of brittle
• crust floating on the plastic upper mantle.

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(Plummer McGeary, 1991)
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(Plummer McGeary, 1991)
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• Isostatic compensation according to the Pratt and
  Airy Hypothesis
• Airy Hypothesis
• Example Young Mountain Belts
• r(h?c)/(?s-?c) ?c density of crust ?s density
  of substratum
• ?w density of sea water
• (Bott, 1982)

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• Pratt Hypothesis
• Example East African Rift
• ?(hD)constant
• ?h density of crust beneath mountain height h
• ?o density of crust beneath ocean of depth d
• ?r density of crust beneath ocean ridge of
  height h
• (Bott, 1982)

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Isostatic anomalyBouguer anomaly-computed
anomaly of rootBouguer anomaly
gobs-g?FAC-BCTCFree air anomaly gobs-g?FAC
This method is effective for the feature which
is about ten or more times wider than the depth
of compensation (Bott, 1982).
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(Bott, 1982)
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(Bott, 1982)
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Appendices
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The radial distribution of density ? (r)

• Assumptions
• The Earth is radially symmetric.
• It is in hydrostatic equilibrium.
• Increase in density with depth is caused by an
  adiabatic compression under hydrostatic pressure.
• The effects of thermal expansion, compositional
  and phase changes are not included.
• Each part, i.e. mantle,core are taken as
  homogeneous so that
• the density changes only due to composition not
  due to any phase change.
• The mean density of the Earth5.5 g/cm3
• Mass of the Earth6.0x1024 kg

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• d?/dr(d?/dP)(dP/dr)
• P hydrostatic pressure
• dP/dr
• Pg?h dP-gr?rdr r ? P ?
• grGMr/r2 dP-(GMr/r2) ?rdr dP/dr-(GMr/r2) ?r
  
• d?/dP
• K-dP/d? d?dV/V-d?/?
• K incompressibility
• d? cubic dilatation
• d?/dP- d?/Kd? ?d?/Kd??/K
• From , and
• d?/dr -(GMr/r2) ?r (?/K)

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• r is known. rRe-z
• Mr is known. MrMe-Mc
• ?r is known or assumption(3.3 g/cm3).
• Vp and Vs are known from seismology at
• the top of the mantle.
• d?/dr is calculated by Adams-Williams equation.

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• The calculation is repeated through mantle in the
  same manner until
• the mante-core boundary is reached. An initial
  guess for density is made
• at the top of the core. The calculations are
  repeated until the center of
• the Earth is reached. The accuracy of the
  calculations are tested by
• the total mass and the moment of inertia of the
  Earth.

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Calculation of gravity, pressure and elastic
parameters inside the Earth

• Incompressibility K and shear modulus ?
• ?(r), Vs(r), Vp(r) are known.

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Gravity and Pressure
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(Bott, 1982)
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(Bott, 1982)
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(Bott, 1982)
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REFERENCES

• Bott, M.H.P., 1982, The Interior of the Earth
  its structure, constitution and
• evolution, Elsevier, p 49-72, 162-166, 197-199,
  239
• (ITU Mustafa Inan Library, QE 28.2 .B68).
• Plummer C.C. and McGeary, D. 1991, Physical
  Geology, Wm.C. Brown Pub., p
• 381-384 (ITU Mustafa Inan Library, QE 28.2 .P58).
• Schön, J.H., 1998, Handbook of Geophysical
  Exploration, Seismic Exploration, V 18
• Physical Properties of rocks Fundamentals and
  Principles of Petrophysics,
• Pergamon press, p 62, 67, 68 (ITU Mustafa Inan
  Library, 431.6 P5 S34 1998).
• Watts, A.B., 2001, Isostasy and Flexure of the
  Lithosphere, Cambridge Univ. Press,
• P 14-21 (ITU, Mustafa Inan Library, QE 511 W38
  2001).