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Structure of the Earth

 Known structureEdit

The interior of the Earth, like that of the other terrestrial planets, is divided into layers by their chemical or rheological properties. The Earth has an outer silicate solid crust, a highly viscous mantle, a liquid outer core that is much less viscous than the mantle, and a solid inner core. The crust is separated from the mantle by the Mohorovičić discontinuity, and the thickness of the crust varies: averaging 6 km under the oceans and 30–50 km on the continents.[1] The inner core may rotate at a slightly higher angular velocity than the remainder of the planet, advancing by 0.1–0.5° per year.[2]

Geologic layers of the Earth[3]
Earth-crust-cutaway-english

Earth cutaway from core to exosphere. Not to scale.
Depth[4]
km
Component Layer Density
g/cm³
0–60 Lithosphere[note 1]
0–35 ... Crust[note 2] 2.2–2.9
35–60 ... Upper mantle 3.4–4.4
35–2890 Mantle 3.4–5.6
100–700 ... Asthenosphere
2890–5100 Outer core 9.9–12.2
5100–6378 Inner core 12.8–13.1

The internal heat of the planet is probably produced by the radioactive decay of potassium-40, uranium-238 and thorium-232 isotopes. All three have half-life decay periods of more than a billion years.[5] At the center of the planet, the temperature may be up to 7,000 K and the pressure could reach 360 GPa.[6] A portion of the core's thermal energy is transported toward the crust by Mantle plumes; a form of convection consisting of upwellings of higher-temperature rock. These plumes can produce hotspots and flood basalts.[7]

Characteristics of The asthenosphere Edit

Earthquake wave paths

Mapping the interior of the Earth with earthquake waves.

The asthenosphere is a portion of the upper mantle just below the lithosphere that is involved in plate movements and isostatic adjustments. In spite of its heat, pressures keep it plastic, and it has a relatively low density. Seismic waves pass relatively slowly through the asthenosphere, compared to the overlying lithospheric mantle, thus it has been called the low-velocity zone. This was the observation that originally alerted seismologists to its presence and gave some information about its physical properties, as the speed of seismic waves decreases with decreasing rigidity.

Under the thin oceanic plates the asthenosphere is usually much closer to the seafloor surface, and at mid-ocean ridges it rises to within a few kilometers of the ocean floor.

The upper part of the asthenosphere is believed to be the zone upon which the great rigid and brittle lithospheric plates of the Earth's crust move about. Due to the temperature and pressure conditions in the asthenosphere, rock becomes ductile, moving at rates of deformation measured in cm/yr over lineal distances eventually measuring thousands of kilometers. In this way, it flows like a convection current, radiating heat outward from the Earth's interior. Above the asthenosphere, at the same rate of deformation, rock behaves elastically and, being brittle, can break, causing faults. The rigid lithosphere is thought to "float" or move about on the slowly flowing asthenosphere, creating the movement of crustal plates described by Plate tectonics

Speed of P-wavesEdit

The speed of P-waves is given by

v_p= \sqrt{ \frac {K+\frac{4}{3}\mu} {\rho}}= \sqrt{ \frac{\lambda+2\mu}{\rho}}

where K is the bulk modulus (the modulus of incompressibility) \mu, the first Lamé parameter, is the shear modulus (modulus of rigidity), \rho is the density of the material through which the wave propagates, and \lambda is second Lamé parameter.

Of these, density shows the least variation, so the velocity is mostly controlled by K and μ.

The elastic moduli P-wave modulus, M, is defined so that M = K + 4\mu/3 and thereby v_p = \sqrt{M/\rho}.

Typical values for P-wave velocity in earthquakes are in the range 5 to 8 km/s .[8]

S waveEdit

\nabla^2(\nabla\times\boldsymbol{u})-\frac{1}{\beta^2}\frac{\partial^2(\nabla\times\boldsymbol{u})}{\partial t^2}=0

which is simply the wave equation applied to the curl of u with a velocity \beta satisfying \beta^2=\frac{\mu}{\rho}

where \tau is the stress, \lambda and \mu are the Lamé parameters (with \mu as the shear modulus).

This describes S-wave propagation. Taking the divergence of seismic wave equation in homogeneous media instead of the curl, yields an equation describing P-wave propgation.

Rayleigh wave dispersion Edit

DispersionRayleighWave

Dispersion of Rayleigh waves in a thin gold film on glass.[1]

Rayleigh waves on ideal, homogeneous and flat elastic solids show no dispersion. However, if a solid or structure has a density or sound velocity that varies with depth, Rayleigh waves become dispersive. One example is Rayleigh waves on the Earth's surface: those waves with a higher frequency travel more slowly than those with a lower frequency. This occurs because a Rayleigh wave of lower frequency has a relatively long wavelength. The displacement of long wavelength waves penetrates more deeply into the Earth than short wavelength waves. Since the speed of waves in the Earth increases with increasing depth, the longer wavelength (low frequency) waves can travel faster than the shorter wavelength (high frequency) waves. Rayleigh waves thus often appear spread out on seismograms recorded at distant earthquake recording stations. It is also possible to observe Rayleigh wave dispersion in thin films or multilayed structures.

Inverse biquadrate gravityEdit

We assume the density of earth is the same as that of moon and Planets are from the sun(CBB). Thus there three density available: the density of sun, moon and crust. From those values, we suggest the structure of the earth.

Simple crust and sun density core modelEdit

radius of core 
R_x= ((\rho_e - \rho_c)/(\rho_s - \rho_c) )^{1/3} R_e

where 
R_e =6380km


\rho_e = 228
 
\rho_c = 2.6

\rho_s = 6.79 \rho_e


R_x= 3358km

Crust-Mantle-Core ModelEdit

depth of core =5100km

depth of crust =35km


then the density of mantle is given as follows 
\rho_m = ( \rho_e r_e^3 + \rho_c r_m^3 -\rho_s r_c^3 - \rho_c r_e^3 ) /(r_m^3 -r_c^3)


\rho_m = 221

Crust-Mantle-Outer Core-Inner Core modelEdit

depth of inner core =5100km

depth of outer core = 2890km

depth of crust = 35km


\rho_{ic} =( \rho_m +\rho_s) /2 = 775.36

then


\rho_{oc} = 260.9

Crust-Upper Mantle-Lower Mantle-Outer Core-Inner Core modelEdit

Gravitational density and temperature

gravitational mass density and temperature

depth of inner core =5100km~

depth of outer core = 2890km~

depth of upper mantle = 35~60km

depth of crust = ~35km



\rho_{um} =( \rho_m +\rho_c) /2 = 111.7


\rho_{lm} = 222.5

name depth density
crust ~35km 2.6
upper mantle ~60km 111.7
lower mantle ~2890km 222.5
outer core ~5100km 260.9
inner core ~6378km 775.4

Crust-Lithosphere-Athenosphere-Mantle-Outer Core-Inner Core modelEdit

See alsoEdit

Notes and referencesEdit

  1. Tanimoto, Toshiro (1995). Thomas J. Ahrens. ed.. Crustal Structure of the Earth. Washington, DC: American Geophysical Union. ISBN 0-87590-851-9, http://www.agu.org/reference/gephys/15_tanimoto.pdf. Retrieved on 3 February 2007. 
  2. Kerr, Richard A. (2005-09-26). "Earth's Inner Core Is Running a Tad Faster Than the Rest of the Planet". Science 309 (5739): 1313. doi:10.1126/science.309.5739.1313a. 
  3. Jordan, T. H. (1979). "Structural Geology of the Earth's Interior". Proceedings National Academy of Science 76 (9): 4192–4200. doi:10.1073/pnas.76.9.4192. PMID 16592703, http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=411539. Retrieved on 24 March 2007. 
  4. Robertson, Eugene C. (2001-07-26). "The Interior of the Earth". USGS. Retrieved on 2007-03-24.
  5. Sanders, Robert (2003-12-10). "Radioactive potassium may be major heat source in Earth's core", UC Berkeley News. Retrieved on 28 February 2007. 
  6. Alfè, D.; Gillan, M. J.; Vocadlo, L.; Brodholt, J; Price, G. D. (2002). "The ab initio simulation of the Earth's core" (PDF). Philosophical Transaction of the Royal Society of London 360 (1795): 1227–1244, http://chianti.geol.ucl.ac.uk/~dario/pubblicazioni/PTRSA2002.pdf. Retrieved on 28 February 2007. 
  7. Richards, M. A.; Duncan, R. A.; Courtillot, V. E. (1989). "Flood Basalts and Hot-Spot Tracks: Plume Heads and Tails". Science 246 (4926): 103–107. doi:10.1126/science.246.4926.103. PMID 17837768, http://adsabs.harvard.edu/abs/1989Sci...246..103R. Retrieved on 21 April 2007. 
  8. http://hypertextbook.com/facts/2001/PamelaSpiegel.shtml
  1. Locally varies between 5 and 200 km.
  2. Locally varies between 5 and 70 km.

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