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Unformatted text preview: T P Assuming that the stress in the earth’s interior is equal to hydrostatic pressure ), ( g h then pressure gradient towards the centre of the earth. ) 2 ( g dr dp r is the radius of the earth. The negative sign implies pressure increase with decrease in radius. Consider a homogeneous layer in which the t temperature variation is adiabatic then.  44  e i p dp dp v dv dp . / / ) 3 ( / p dp dp But ) 4 ( dp dp d dp dr dp Use (2) and (3) in (4) ) 5 ( g dr d But so r GM g , 2 ) 6 ( 2 r GM dr d Equation (6) is applicable to region of uniform composition within the earth, which is, starting from mantle down. It shows uniform density increase (Fig.1) Where = adiabatic incompressibility (i.e. bulk modulus) M = Mass of the region of the earth with the earth less by the mass of the crust r = radius of the earth’s region with uniform composition G = Gravitational constant  45  3.2 Variation of Pressure P with Depth This has to do with the pressure distribution and variation of acceleration due to gravity. ) 1 ( Re 2 r Gm g that call ) 2 ( g r P and So pressure gradient ) 3 ( 2 r Gmp dr dp Equation 3 shows that pressure decreases with depth, i.e. as r decreases (Fig.1) Also; it shows that pressure has direct relation with the density. 3.3 Variation of Acceleration due to gravity with depth Recall that . 2 r GM g So, variation of g with depth can be calculated using the relation above. Its value does not differ by more than 1% from 990 km until a depth of 2400 km is reached where it decreases to zero (Fig.1) 3.4 Variation of Pressure P and S waves with Depth In seismology P and S waves are used to study the interior of the solid earth. P Wave is a longitudinal wave that can pass through liquid, solid and gas. S Wave is a Wave is a longitudinal wave that can pass through liquid, solid and gas....
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 Winter '12
 JOHN
 Equator, earth surface, solid earth, geomagnetism

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