3 p dp dp but 4 dp dp d dp dr dp use 2 and 3 in 4 5 g

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/ / ) 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
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- 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 transverse wave that can travel vertically and horizontally and can not pass through fluids. P and S- waves are called body waves because they can pass through the earth’s interior. They however possess different velocities while passing through an earth
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- 46 - material. usually P- wave is always faster than S- wave. Let  and β be the P and S waves Velocities. It has been proved that: ) 1 ( 3 2 modulus Bulk ) 2 ( 2
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