# 3 using 1 2 and 3 we can show that 3 4 also 3 4 2 2 w

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) 3 ( Using 1, 2 and 3, we can show that 3 4 Also 3 4 2 2  W here λ and μ are called Lamês consonants. The relations of and β with depth are shown in (Fig.1 Depth β α P ρ ρ P α β g g Fig.1: Variation of α ,β, ρ and P with depth in the solid earth. Parameter Of Interest

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- 47 - 3.5 Self assessment Exercise (1) State the mathematical relation for hydrostatic pressure. (2) What is the implication of the negative sign in the density gradient expression in equation (6)? (3) Sketch the variation of pressure and density with depth, state one similarity and difference each. 4.0 Conclusion It has been established that density, pressure, and seismic velocities, vary differently with depth within the solid earth. The models developed are easily applicable to layer below the crust where there is some element of homogeneity than in the crust that is characterised by inhomogeneity. 5.0 Summary At the end of this unit you have learnt that: (i) density is directly proportional to depth, 2 r Gm dr d in show as (ii) Pressure is inversely proportional to depth, 2 r Gm dr dp in show as (iii) Acceleration due to gravity increases with depth up to a point when it then decreases to zero (iii) Seismic waves vary differently with depth.
- 48 - 6.0 Tutor Marked Assignment (1) , 3 2 : that Given and 2 3 4 Pr that ove (2) With the aid of a diagram, describe the variation of S- wave velocity in a homogeneous part of the solid earth. 7.0 Further Reading and Resources Ben- Zion, Yehuda; Lee, William, H.K.L. (Eds.) (2006): Advances in Studies of Heterogeneities in the earth’s Lithosphere Pageoph Tropical volume. The Keiiti Aki, vol. II.A Birkhäuser Book. Telford, W.M., Geldart, L.P., Sheriff, R.E. and Keys, D.A. (1976): Applied Geophysics. Cambridge University Press, London
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