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Earth as an elastic body

# Earth as an elastic body - s = h(del-H = h-W/g then h is...

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Earth as an elastic body Chans an elastic body Changes in g give a deformation similar to the above. (Note we have calculated the changes in potential height: this will only translate into a change in shape if the body is deformable.) If perfectly elastic the elongation axis would be towards the deforming body; otherwise there will be a phase lag. For the solid earth the phase lag is small, though not for the sea tides. The reason for the small solid earth lag is because the period of natural oscillation is <<0.5days (it's actually around 57 minutes) so the earth can continuously and rapidly adjust. The natural period of the ocean tides is several days. If we assume the oceans could adjust then the level of water would rise to a point of static equilibrium. If the marine tide = del-H then the work done against gravity would be g(del-H)=-W For the solid earth work is also done in the elastic deformation and so the height of the earth tide delH s is less than del-H If del-H
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Unformatted text preview: s = h(del-H) = h(-W/g) then h is independent of r and psi and is called the Love Number . The liquid surface remains an equipotential. On a solid surface there is an additional potential due to the deformation of the earth and the consequent redistribution of the mass. We expectthis to be proportional to W(r,P) - say kW. k is another Love number. A liquid surface covering the globe would remain ring the globe would remain an equipotential and be lifted (1+k)W/g relative to the centre of the earth,or (1+k-h)W/g relative to the sea bed. We can measure h and k by observing g at the surface. Variations of g g = g [1-(2W/rg )(1 - 3h/2 + k)] W is at the surface a semi-diurnal variation in g pf c. 2 in 10 7 . Changes in g of 1 in 10 10 or 1 in 10 11 can be measured. (1 + 3h/2 + k) is c. 1.1 to 1.26%. Vertically (1 + k - h) = 0.54 - 0.82. This then gives k = 0.28 and h = 0.6. Thus the rise and fall of the earth's surface is half that of the ocean - several metres!...
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