{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Earth as an elastic body

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

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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!...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern