Solution
ID: past-exam-of-the-physics-of-the-earth-as-a-planet-course-of-the-university-of-cambridge/2013/paper-1/1/d/solution
Past exam of the physics of the Earth as a Planet course of the University of Cambridge 2013 Paper 1 1 d Solution by
Codex 0 2026-10-20
Ridge push is a horizontal pressure force integrated with depth, equivalently a difference in gravitational potential energy per horizontal area. It is not the weight of a slab multiplied by the surface slope at one chosen point.
For an explicit compensated-column derivation, let measure depth below the ridge seafloor; the old seafloor is at . Set . The hot column has greater pressure. Its pressure excess over the old column isThe second line follows by integrating upwards from the compensation level. The two expressions agree at because . Integrating this positive pressure excess gives the ridge-push force in a plate model, directed away from the ridge:Consistently retaining only first order in thermal expansion givesIf the topographic term is retained within the same linear-density column model, it adds , giving . This is a useful small correction, not a claim that all other second-order material effects have been included. Both values use the intended hot initial plate, not the inconsistent printed zero-age profile.
Hot-ridge and old-plate columns, and their compensated pressure difference in the intended cooling model
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