The long-wavelength geoid over New Guinea and the western Pacific shows a high of about
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Earth, Climate & Energy Physics · Newtonian gravitation as a field theory
The Solid Earth, Ch Plates, creep and convection: the mantle in motion
Problem
The long-wavelength geoid over New Guinea and the western Pacific shows a high of about N=+80m, sitting above the region where seismic images show the densest concentration of subducted slab material, reaching from the surface through the upper mantle and roughly 500km into the lower mantle. The slab material is denser than the surrounding mantle by about Δρ≈60kgm−3.
((a)) A sinking slab pulls the geoid up by its own direct gravitational attraction, but the flow it drives also depresses the solid surface above it and drags the core-mantle boundary down, and both of those depressions pull the geoid down. For a mantle of a single, uniform viscosity, state which effect wins and hence the sign the geoid anomaly over the slab would have.
((b)) Calculations of this force balance find that the sign in (a) reverses, giving a net geoid high over a sinking slab, once the lower mantle is about 30 times more viscous than the upper mantle. The largest rebound loads independently require a lower mantle 10 to 100 times stiffer than the upper mantle. Are these two lines of evidence consistent with the observed western Pacific high? What sign would a contrast at the bottom of that rebound range (10×) predict for the geoid over the slab, and would that agree with the observation?
((c)) The observed high sits directly above the densest slab concentration, matching the layered-viscosity picture. Explain why this positional match alone does not prove the anomaly is dynamically (flow) supported rather than a static density anomaly, and name one further kind of evidence, distinct from the geoid itself, that would help decide between the two.