Solution (source code)

= Solution

<Elasticity> lets the <lithosphere> share a load with neighbouring regions through <lithospheric flexure>. \b[Beneath the centre of a localized load, subsidence is generally smaller than the local <isostasy> estimate, so the deposited surface stands higher.] The surrounding plate also bends down, and a more distant <flexural forebulge> may rise. The extra support is regional bending resistance, rather than removal of the load's <mass>.

\Image[/past-exam-of-the-plate-tectonics-course-of-the-university-of-oxford/2023-volcanic-loading.png]
{title=An original elastic-plate calculation contrasting narrow and broad loads at the same flexural rigidity; a broad load approaches local isostasy}

The controlling comparison is load width against the <lithosphere>'s flexural length, which increases with <flexural rigidity> and decreases with the relevant buoyant <geophysical density contrast>. Equivalently, the <flexural support ratio> becomes large for short-wavelength loading. A very broad nearly uniform load produces little curvature in its interior, so even a strong <elastic lithosphere> has a nearly local <isostatic adjustment> there. Bending matters most near its edges. A narrow load requires more curvature and can be supported appreciably by the surrounding <elastic lithosphere>.

The <Deccan Traps> form a broad continental <large igneous province>. The volcanic edifices of the <Hawaiian Islands> are more localized loads on an old <oceanic lithosphere>, for which regional bending and a flexural moat are prominent. \b[Under the usual broad-Deccan versus narrow-Hawaiian-load comparison, elastic strength matters more for the <Hawaiian Islands>.] The more coherent mantle-dominated strength of an old oceanic plate can reinforce this contrast. It cannot be deduced simply from “oceanic” versus “continental”: a cold Indian <craton> can be strong, and a site's <effective elastic thickness> depends on its thermal and loading history.

For an initially submerged Hawaiian load, replacing <seawater> changes both the load and buoyant restoring contrast. At fixed deposited thickness, the added load relative to the initial <water> column uses the rock-minus-water <density>, and the restoring term uses the mantle-minus-water <density>. An emerged island requires separate treatment of its subaerial and submerged portions. These corrections change the local <isostasy> reference but do not remove the importance of load width for <lithospheric flexure>. The broad <Hawaiian swell> should also be distinguished from the narrower volcanic load: deeper thermal or dynamic support of the <Hawaiian swell> is not the same mechanism as elastic support of the volcanic ridge.

Finally, over long periods <material creep>, yielding and thermal modification can reduce elastic support. Without measured load geometries, ages and <effective elastic thicknesses>, the ranking is a justified qualitative expectation rather than a theorem valid for every continental and oceanic load.