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Having read a little about sill formations like the Palisades Sill (eastern USA) and Whin Sill (UK), I understand that strata became separated by the injected layer of magma, with monumental thicknesses achieved in the two examples mentioned.

However, when one considers the weight of the overlying rock, especially if a sill has formed up to several kilometres below the surface, is it the case that the strata and rocks immediately beneath the growing, injected magma layer were sinking, i.e. a descent of the lower solid layer(s) — with magma being injected from somewhere via fissures, etc., to form the sill above — until static equilibrium was achieved? Or did the pressure from the injected magma layer cause the overlying rocks — and therefore the ground surface — to be forced up?

Are there studies that have shown what occurs, for old sills or even ones that have been monitored whilst actively forming?

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It's both. The rocks above the sill go up, whereas those below it go down. For shallow diking events it's mostly up.

This is all based on theory of linear elasticity. People model deformation using elasticity all the time, especially for studying deformation at volcanoes which one can measure using GPS, leveling, InSAR, etc.

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