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A mainly basaltic continental large igneous province in India, emplaced around the end of the Cretaceous. Its surface deposits provide a major example of volcanic loading. Deposited volume, loaded area and density must be distinguished when estimating isostatic adjustment.

Let a deposited layer have thickness $H$ and density ${\rho }_b$, replacing a fluid of density ${\rho }_f$, while the original crust translates downward by $w$ above mantle of density ${\rho }_m$. Assume all deposited material stays in the same fluid environment, unchanged pre-existing layer thicknesses, an external material source, and complete local isostatic adjustment without bending resistance.

At a fixed compensation depth, added column mass is $({\rho }_b-{\rho }_f)H$ per unit area, whereas depression replaces a column contrast $({\rho }_m-{\rho }_f)w$. Equal hydrostatic pressure therefore requiresIt follows thatThe pre-existing ground subsides by $w$, while the top of the new layer rises by $\Delta z$ if ${\rho }_b<{\rho }_m$. For a subaerial deposit, air density is negligible. For a fully submerged deposit, use seawater density. A deposit that crosses the fluid surface requires separate treatment of its submerged and emerged portions. Specifying only volume $V$ leaves the answer dependent on loaded area through $H=V/A$.

The volume alone does not determine a unique change of elevation. A local isostatic response to an added surface layer depends on its thickness and density, so the Deccan Traps' footprint must be specified or retained as a parameter.

Let the deposited basalt have uniform thickness $H=V/A$ and density ${\rho }_b$, where $V=10^{15}{\mathrm{m}}^3$ and $A$ is the loaded area. Let $w$ be downward displacement of the original land surface, and let ${\rho }_m$ be the density of displaced mantle. Assume a subaerial, laterally extensive deposit, negligible air density, unchanged thickness and density of the pre-existing crust, and complete local isostatic adjustment. Take the magma supply to be external to the local compensation column, and neglect cooling, erosion, magmatic underplating and any deep thermal or source-depletion anomaly.

Choose a compensation depth beneath all the displaced interfaces. The added column mass per unit area is ${\rho }_{b}H$. Downward translation of the pre-existing crust replaces a thickness $w$ of mantle within the column, reducing its mass by ${\rho }_{m}w$. Equality of hydrostatic pressure at the compensation depth therefore givesThe newly formed top of the basalt stands $H$ above the depressed original surface. Consequently the change of the region's top-surface elevation isThus the original substrate subsides, but the top of the deposit rises if ${\rho }_b<{\rho }_m$. Distinguishing these two surfaces prevents reporting the large downward displacement as the change in plateau elevation.

For an explicitly illustrative choice $A=10^{12}{\mathrm{m}}^2$, ${\rho }_b=2900\mathrm{kg}{\mathrm{m}}^{-3}$ and ${\rho }_m=3300\mathrm{kg}{\mathrm{m}}^{-3}$, the deposit is 1000 m thick, the substrate subsides about 879 m, and the final surface rises about 121 m. This is a conditional estimate, not a number fixed by the paper. Half that footprint would double all three heights under the same assumptions. For a nonuniform deposit, local isostasy gives the same relation pointwise with $H(x,y)$; the total volume still cannot specify a unique local elevation.

Elasticity lets the lithosphere share a load with neighbouring regions through lithospheric flexure. 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.

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. 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.

Cooling makes the oceanic lithosphere denser and contracts it; isostatic adjustment therefore lowers the seafloor. The cooling layer includes substantial mantle, not just the approximately fixed-thickness igneous oceanic crust.

New plate near a spreading ridge is hot and relatively buoyant. As it moves away, conductive cooling penetrates more deeply, and material formerly in the hot asthenosphere becomes part of the colder thermal boundary layer. To first order,where $\alpha$ is the volumetric thermal expansion coefficient, ${\rho }_m$ a reference mantle density, $T_m$ the hot reference temperature, and $t$ plate age. A positive depth-integrated density anomaly makes the column negatively buoyant relative to the ridge column. Isostasy is restored by downward displacement and mantle redistribution; cold rock also occupies less volume.

At a fixed sufficiently deep datum, deepening the seafloor by $\Delta d$ removes an equivalent thickness of rock from the column and replaces it with less dense seawater. In the usual constant-property approximation this giveswhere ${\rho }_w$ is seawater density and $z_c$ lies below the relevant thermal anomaly. This explains why contraction alone and water-loaded seafloor subsidence are not identical numerical quantities.

For a half-space cooling model,so integration yieldsHere $\kappa$ is thermal diffusivity and $z$ is measured downward from the surface of the thermal model. The leading oceanic thermal subsidence is proportional to $\sqrt{t}$. A finite oceanic plate cooling model limits this growth at old ages. Sediment loading, dynamic topography, anomalous crust thickness and hydrothermal heat transport can produce departures from the simple relation.^[ref]

Addition of erupted or intruded rock as a gravitational load on a planetary surface or interior. Deposited thickness, density, geometry and emplacement history control isostatic adjustment and lithospheric flexure. Thermal and compositional changes in the source can supply additional effects distinct from the weight of the deposited material.