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A quantitative model of gneiss dome formation must account for the spontaneous development of large structural relief, relative to surface relief, at the base of the brittle layer for appropriate physical parameterization of the crustal rheology and the modification of topography by erosion. An earlier model has been augmented to include (i) crustal necking, as well as contributions to dome initiation from (ii) density instability and from (iii) an erosional law in which sinusoidal components in surface topography are amplified at wavelengths L > L* and decay for L < L*. A further modification replaces a ductile halfspace with a downward softening viscous layer resting on rigid mantle at a weak planar detachment. Necking alone predicts crustal instability for only a few candidate creep laws and maximum rock strength near the upper surface. Density instability and erosional amplification make independent, additional contributions to the strength of instability of the same magnitude as that from necking, extending the domain of dome initiation to much larger ranges in the dimensionless parameters that govern model behavior.

Our results indicate that crustal extension tends to strongly localize for a broad range of rock types dominating crustal rheology, leading to crustal necks centered on large amplitude antiformal structures. The tendency for the necks to form spontaneously and amplify rapidly is strongly enhanced by a destabilizing density contrast at depth and erosional evacuation of material from the necks. The analysis shows that crustal necks with a length scale of 50–100 km, 4–5 times the thickness of the brittle crust, tend to dominate the initial structures. These are likely to develop into domal structures, river anticlines, and, more generally, zones of localized deformation and rock uplift, especially where erosion is rapid.

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