The roles of elastic properties, magmatic pressure, and tectonic stress in saucer-shaped sill growth

Near‐surface igneous sills commonly exhibit saucer‐like shapes, formed due to interaction with the Earth's surface once some critical sill length is reached relative to its depth. Sill geometry has been strongly linked to the host material conditions, particularly in terms of the elastic properties and shear cohesion of the host rock, operating as primary controls on sill geometry. Here we conduct dynamic numerical simulations for sill growth in the near surface, in which we vary the host rock properties, magma pressure profile internal to the sill ∆P, and the externally applied tectonic stress σr, to consider their contributions to sill geometry. We find that elastic properties alone have little impact on sill geometry. Saucer shapes reflect the additive stress components of the magma overpressure within the sill, and the tectonic stress, controlled by the locus of the maximum energy release rate Gmax. Initially Gmax is in‐plane with the sill, but deflects to ~25° at a critical base length rc relative to depth, due to interaction between the sill and the free surface. Increasing σr decreases this angle and increases rc of the sill. ∆P controls sill growth rate, but has little effect on overall geometry. Host rock cohesion and elastic properties control the absolute magnitudes of σr required to effect a change in sill geometry.