The Roles of Elastic Properties, Magmatic Pressure, and Tectonic Stress in Saucer‐Shaped Sill Growth

Abstract

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 ΔP, and the externally applied tectonic stress σ r , 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 G max . Initially, G max is in-plane with the sill but deflects to~25°at a critical base length r c relative to depth, due to interaction between the sill and the free surface. Increasing σ r decreases this angle and increases r c of the sill. ΔP controls sill growth rate but has little effect on overall geometry. Host rock cohesion and elastic properties control the absolute magnitudes of σ r required to effect a change in sill geometry.Plain Language Summary Horizontal magma pathways-sills-are a crucial part of volcanic plumbing systems, acting as potential feeder conduits to volcanic eruptions, and as magma storage systems. Saucer-shaped sills, which exhibit a flat inner region and inclined outer region, are a common type of magma pathway in the shallow crust. Models for saucer-shaped sills, both as physical analog models or numerical simulations, typically underpredict the length of the inner flat region and overpredict the outer inclined region; models are typically too short and too steep. Here we use numerical simulation to investigate parameters that may control sill shape. We find that the dominant controls on sill shape are the competing effects of (1) bending of the rocks above the sill, which promotes a transition to inclined growth, typically at~25°, and (2) plate tectonic shortening, which serves to decrease the angle of incline, toward 0°when the horizontal force is high. Increasing the applied horizontal tectonic force can produce sills that are up to five times longer in the inner region, before growing as inclined sills at~5°. This matches very closely with observations of natural sills, indicating that tectonic forces are an important consideration in the growth of sills.

Segment tip geometry of sheet intrusions, II: Field observations of tip geometries and a model for evolving emplacement mechanisms

“…2018; Burchardt et al 2019], magma driving pressure relative to the tectonic stress [Gill and Walker 2020], depth of emplacement [Gill and Walker 2020], and the remote stress state [e.g. Pollard 1973;Pollard et al 1975;Rubin 1993;Walker and Gill 2020].…”

“…Inflow of pore fluids may cause non-localised inelastic damage in the process zone ahead of the intrusion, which increases the energy required for continued fracture propagation [Rubin 1993;Gudmundsson 2011]. However, the pressure gradient arising from low pressure in the cavity also serves to drive magma flow toward the tip [Gill and Walker 2020]. Importantly in the Barenblatt model, if the magma driving pressure cannot drive further propagation of the fracture plane, it will instead cause inflation and rounding of the magma front, blunting the preserved tip geometry.…”

Segment tip geometry of sheet intrusions, II: Field observations of tip geometries and a model for evolving emplacement mechanisms

“…Haug et al, 2017, 2018]. Other factors affecting emplacement mechanism include the magma viscosity [Mattsson et al, 2018;Burchardt et al, 2019;Wilson et al, 2019], magma driving pressure relative to the tectonic stress [Gill and Walker, 2020], the depth of emplacement (Gill and Walker, 2020), and the remote stress state [e.g. Pollard 1973;Pollard et al, 1975;Rubin, 1993;Chanceaux and Menand, 2016;Walker and Gill, 2020].…”

“…However, the pressure gradient arising from low pressure in the cavity also serves to drive magma flow toward the tip [Gill and Walker, 2020]. Importantly in the Barenblatt model, if the magma driving pressure cannot facilitate further propagation of the fracture plane, the driving pressure will instead be accommodated by inflation and rounding of the magma front, without an increase in fracture length.…”

Segment tip geometry of sheet intrusions, I: Theory and numerical models for the role of tip shape in controlling propagation pathways.

“…Preserved tips and isolated segments are therefore treated as being representative of the growth stages of sheet development (Magee et al, 2019). This classical model for sheet emplacement has been generally considered as an elastic-brittle process, in which magma pressure in the intrusion performs work on the intrusion walls in a hydraulic fracture (Rubin, 1995;Gill and Walker, 2020). Deformation ahead of the tip occurs as elastic bending of the host rock to accommodate the gradual gradient of the intrusion thickness (Fig.…”