The influence of hotspot topography on mega-dyke propagation: theory and models

Radial mega-dyke swarms, found on Earth, Mars and Venus, radiate away from a central source in an asterisk-like pattern. Individual mega-dykes can reach lengths of 100s of kms and up to 100 metres in width (Ernst and Baragar, 1992), yet this similarity in the characteristic length among dykes of an individual swarm over such long distances remains enigmatic. In this study, we present theory and numerical models of dyke length. Here we hypothesise that the level of neutral buoyancy is inclined, allowing dykes to flow downslope. We postulate that the source of this inclination is crustal doming above a rising hotspot swell.

Existing models of fractures perched at their level of neutral buoyancy show the final length of the fracture L is highly dependent on the initial chamber pressure p, L∝p^7/2 (Bolchover and Lister, 1999). Changes in this pressure of 10’s of MPa can cause the final length of the fractures to extend between the metre scale to 1000’s of kilometres. This suggests that the chamber pressure would have to be very stable for the injection of all dykes in a given array. In our model we will show that when the dyke propagates downslope then the dyke length is less sensitive to this source pressure. In our model, the wall rock deforms elastically but breaks when the fracture toughness is exceeded. Lubrication theory is used to model the flow within the dyke and the magma is allowed to solidify on contact with the wall. We simulate the dykes using PyFrac (Zia and Lecampion, 2020) and a simplified scheme akin to a pseudo-3D hydro-fracture model (Adachi et al., 2010). We derive equations to describe the energy sources and sinks driving the dyke to propagate laterally.

We show how the dyke height and speed increases as the slope of the level of neutral buoyancy is increased. Using our energy analysis, we show that for a dyke propagating down a constant slope the dissipation is balanced by the gravitational potential energy, resulting in a near constant tip speed. Retrieving the dyke tip speed from the model we estimate the final length of the dyke. We show that for dykes driven laterally by a stress gradient the final length is less sensitive to the magma chamber pressure. Our results show quantitatively how radial mega-dyke arrays are related to ground deformation above a rising hotspot head.

Adachi, J.I., Detournay, E. and Peirce, A.P., 2010. Analysis of the classical pseudo-3D model for hydraulic fracture with equilibrium height growth across stress barriers. International Journal of Rock Mechanics and Mining Sciences, 47(4), pp.625-639.

Bolchover, P. and Lister, J.R., 1999. The effect of solidification on fluid–driven fracture, with application to bladed dykes. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 455(1987), pp.2389-2409.

Ernst, R.E. and Baragar, W.R.A., 1992. Evidence from magnetic fabric for the flow pattern of magma in the Mackenzie giant radiating dyke swarm. Nature, 356(6369), pp.511-513.

Zia, H. and Lecampion, B., 2020. PyFrac: A planar 3D hydraulic fracture simulator. Computer Physics Communications, 255, p.107368.