Dynamics of magmatic intrusions in the upper crust: Theory and applications to laccoliths on Earth and the Moon

Abstract

[1] To understand the dynamics of shallow magmatic intrusions, I propose a theoretical model of magma spreading laterally below an elastic crust. Nondimensionalization of the flow equation leads to the identification of characteristic scales for the intrusion: while the characteristic intrusion length is controlled by the elastic response of the crust, its characteristic thickness primarily depends on magma properties and injection rate. Three spreading regimes are identified and characterized by different morphologies as well as by scaling laws for thickness versus length and thickness versus time. The first spreading regime is controlled by the elastic response of the crust and the shape of the flow is self-similar. When the time, length, and thickness become larger than an elastic time, length, and thickness scale, the edges of the flow become steeper and the system transitions to a gravity current regime. When the intrusion is thick enough to accommodate the pressure head, the flow enters a regime of lateral propagation and keeps a constant thickness. The intrusion shape in the elastic regime fits the observed shape of terrestrial laccoliths. The elastic scaling law for intrusion thickness versus length fits observations of laccoliths at Elba Island, Italy, and provides for a physical explanation for the observed relationship between length and thickness on terrestrial laccoliths. Laccoliths are predicted to form over short time scales, depending on magma viscosity, that vary between approximately a month to several years for felsic magmas on Earth. On the Moon, several elongated low-slope domes have recently been identified as possibly formed by laccolith intrusions at depth, although they are much larger than terrestrial laccoliths. Because the Moon has a smaller gravity than on the Earth, a deeper magma source, and a more mafic magma composition than for terrestrial laccoliths (implying smaller pressure gradient and dike width), lunar intrusions have a larger characteristic length and a smaller characteristic thickness. After nondimensionalization, the morphologies (length versus thickness) of terrestrial and inferred lunar laccoliths follow the same curve and are well fitted by the elastic scaling law. This model thus explains the size discrepancy between terrestrial laccoliths and lunar low-slope domes. Therefore, low-slope domes identified on the Moon are good candidates for laccolith-type intrusions at depth.

Two-Phase Fluid Displacement and Interfacial Instabilities Under Elastic Membranes

“…Such fluid-structure interactions are abundant in nature and technology at all scales; examples include the lateral intrusion of magma under a terrestrial crust [2,3], blood creeping underneath the skin giving bruises their signature color, hydraulic fracturing [4] and the manufacturing of semiconductors [5]. These nonlinear systems are susceptible to interfacial instabilities when multiphase flows are involved, which inspires the present work.…”

“…For small deformations, the membrane obeys linear elasticity so that p = B∇ 4 h [16], where B is the bending modulus of the membrane. Substituting (2) into (1) and using the expression for the pressure, we obtain the governing partial differential equation (PDE) for the deflection of the membrane [2]:…”

“…Single-phase spreading To start, let us consider the spreading of a fluid with viscosity µ under an elastic membrane with zero initial height [2]; see Fig. 1a.…”

Displacement flows under elastic membranes. Part 1. Experiments and direct numerical simulations

“…In the present paper we study the canonical problem, shown schematically in figure 1, which has received much attention in recent years (Jensen et al 2002;Grotberg & Jensen 2004;Michaut 2011;Pihler-Puzović et al 2012Al-Housseiny et al 2013;Lister et al 2013;Hewitt et al 2015). A thin, uniform layer of viscous fluid is contained between a rigid plate and an elastic membrane which forms the upper boundary of the cell.…”

“…Elastohydrodynamic interactions of this type arise in applications ranging from geophysical phenomena such as the formation of laccoliths (Michaut 2011;Lister et al 2013) and gravity-driven surface lava flows under solidified crusts (Slim et al 2009;Hewitt et al 2015) to physiological processes. For instance, the formation and growth of blisters (Chopin et al 2008) involves a competition between elastic and adhesive forces.…”