Numerical modeling of magma withdrawal during explosive caldera‐forming eruptions

Abstract

Abstract. We propose a simple physical model to characterize the dynamics of magma withdrawal during the course of caldera-forming eruptions. Simplification involves considering such eruptions as a piston-like system in which the host rock is assumed to subside as a coherent rigid solid. Magma behaves as a Newtonian incompressible fluid below the exsolution level and as a compressible gas-liquid mixture above this level. We consider caldera-forming eruptions within the frame of fluid-structure interaction problems, in which the flow-governing equations are written using an arbitrary Lagrangian-Eulerian (ALE) formulation. We propose a numerical procedure to solve the ALE governing equations in the context of a finite element method. The numerical methodology is based on a staggered algorithm in which the flow and the structural equations are alternatively integrated in time by using separate solvers. The procedure also involves the use of the quasi-Laplacian method to compute the ALE mesh of the fluid and a new conservative remeshing strategy. Despite the fact that we focus the application of the procedure toward modeling caldera-forming eruptions, the numerical procedure is of general applicability. The numerical results have important geological implications in terms of magma chamber dynamics during explosive caldera-forming eruptions. Simulations predict a nearly constant velocity of caldera subsidence that strongly depends on magma viscosity. They also reproduce the characteristic eruption rates of the different phases of an explosive calderaforming eruption. Numerical results indicate that the formation of vortices beneath the ring fault, which may allow mingling and mixing of parcels of magma initially located at different depths in the chamber, is likely to occur for low-viscosity magmas. Numerical results confirm that exsolution of volatiles is an efficient mechanism to sustain explosive caldera-forming eruptions and to explain the formation of large volumes of ignimbrites.

Basaltic calderas: Collapse dynamics, edifice deformation, and variations of magma withdrawal

“…Or does the collapse occur by magma underpressure in the reservoir? These questions have already been addressed in the case of silicic calderas [ Druitt and Sparks , 1984; Martí et al , 2000; Folch et al , 2001; Roche and Druitt , 2001], yet whether the proposed explanations hold for basaltic calderas remains unverified. The pressure evolution in the magma chamber after each collapse increment may be expressed using the following relationship [ Kumagai et al , 2001]: p 0 and p 1 are the pressure in the magma chamber before and after a given collapse increment, respectively, p is the pressure increase due to the intrusion of the caldera block into the magma chamber, p ′ is the pressure decrease due to magma outflow and t is the time between two collapse increments, i.e., T .…”

“…Or does the collapse occur by magma underpressure in the reservoir? These questions have already been addressed in the case of silicic calderas [Druitt and Sparks, 1984;Martí et al, 2000;Folch et al, 2001;Roche and Druitt, 2001], yet whether the proposed explanations hold for basaltic calderas remains unverified. The pressure evolution in the magma chamber after each collapse increment may be expressed using the following relationship [Kumagai et al, 2001]:…”

Magmatic processes associated with caldera collapse at Ossipee ring dyke, New Hampshire

“…At Ossipee, however, there is no evidence for two separate eruptions or sharp changes in magma composition that would allow this type of restricted mixing. (3) As the caldera subsided, dynamic collapse-driven mixing occurred at the base of the magma chamber (Marshall and Sparks, 1984), driven by vortices developing around the base of the subsiding block (Folch et al, 2001).…”

“…During piston-style subsidence in a magma chamber of uniform viscosity (<10 Pa s), fl ow vortices develop at the base of the ring dyke that can drive mixing and mingling (Folch et al, 2001). Folch et al (2001) concluded that vortices are only likely to develop where viscosities are lower than 10 4 Pa s. The viscosity of the quartz syenite with 35% crystals may be closer to 10 5 Pa s (Lejeune and Richet, 1995;Hess and Dingwell, 1996).…”

“…At Ossipee and many other calderas, the situation is more complex than the situation modeled by Folch et al (2001), since the caldera did not subside as a coherent block and, furthermore, the chamber contained magmatic layers with contrasting viscosities (Fig. 9A) (Chapman, 1976).…”