Rheological Controls on Magma Reservoir Failure in a Thermo‐Viscoelastic Crust

Abstract

As volcanoes undergo unrest, understanding the conditions and timescales required for magma reservoir failure, and the links to geodetic observations, are critical when evaluating the potential for magma migration to the surface and eruption. Inferring the dynamics of a pressurized magmatic system from episodes of surface deformation is heavily reliant on the assumed crustal rheology, typically represented by an elastic medium. Here, we use Finite Element models to identify the rheological response to reservoir pressurization within a temperature‐dependent Standard Linear Solid viscoelastic (“thermo‐viscoelastic”) domain. We assess the mechanical stability of a deforming reservoir by evaluating the overpressures required to initiate brittle failure along the reservoir wall, and the sensitivity to key parameters. Reservoir inflation facilitates compression of the ductile wall rock, due to the non‐uniform crustal viscosity, impacting the temporal evolution of the induced tensile stress. Thermo‐viscoelasticity enables a deforming reservoir to sustain greater overpressures prior to failure, compared to elastic analyses. High‐temperature (e.g., mafic) reservoirs fail at lower overpressures compared to low‐temperature (e.g., felsic) reservoirs, producing smaller coincident displacements at the ground surface. The impact of thermo‐viscoelasticity on reservoir failure is significant across a wide range of overpressure loading rates. By resisting mechanical failure on the reservoir wall, thermo‐viscoelasticity impacts dyke nucleation and formation of shear fractures. Numerical models may need to incorporate additional processes that act to promote failure, such as regional stresses (e.g., topographic and tectonic), external triggers (e.g., earthquake stress drops), or pre‐existing weaknesses along the reservoir wall.

A Computational Framework for Time‐Dependent Deformation in Viscoelastic Magmatic Systems

“…Viscoelastic deformation of volcanoes has been studied numerically by numerous authors (e.g., Del Negro et al., 2009; Gregg et al., 2013; Head et al., 2022; Hickey & Gottsmann, 2014; Segall, 2019). However, we are unaware of a systematic analysis of the numerical and computational issues associated with this problem.…”

Unveiling the Rheological Control of Magmatic Systems on Volcano Deformation: The Interplay of Poroviscoelastic Magma‐Mush and Thermo‐Viscoelastic Crust

“…The speed at which this pulse travels is proportional to the viscous timescales (and by extension, thermal conditions) of the wall rock, which are highly heterogeneous. The tensile pulse will initially be attached to the reservoir and dissipate into the colder host rocks (Head et al., 2022). The viscoelastic stresses will develop slowly in the cooler (more viscous) rocks away from the reservoir, inhibiting viscous deformation (Figures 8a and 8b); the viscoelastic stress will travel much faster from a hotter reservoir because of shorter crustal relaxation timescales (Figures 8d and 8e).…”

“…Expansion of the mush by melt injection causes the tensile stress in the rock surrounding the reservoir, and the resulting ground deformation, to increase with time. The thermo‐viscoelastic effect of the wall rock is more apparent than the viscous effect of the mush because of the broader range of relaxation times (Head et al., 2022). In a colder reservoir, poroviscoelasticity causes less syn‐injection deformation, which outcompetes the additional increase in the deformation caused by the viscoelastic wall rock and leads to less syn‐injection deformation than in the base‐model (elastic; Figure 6).…”

“…The relative contributions of the elastic shear modulus are split according to the weighting of fractional shear moduli, μ 0 and μ 1 (Figure 1b), where μ 0 + μ 1 = 1. The viscous component of deformation is treated as incompressible, such that volumetric strains are assumed to be purely elastic and viscoelastic deformation is represented in terms of the deviatoric strain components (Head et al., 2022; Segall, 2010).…”

Decompression and Fracturing Caused by Magmatically Induced Thermal Stresses

“…To investigate stresses and deformation in a visco-elasto-plastic host rock, several studies applied thermo-mechanical numerical modeling. Some utilize a visco-elastic rheology to quantify stresses and determine the onset of failure (e.g., Gregg et al, 2012;Head et al, 2022;Novoa et al, 2019;Zhan & Gregg, 2019) and others utilize an elasto-plastic or visco-elasto-plastic rheology (e.g., Gerbault et al, 2012Gerbault et al, , 2018Novoa et al, 2022;Souche et al, 2019). However, thermal processes, especially volume changes due to thermal expansion are rarely considered.…”