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The physical processes of mush reawakening
The rejuvenation of magmatic mush prior to eruption requires the destabilization of the force chains and the generation of eruptible magmas. Different scenarios have been proposed in the literature. Some of them involved the injection of hot and mobile magma whereas others not. Here, we focus on mush reawakening scenarios in which the triggering event is the recharge in new magma, as highlighted in several eruptions (e.g. Murphy et al., 2000; Pallister et al., 1992; Takahashi and Nakagawa, 2013; Tomiya and Takeuchi, 2009). Thus, we do not consider scenarios that do not involve the input of enthalpy and momentum by new injection such as vibro-agitation (Davis et al., 2007), deep fragmentation (Gottsmann et al., 2009), syn-eruptive processes (Cashman and Giordano, 2014; Karlstrom et al., 2012), or relevant of cases where an eruptible magma chamber is already formed (e.g. Girona et al., 2015).
Bachmann and Bergantz (2006) proposed a scenario named gas sparging in which a hot and wet intruder emplaces at the base of the mush and reheats it without mass transfer of melt or crystals. The heat is transferred through conduction and advection by percolation of exsolved volatiles released during the second boiling of the intruded magma, which induces an upward flow [B] Evolution of the mush rejuvenation function volatiles flux. The abscissa is a dimensionless diffusive time and the ordinate is a dimensionless temperature. After Bachmann and Bergantz, 2006. [C] Evolution of the thickness of the remobilized layer function of the presence of absence of microfracturation. The blue curve corresponds to the case with fracturation and the green one without. After Huber et al., 2011.
of the host melt (Fig 1.4A). A significant upward flux in volatiles decreases the reactivation time (Fig 1.4B) and increases the accumulated volume of eruptible magma. However, the effectiveness of this advection process is limited to a narrow range of crystallinity at which crystal repacking occurs and channels of exsolved volatiles may be formed (Bachmann and Huber, 2019; Parmigiani et al., 2016, 2014). The thermomechanical model from Huber et al., 2011, extends the gas sparging one and considers sequences of microfracturing of the locked mush above the remobilization front to release the local overpressure generated by the partial melting of the crystals. This phenomenon accelerates and enhances the rejuvenation of mush (Fig 1.4C) by destabilization of the force chains. These two models consider the progressive rejuvenation of the mush without gravitational instability (stable front remobilization) and require relatively long reactivation times (thousands of years for large systems).
Other models consider the occurrence of gravitational instabilities between the rejuvenated and locked part of the mush. The rejuvenation of the mush is also initiated by the advection of heat from a mobile magma stalled at the floor of the mushy reservoir (Burgisser and Bergantz, 2011; Couch et al., 2001). The unzipping model from Burgisser and Bergantz, 2011, and the self-mixing one from Couch et al. (2001), rely on the formation of a growing mobile layer at the interface between the host and the intruder by the melting of the crystals. This thermal boundary layer becomes less dense than the overlying mush and unstable. In the self-mixing model, this instability generates Rayleigh-Taylor instabilities that advect heat and mix with the host mush (Fig 1.5A). In the unzipping model, once the mobile layer reaches a critical thickness, it starts to convect internally. As this convective layer continues to grow, it becomes unstable and forms a larger buoyant instability by merging of adjacent convective cells, which leads to the overturn of the mush (Fig 1.5B). The two scenarios postulate the fluid-like behavior of the mush, which is consistent for weak mush just below the jamming transition (Bergantz et al., 2015). However, the scenario of unzipping appears more probable than that of self-mixing because the apparent viscosity contrast between the mush and mobile layer prevents the formation of simple convection (Burgisser and Bergantz, 2011). The unzipping model presents a rapid mechanism to rejuvenate a mush on timescales ranging from several months to decades after the emplacement of the hot mush layer (Fig 1.5C‒D).
All of these models concentrate on specific processes of the mush remobilization, but rely on the assumption that the triggering event is the emplacement of a hot magma sill at the base of the mush without exchange of melt or solids. However, recent CFD-DEM numerical simulations focused on basaltic mush dynamics have shown that when injected, a crystal-free melt may fluidize and ascent through the mush (Bergantz et al., 2017, 2015; Schleicher et al., 2016; Schleicher and Bergantz, 2017). In these mafic simulations, the presence of granular soft faults delimits a region called the mixing bowl, in which mechanical mixing between the host and injected melts occurs. It raises the question of the behavior of injections in the context of evolved magmatic mush, which may influence their remobilization dynamics. It shows the necessity to extend these mafic studies to conditions relevant of evolved magmatic reservoirs and incorporate the effects of the difference in compositions and temperature between the host and intruded magma, which may impose a strong contrast between their apparent viscosities and densities. Understanding and predicting the emplacement dynamics of new magma into a mush is of critical importance for our insight of mush remobilization processes.
Figure 1.5: Remobilization of mush with gravitational instabilities. [A] Principle of the ‘self-mixing’ model (Couch et al., 2001). The intrusion of a mafic magma stalls at the base of the mush and reheats it, forming a mobile layer due to the decrease in the crystallinity. This thermal boundary layer becomes buoyant and instable, producing rising plumes within the mush that mix with it. After Couch et al., 2001. [B] Snapshots of a numerical experiment showing the formation of plumes in a fluid with a strong temperature dependent viscosity, illustrating the unzipping scenario (Ke and Solomatov, 2004). In the three snapshots, the color of the fluid depends on its viscosity. Black colors indicate a very viscous fluid, and grey ones lower viscosities. The time increases to the left. In this experiment, the medium is heated by a plate located at the base of the tank. Modified after Ke and Solomatov, 2004. [C] Principle of the ‘unzipping’ model (Burgisser and Bergantz, 2011). The abscissa is the time and the ordinate the thickness of the mobile layer with logarithmic scales. The occurrence of the gravitational instability leads to the overturn of the mush (red curve) that significantly accelerates the reawakening process compared to a stable front remobilization (blue curve). After Burgisser and Bergantz, 2011. [D] Results of a Monte-Carlo simulations with the unzipping model. The axes are the mush effective viscosity in abscissa and the time in ordinate, both with logarithmic scales. For each simulation, three dots are displayed, indicating the onset of convections within the mobile layer (blue dots), the remobilization time with unzipping (green dots) and the reawakening time with a stable front remobilization (red dots). These results illustrate the efficiency of the unzipping to rapidly remobilize a magmatic mush. After Burgisser and Bergantz, 2011.
Imaging unrest events and seismic properties of eruptible magmas
The monitoring of unrest events with seismic tomography images relies to our ability to detect and image fluid dominated regions across magmatic systems. This method is based on the inversion of seismic signals travelling through the magmatic systems from active or natural sources. Upper crustal magma reservoirs usually show the presence of low seismic velocity anomalies (e.g Indrastuti et al., 2019; Lees, 1992; Miller and Smith, 1999; Paulatto et al., 2012; Waite and Moran, 2009). These low velocities zones are usually interpreted as indicating the presence of partially molten rocks and mush (Fig 1.6). Furthermore, the presence of high ratio between compressional and shear waves velocities (Vp/Vs) beneath volcanoes also suggests the presence of a fluid phase (e.g. Chiarabba and Moretti, 2006; Kiser et al., 2016; Nakajima et al., 2001). However, the finite values of these ratios indicate that shear waves can travel across these upper crustal magmatic reservoirs, which does not support the presence of large accumulation of eruptible magmas. If detectable, these batches of magmas must be characterized by a zero velocity zone for the S waves and a sharp decrease of the P wave velocity at natural frequencies (Caricchi, 2008), as observed across the East Pacific ridge (Singh et al., 1998). The lack of evidence of melt dominated regions by seismic imaging can be explain by the episodically presence of magma chambers that rapidly reach a mushy state (Fig. 1.3), the averaging and smoothing effects of seismic tomography, or the fact that magma chambers may be hidden by the crystal mush because of the attenuation of wave in the mush. Tomographic images are computed with the first waves arrivals, that correspond to the fastest way between the source and the stations, which may be outside the magmatic system because of the low seismic velocity in magmatic system compared to the host crust. It results in the decrease of our ability to image magma bodies characterized by low velocities with such method based on wave travel times.
During the past decades, the seismic wave attenuation tomography has shown to be a promising tool to image subsurface structures (e.g. Prudencio et al., 2018) and magmatic plumbing systems (e.g. De Siena et al., 2014; Gori et al., 2005). Two types of attenuation exist, the scattering one related to geometric dispersion generated by rough heterogeneities, and the intrinsic attenuation related to the absorption and dissipation of the seismic energy by the medium in which the wave is travelling. Within magmatic systems, the presence of high attenuations are usually interpreted as evidencing the presence of partially molten bodies, whereas low attenuation anomalies are linked to the presence of fully crystallized magma bodies. Quantitative interpretation of these results in terms of magma physical properties bears on our poor knowledge of the seismic properties of eruptible magmas and especially of their intrinsic attenuation. Few theoretical works and experiments have been performed to study the seismic properties of magmas. Most of these works focused on the properties of partially molten rocks (e.g. Mavko, 1980), or measured experimentally the velocities of both P and S waves at high frequencies before extrapolating them to seismic one (e.g. Caricchi et al., 2008). Other models predict the attenuation of seismic waves generated by the presence of melt filled crack but have to assume an intrinsic attenuation coefficient of the magma contained in this cracks (e.g. Kumagai and Chouet, 2000). Thanks to thermodynamic models, the materials properties (bulk modulus, density, viscosity, and heat conductivity/capacity) of the melt, which control the velocities and attenuations of waves in pure melt, can be easily predicted as a function of its composition, temperature, and pressure (Ghiorso, 2004; Ghiorso and Kress, 2004; Giordano et al., 2008). However the presence of particles in a suspension can greatly affect the wave velocities and attenuation as shown in experimental studies (e.g. Kuster and Toksoz, 1974b). Thus, it is necessary to have a physical model able to link the materials properties and concentration of the constituents of a magmatic mixture, to their velocities and attenuation coefficients in order to interpret the results of seismic tomographies with quantitative (amount of eruptible magma accumulated), and qualitative (physical properties of this magma) assessments.
Different theoretical models were proposed to predict wave velocities and attenuation coefficients in suspensions as a function of the constituent properties and concentrations. Two main approaches are used to predict the effective elastic and anelastic properties of suspensions: the scattering theory (e.g. Berryman, 1980; Kuster and Toksöz, 1974a) and the coupled phase theory (e.g. Atkinson and Kytömaa, 1992; Evans and Attenborough, 1997; Harker and Temple, 1988). The first approach models the scattering of an incident plane wave by immobile spherical inclusions and decomposes it in harmonics. This approach presents the advantage to be valid at any frequencies. The second is restricted to low frequencies but is able to take into account the relative motions between the phases and can explicitly incorporate mechanisms of momentum, heat and mass transfers between the constituents. Its applicability is limited to the long wavelength assumption for which the seismic wavelengths have to be much larger than characteristic size of suspended phase. This assumption is valid at natural frequencies for magmas because the crystal sizes are very small compared to the seismic wavelengths, which makes this method particularly suitable to be applied to eruptible magmas. However, applying the coupled phase approach to eruptible magmas requires novel modifications of the constitutive equations in order to incorporate the viscous dissipation in the melt phase and the lubricated interactions between close crystals when approaching to the magma-mush transition.
Figure 1.6 : Results and interpretations of Vp tomography at Soufriere Hill Volcano (SVH), Monsterrat Island (Paulatto et al., 2012). [A] Measured seismic anomalies in km s-1. [B] Computed temperatures related to the seismic anomalies assuming that no melt is present. [C] Estimation of the melt volume fraction assuming a constant temperature (700°C) and considering the melt pocket as interconnected thin lenses. [D] Estimation of the melt volume fraction assuming a constant temperature (700°C) and considering the melt pocket as isolated spheres. All after Paulatto et al., 2012.
Manuscript organization and scientific questions
The rest of this manuscript is organized in six chapters. The first one (chapter 2) presents basic concepts of fluid mechanics required in the next chapters, and the theory of the software and code, MFIX (Multiphase Flow with Interphases eXchange), which is used in chapters 3, 4, and 5. In chapter 3, we constrain the importance and effects of lubrication on the dynamics of mush. Chapters 4 and 5 explore the dynamics of a magmatic mush and aim at determining the physical mechanisms that promote the reawakening of a magmatic mush. The last chapter explores the seismic properties of eruptible magmas.
In more details, chapter 3 examines what are the relevant forces that control the motion of crystals in a mush. Contact, buoyancy, pressure and drag forces were considered in previous simulations (Bergantz et al., 2015; Schleicher et al., 2016; Schleicher and Bergantz, 2017). However, lubrication (forces arising from the relative motion between close crystals) have not been incorporated yet. The magnitude of these forces is proportional to the surrounding melt viscosity and inversely proportional to the distance between the edges of neighboring crystals. In the context of evolved magmas, close the rheological lock-up, the importance and effect of these forces must be addressed. It implies to find what are the non-dimensional numbers that are the most relevant to discriminate which forces controls the motion of an individual crystal. CFD-DEM numerical simulations that include these lubrication forces are performed to explore their effects on mush macroscopic dynamics. The main objectives in this chapter is to determine the effects of lubrication forces on the macroscopic dynamic of crystals bearing magmas and mush. For that it required to define the relevant dimensionless numbers that scale the importance of each force controlling the motion of individual mush crystals at the grain scale and implement lubrication forces in the MFIX CFD-DEM model.
Chapter 4 explores the intrusion mechanisms of mobile magmas within weak mush and aims at identifying which conditions promote the most the rejuvenation of a magmatic mush. It extends studies performed during the last half decade (Bergantz et al., 2015; Schleicher et al., 2016; Schleicher and Bergantz, 2017) in order to study evolved mush dynamics. The effects induced by the presence of viscosity and buoyancy contrasts on the emplacement of new magmas must also be characterized before discussing the implications of the mechanics of magma intrusion on the reawakening of mushy reservoirs. Here the main objective is to constrain the short-term behavior of an intrusion within a mush. In this way, the CFD-DEM model has to be adapted to replicate conditions relevant of chemically evolved magmas without unrealistic increase of the computational cost. It also requires to identify the relevant dimensionless parameters that are helpful to predict the behavior of the intruder.
Chapter 5 aims at exploring the interactions and mixing between intruded magma and resident mush and the effects of the intrusion on the physical properties of the host. It uses the results of Chapter 4 to constrain simulations mimicking conditions that are shared by many magmatic reservoirs. In particular, thermal processes may play an important role in the interactions between the mush and the intrusion and they have to be considered in the simulations. It requires to implement the temperature dependence of density and viscosity of the melt and to simulate the dynamics of the mush after intrusion emplacement. The description of the interactions between the intrusion and its host also calls for the quantification of the efficiency and the localization of mixing. The sixth chapter goal is to predict the seismic properties (velocity and attenuation) of eruptible magmas, which are poorly understood. Chapter 6 uses the coupled phase approach, which presents the advantage of accounting for different physical processes and coupling between the phases. This allows us to explore the relative importance of different dissipative mechanisms and to give quantitative predictions of attenuation coefficients. However, it necessitates the modification of the constitutive equations in order to be applicable to magmas. The aims of this chapter is to predict the P waves velocities and attenuation coefficients in eruptible magma, which requires to adapt the couple phase approach to conditions relevant of magmas and identify the main attenuation mechanisms.
Table of contents :
Chapter 1 : General introduction
1.1 Motivations
1.2 The physical processes of mush reawakening
1.3 Imaging unrest events and seismic properties of eruptible magmas
1.4 Manuscript organization and scientific questions
Chapter 2 : CFD-DEM Model
2.1 Introduction
2.2 Governing equations of the fluid phase
2.2.1 Mass conservation
2.2.2 Momentum conservation
2.2.3 Energy equation
2.2.4 State equations
2.2.5 Effect of the presence of the solid phase
2.3 Governing equations of the solids
2.3.1 Constitutive equations
2.3.2 Contact Model
2.3.2.a Collisional interactions
2.3.2.b Frictional interactions
2.3.3 Heat transfer between the solids
2.3.3.a Solid-Solid conduction
2.3.3.b Solid-Fluid-Solid conduction
2.3.3.c Relative importance of the two conduction modes
2.4 Couplings between the phases
2.4.1 Momentum coupling
2.4.2 Thermal coupling
2.5 Numerical solver
2.5.1 Overview of the SIMPLE algorithm
2.5.2 DEM solver
2.5.3 Interpolation schemes
2.5.3.a Particle side
2.5.3.b Fluid side
2.5.4 Boundary conditions
2.5.5 Dimensionless numbers
Chapter 3 : Effects of lubrication on mush dynamics
3.1 Introduction
3.2 Method
3.2.1 Formulation of the BBO equation
3.2.2 CFD-DEM Model
3.3 Results
3.3.1 Grains scale
3.2.1.a Scaling of the relative importance of the forces exerted on a particle
3.2.1.b Dimensionless formulation
3.3.2 Macroscopic scale
3.2.2.a Experiment 1 : Rayleigh-Taylor instabilities
3.2.2.b Experiment 2 : Injection of a fresh magma into a mush
3.3.3 Interpretation
3.4 Discussion
3.4.1 Influence of the crystals size and shape
3.4.2 Comparison with other studies
3.4.3 Implication on magma rheology and magmatic system dynamics
3.4 Conclusion
Supplementary section S3.1
Supplementary section S3.2
Supplementary section S3.3
Supplementary section S3.4
Supplementary section S3.5
Chapter 4 : CFD-DEM modeling of recharge events within mush
4.1 Introduction
4.2 Method
4.2.1 Numerical method
4.2.2 Numerical setup and experiments
4.2.3 Dimensionless parameters
4.3 Results
4.3.1 Effect of buoyancy and viscosity
4.3.2 Injection velocity
4.3.3 Results summary
4.4 Discussion
4.4.1 Model limitations
4.4.2 Implication on mush dynamics and on the modeling of crystal-bearing magmas
4.5 Conclusion
Supplementary section S4.1
Supplementary section S4.2
Supplementary section S4.3
Chapter 5 : Numerical simulations of the mixing caused by a magma intruding a resident mush
5.1 Introduction
5.2 Method
5.1 Results
5.2 Discussion
5.1 Conclusion
Chapter 6 : The seismic properties of eruptible magmas
6.1 Introduction
6.2 Theoretical assumptions
6.3 Method
6.3.1 Conservative equations of the phases
6.3.2 Fluid-solid and solid-solid couplings
6.3.3 Calculation of the acoustical properties of the suspension
6.3.4 Magmas under consideration
6.4 Results
6.4.1 Magmas physical properties
6.4.2 Fluid-solid momentum coupling
6.4.3 Solids-solids momentum coupling
6.4.4 Wave velocities and attenuation coefficients in suspensions
6.4.4.a Compressional waves
6.4.4.b Shear waves
6.4.5 Compressional waves in suspensions
6.4.6 Shear waves in suspensions
6.4.7 Application to magmas
6.5 Discussion
6.5.1 Limitations
6.5.2 Model validation
6.5.3 Implications for magmas
6.5 Conclusion
Supplementary section S6.1
Chapter 7 : General conclusions
Manuscript references
