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SUMMARY The geophysical detection of magma bodies and the estimation of the dimensions, physical properties and the volume fraction of each phase composing the magma is required to improve the forecasting of volcanic hazards and to understand transcrustal magmatism. We develop an analytical model to calculate P waves velocity in a three-phase magma consisting of crystals and gas bubbles suspended in a viscous melt. We apply our model to calculate the speed of sound as a function of the temperature in three magmas with different chemical compositions, representative of the diversity that is encountered in arc magmatism. The model employs the coupled phase theory that explicitly accounts for the exchanges of momentum and heat between the phases. We show that the speed of sound varies nonlinearly with the frequency of an acoustic perturbation between two theoretical bounds. The dispersion of the sound in a magma results from the exchange of heat between the melt and the dispersed phases that affects the magnitude of their thermal expansions. The lower bound of the sound speed occurs at low frequencies for which all the constituents can be considered in thermal equilibrium, whereas the upper bound occurs at high frequencies for which the exchange of heat between the phases may be neglected. The presence of gas in a magma produces a sharp decrease in the velocity of compressional waves and generates conditions in which the dispersion of the sound is significant at the frequencies usually considered in geophysics. Finally, we compare the estimates of our model with the ones from published relationships. Differences are largest at higher frequencies and are <10 per cent for typical magma. 

Currently, our ability to interpret the mechanics of magma mingling and mixing is limited by an incomplete understanding of the modes of mixing across all melt fractions and compositions. Here, we present numerical simulations of the emplace- ment of crystal-free magma in crystal-rich reservoirs employing a computational fluid dynamics and discrete element method (CFD–DEM). We performed two runs corresponding to the emplacement of basalt into two end-member types of magmas mush (basaltic and dacitic). We found that the intruded volumes have similar shapes and are surrounded by a halo where the crys- tal volume fraction of the mush is lower. The dynamics of intruded melt are, however, different. Importantly, the mingling of the intruded and host materials starts after emplacement and consists in the incorporation of mush material into the intruded magma. Our findings imply that purely thermo-mechanical processes controlled by grain-scale dynamics are sufficient to explain fundamental aspects of recharge. 

An obstacle to developing a general mechanical framework for magma mush is the emergence and complexity of a crystal fabric. To illuminate the conditions that produce a crystal fabric we performed time-dependent numerical simulations using a Computational-Fluid-Dynamics and Discrete-Element-Method (CFD-DEM) model in three dimensions. The specific focus was on the role of shear strain in the creation of a preferential orientation of crystals in mush. CFD-DEM method allows for the simultaneous coupling and frictional interactions of melt and crystals undergoing shear strain. The crystal shapes are represented using spheroids (either oblate or prolate). Simulations consist in imposing a compression stress (pressure) and a simple shear to a dense suspension of crystals in a viscous liquid, and monitoring the evolution of the orientation and strength of the shape fabrics. We ran a series of simulations by varying the size and aspect ratio of the particles. We considered samples in which all the solids have the same volume and shape, and cases including size and aspect ratio distributions. Results show that the strength of the shape fabric and the angle between the crystal preferential orientation and the compression plane both increase with the shear strain up to steady state values, which are primarily controlled by the aspect ratio of the particles. The stronger the aspect ratio, the greater the magnitude of the preferential orientation and the lower its angle relative to the compression plane. When introducing a distribution in the size of the crystals, we observed a decrease in the strength of the shape fabric and an increase in the angle between the preferential orientation of the crystals and the compression plane compared with samples composed of crystals having the same shape and size. Similarly, the distribution in the aspect ratio further decreases the strength of the shape fabric and increases the angle between the preferential orientation of the solids and the compression plane. Finally, we employed an alternative approach to quantify the amount of foliation and lineation and show that the samples always display a stronger foliation than lineation, although the shear strain increases both the foliation and the lineation. 

The mechanical behavior of crystal-rich mush controls the dynamics and evolution of magma bodies but is poorly understood, . The presence of a semi-rigid contact network in the crystal phase greatly affects the rheology of mush but the contributions of crystal shape to the force, contact and shape fabric remains poorly characterized. This in turn influences the transmission of stress in the mush, the packing stiffness, and the volume fraction at jamming. It is also unclear whether the total amount of deformation of a mush can be quantitatively determined from the shape preferred orientation of the crystals. We performed 3D numerical simulations using a coupled computational fluid dynamics and discrete element method to illuminate the dynamic states of non-spherical crystals in a viscous melt. Simulations consisted of the simple shear of a mush under a constant pressure upper boundary. Crystals are represented by elongated cuboids having an aspect ratio of four. Our results differ from those obtained with smooth spheres and shed light on the influence of the crystal shape and orientation fabric on the mechanical properties of a mush. We found two distinct behaviors associated with the transient and steady-state, however at all times strain is nonaffine. During the transient, the strain is accommodated by the emergence of multiple shear bands and tends to concentrate on a single one. The shear bands emerge because of steric blocking and space limitations preventing the rotation of elongated particles, generating the local and temporary jamming of the crystal network. On the contrary, in the residual and steady-state, the strain is accommodated by one main shear band. The analysis of the orientation of the crystals shows that the deformation of the mush tends to increase the foliation of the crystals more than their alignment. 

Magmatic reservoirs located in the upper crust have been shown to result from the repeated intrusions of new magmas, and spend much of the time as a crystal-rich mush. The geometry of the intrusion of new magmas may greatly affect the thermal and compositional evolution of the reservoir. Despite advances in our understanding of the physical processes that may occur in a magmatic reservoir, the resulting architecture of the composite system remains poorly constrained. Here we performed numerical simulations coupling a computational fluid dynamics and a discrete element method in order to illuminate the geometry and emplacement dynamics of a new intrusion into mush and the relevant physical parameters controlling it. Our results show that the geometry of the intrusion is to first order controlled by the density contrast that exists between the melt phases of the intrusion and resident mush rather than the bulk density contrast as is usually assumed. When the intruded melt is denser than the host melt, the intrusion pounds at the base of the mush and emplaced as a horizontal layer. The occurrence of Rayleigh-Taylor instability leading to the rapid ascent of the intruded material through the mush was observed when the intruded melt was lighter than the host one and was also unrelated to the bulk density contrast. In the absence of density contrasts between the two melt phases, the intrusion may fluidize the host crystal network and slowly ascend through the mush. The effect of the viscosity contrast between the intruded and host materials was found to have a lesser importance on the architecture of intrusions in a mush. Analyzing the eruptive sequence of well documented eruptions involving an intrusion as the trigger shows a good agreement with our modeling results, highlighting the importance of specifically considering granular dynamics when evaluating magmas and mush physical processes.