Melt migration by reactive porosity waves

<p>The formation of alkaline magmas observed worldwide requires that low degree-melts, potentially formed in the asthenosphere, were able to cross the overlying lithosphere. Fracturing in the upper, brittle part of the lithosphere may help to extract this melt to the surface. However, the mechanism of extraction in the lower, ductile part of the lithosphere is still contentious. Metasomatic enrichment of the lithospheric mantle demonstrates that such low-degree melts interact with the lithosphere, but the physical aspect of this process remains unclear.</p><p>Here, we aim to better understand, first, the percolation of magma in a porous viscous medium at pressure (P) and temperature (T) conditions relevant for the base of the lithosphere, and second, the impact of chemical differentiation on melt migration. We investigate theoretically the process of melt migration employing the fundamental laws of physics and thermodynamics. We simulate melt percolation numerically with a one-dimensional (1-D) Thermo-Hydro-Mechanical-Chemical (THMC) model of porosity waves coupled with thermodynamic results obtained from numerical Gibbs energy minimisation calculations. We perform THMC modelling and Gibbs energy minimisations with self-developed numerical algorithms using MATLAB and linear programming routines. We employ a simple ternary system of Forsterite/Fayalite/Enstatite for the solid and melt. Model variables, such as solid and melt densities or mass concentrations of MgO and SiO in solid and melt, are a function of pressure (P), temperature (T) and total silica concentration of the system (X). These variables are pre-computed with Gibbs energy minimisation and implemented in the THMC porosity wave transport code via parameterized equations, determining the T-P-X dependence of the model variables.</p><p>First results show that the total silica concentration and the temperature gradient are important parameters to consider in melt migration by reactive porosity waves. We discuss results of a systematic series of 1-D simulations and we present preliminary results form a 2-D reactive porosity wave model.</p>

Magma ascent mechanisms in the transition regime from solitary porosity waves to diapirism

In partially molten regions inside the earth melt buoyancy may trigger upwelling of both solid and fluid phases, i.e. diapirism. If the melt is allowed to move separately with respect to the matrix, melt perturbations may evolve into solitary porosity waves. While diapirs may form on a wide range of scales, porosity waves are restricted to sizes of a few times the compaction length. Thus, the size of a partially molten perturbation controls whether a diapir or a porosity wave will emerge. We study the transition from diapiric rise to solitary porosity waves by solving the two-phase flow equations of conservation of mass and momentum in 2D with porosity dependent matrix viscosity. We systematically vary the initial size of a porosity perturbation from 1 to 100 times the compaction length. If the perturbation is much larger than a regular solitary wave, its Stokes velocity is large and therefore faster than the segregating melt. Consequently, the fluid is not able to form a porosity wave and a diapir emerges. For small perturbations solitary waves emerge, either with a positive or negative vertical matrix velocity inside. In between the diapir and solitary wave regimes we observe a third regime of solitary wave induced focusing of melt. In these cases, diapirism is dominant but the fluid is still fast enough to locally build up small solitary waves which rise slightly faster than the diapir and form finger like structures at the front of the diapir. In our numerical simulations the width of these fingers is controlled by the compaction length or the grid size, whichever is larger. In cases where the compaction length becomes similar to or smaller than the grid size the finger-like leading solitary porosity waves are no more properly resolved, and too big and too fast waves may be the result. Therefore, one should be careful in large scale two-phase flow modelling with melt focusing especially when compaction length and grid size are of similar order.

The transition between solitary wave and diapir emergence from a high porosity disturbance in two-phase flow

<p>Many processes in the earth involve the melting of rocks and the percolation of the produced melt through the residuum. These processes have been extensively studied but there is still much left what is not completely understood. In this work we focus on the emergence of solitary porosity waves, which can emerge from disturbances in regions where melt is allowed to percolate relatively to the matrix. These waves are regions of higher melt fractions that ascend with a constant velocity while not changing their shape during this ascending process. The size of these waves depends on the compaction length, which depends on just poorly known parameters such as the permeability and the viscosity of the matrix. As they can vary over several orders of magnitudes it might have a strong influence on porosity waves and their emergence from local disturbances with higher porosities than the background.</p><p>In this work we start with a 2D Gaussian-bell shaped disturbance with a certain porosity amplitude and vary the initial radius which is non-dimensionized by the characteristic compaction length. For some cases this disturbance results in an ascending solitary wave and for others it rises upwards as a diapir. For a few cases a kind of fingering can be observed which  looks like a small emerging porosity wave which is just slightly faster than the following melt of the initial larger disturbance. This leads to a melt ascent with a strongly focused front.</p><p>Comparison of porosity wave dispersion curves with analytical ascent rates of a Stokes sphere helps explaining this transition of diapirs to solitary waves via a melt ascent with a strongly focused front.</p>