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In this thesis, laboratory investigations have been conducted to investigate several processes occurring during the melt segregation (crystal settling and compaction processes), as well as during emplacement of plutons. With the help of three different sets of centrifuge experiments rates of these three magmatic processes have been evaluated. In the first series of the centrifuge experiments, the diapiric ascent of buoyant material from two source layers at different depths was studied. Through five models, the hypothesis of ascending diapirs was tested and it was demonstrated whether a rising diapir ascends straight upward or if its ascent might be deviated by another buoyant, softer – and consequently easier to travel through – layer which is located within the overburden strata. We were interested under which conditions they can be formed. For this purpose we placed perturbations on top of both the buoyant layers; either with a set-off of both the protrusions (for three of these experiments), or with both protrusion sitting directly on top of each other (for one of the experiments). In the first experiment, we omitted the perturbations, to test which pathways diapirs take which grow from natural Rayleigh-Taylor instabilities. Three others experiments differed in the viscosity contrast between the overburden and the buoyant material. Through the experimental runs, the effects of different overburden viscosities and perturbation positions on the number of the diapirs were observed. The modeling results show that two diapirs rising from the offset perturbations do not take the same pathway through the overburden layer. Rather, each diapir takes a different pathway, with the deeper diapir piercing through its overburden while rising, regardless if it was a buoyant layer or denser overburden layers. However, when the two perturbations were situated directly above each other in the different PDMS layers, this resulted in the formation of one big diapir rather than several smaller ones, and the overburden layer was less deformed than with offset perturbations. Diapiric structures as those derived from the models without perturbation and where the perturbation are offset occur within Great Kavir Basin (Iran), where numerous salt diapirs grew from several salt horizons, which show a similar spatial distribution. The resulting structure observed in the model where the two perturbations situated directly above each other, is close to what is observed in composite batholiths such as the Flasergranitoid Zone within the Bergsträßer Odenwald Crystalline Complex (Germany). The second series of models were aimed to study crystal settling within a magma. For this purpose experiments with an artificial magma of 30 vol% olivine in 70 vol% basaltic melt were conducted to elucidate the formation mechanisms and time scales of gravitational cumulates. Through the experiments, two physical processes have been observed: (i) purely mechanical compaction, and (ii) chemical compaction induced by dissolution and re-precipitation of settled crystals. The results reveals that the mechanical settling of the dense olivine suspension occurs at about 1/6 the speed of simple Stokes settling, and a sedimentation exponent n of 4.1 is found. Evidences of chemical compaction induced by dissolution and re-precipitation of settled crystals have been highlighted by a detailed analysis of the fine structure of olivine grain boundaries. This last has revealed (1) the presence of Ca, which is characteristic only for MORB-melt, at the interface of two adjacent Ol-grains even when no melt is present; (2) a not fully crystallized boundary layer between two adjacent olivine grains. The crystal size distribution curves and the grain size growth exponent n ~3.6 indicate that diffusion controlled Ostwald ripening is the dominant crystal growth mechanism in concentrated magmatic suspensions. Finally, the formation times in natural olivine adcumulates have been calculated. The last series of centrifuge experiments deals with the crystal-melt settling-floating mechanism in a system composed of natural two pyroxene gabbro. The results have revealed a vertical evolution of the major and trace elements in the melt phase. Then, a numerical modelling of the sedimentation process of the crystals has been made in order to describe the compaction evolution with time. In comparing the numerical simulation with the centrifuge modelling, the stratification of the compacted layer in the runs is reproduced in numerical models. Moreover, on the base of the numerical and centrifuge modelling, a sedimentation exponent describing a deviation of settling in concentrated suspensions from Stokes sedimentation has been evaluated. Finally, the numerical simulation is applied to the Muskox intrusion to estimate the formation time and the melt fraction evolution in using the hindered sedimentation model calculations.
Melt segregation inside the earth consists of two different processes: 1) Generation of partially molten rock and 2) separation of melt, produced from partially molten rock, from the solid residual matrix. This thesis focuses on the later process. The 2 phase flow dynamics combines the study of flow dynamics of melt and matrix. Several studies have given the background theoretical frameworks for the flow dynamics of melt inside the earth. [McKenzie, 1984] summarizes the studies of [Ahern and Turcotte, 1979; Frank, 1968; Sleep, 1975] and gives a complete set of governing equations for the 2-phase flow problem.
[Bercovici et al., 2001] gives a general formulation considering the univariate system of equations related to matrix and melt flow which includes the interfacial surface force. The assumption of melt having negligible viscosity compare to the matrix has been abandoned. Therefore, based on these formulations, we have constructed our numerical model and thereafter a fortran code PERCOL2D to get an insight of melt percolation process through porous media. Additionally, we have used the Helmhotz decomposition, which splits a smooth and rapidly decaying vector field into an irrotational vector field and an incompressible vector field [Srámek, 2007], for matrix and fluid viscosity in order to lower the number of linearly independent variables to minimize the computational complications. The melt residing at inter-granular areas of lithosphere, forms an interconnected network even at low porosity. Therefore, being less dense than the matrix, melt moves up through porous media due to its buoyancy. Compaction of matrix, which occurs to compensate the melt separation, is considered in this thesis, where the effective bulk and shear viscosity of matrix are function of melt fraction. We have effective bulk viscosity of matrix as inversely proportional to melt fraction. Porosity dependence of effective bulk and shear viscosity leads to stronger melt focusing in highly porous region like mid ocean ridges [Katz, 2008] since the ratio of bulk and shear viscosity is smaller (< 10) than the constant viscosity case for the porous waves having non dimensional amplitude 5% or higher. Moreover, it is observed in [Richard et al., 2012] that the solitary wave formed in porosity dependent viscous matrix settings are steeper than the one formed in the constant matrix viscosity setting.
Firstly some 1D numerical experiments with PERCOL2D have been carried out using fixed and periodic boundary conditions for zero source term (i.e. no melting or no freezing) and negligible surface tension.
3 series of model setups with different initial conditions have been carried out varying the width, non-dimensional amplitude and the background porosity value of the initial input of porous wave.
A mathematical derivation for 1D solitary wave solution for the two phase flow through porosity dependent compacting media, is obtained in this thesis which is different than the study of [Barcilon and Lovera, 1989; Barcilon and Richter, 1986; Scott and Stevenson, 1984; Spiegelman, 1993a,b] as the effective viscosity of matrix is constant there.
Although [Simpson and Spiegelman, 2011] gives the solitary wave solutions in 1D, 2D and 3D considering the porosity dependent effective viscosity of the matrix, but using the small background porosity approximation, they neglect the background porosity (i.e φ0) and therefore the effect of variation of compaction lengths, which causes variation in the shape and dynamics of the solitary wave. Therefore, the study [This thesis, Richard et al., 2012] can be used for more general purpose. Solitary waves in varying viscous medium, are steeper (cf fig.5.1) compared to the one in constant viscous medium and their speed decreases as an inverse function of the background porosity. Additionally, this analytical solution is used in our code PERCOL2D and also in FDCON for numerical benchmarking (1D) of PERCOL2D.
The role of melt grain contiguity is considered in the revised viscosity formulation [Schmeling et al., 2012] based on elastic moduli theory of a fluid filled poro-elastic medium. This formulation is used in this thesis to produce a comparative dispersion relationship between speed of the wave and the non dimensional amplitude of porous wave, based on both the viscosity formulations (fig. 6.20) where one can see that the model based on [Bercovici et al., 2001] formulation, converges to the same dispersion relationship obtained from [Simpson and Spiegelman, 2011]. Whereas, the dispersion relationship using [Schmeling et al., 2012] formulations, shows time-dependent decrease of phase velocity with increasing amplitude and it is not yet clear that whether these solutions converge to steady state porosity waves before the porosity becomes 1.
Melting inside earth is a common phenomenon and can be observed in many different regions where melt travels through the mantle and crust to eventually reach the surface where it crystallizes to build large volcanic provinces, whole stratigraphic layers of flood basalts, or even the oceanic crust. Often, melt reaching the surface is a good source of information. It can be used to achieve a better understanding about processes taking place in deeper regions inside the mantle and it is therefore essential to fundamentally understand melting and melt percolation processes. In order to achieve a deeper understanding, the aim of this thesis is to investigate processes that are connected to melting by using numerical models.
The physical model used is a so called two-phase flow model which describes the ability of melt to percolate through a viscously deforming, partially molten matrix. A famous feature of two-phase flow are solitary porosity waves, which are waves of locally higher porosity ascending through a partially molten background, keeping its shape constant, driven by decompaction and compaction of the solid matrix in front and behind the wave.
The viscosity law for shear- and volume viscosity was strongly simplified in most previous studies that modeled solitary waves. Often the porosity dependency is underestimated or its influence on the volume viscosity is even neglected, leading to too high viscosities. In this work more realistic laws are used that strongly decrease for small melt fractions. Those laws are incorporated into a 2D Finite Difference mantle convection code with two-phase flow to study the ascent of solitary porosity waves.
The model results show that an initial Gaussian-shaped wave rapidly evolves into a solitary wave with a certain amplitude, traveling upwards with constant velocity. Even though strongly weaker viscosities are used, the effect on dispersion curves and wave shape are only minor as long as the background porosity is rather small. The results are still in agreement to semi-analytical solutions which neglect shear stresses in the melt segregation equation. Higher background porosities and wave amplitudes lead to significant decrease in phase velocity and wave width, as the viscosity is strongly effected. However, the models show that solitary waves are still a possible mechanism for more realistic matrix viscosities.
While the ascending of porosity waves are mostly described by the movement of fluid melt, partially molten regions inside Earth trigger upwelling of both, solid and fluid phases, which can be called diapirism. While diapirs can have a wide variety of wavelengths, porosity waves are restricted to a few times the compaction length. The size of a melt perturbation in terms of compaction length therefore describes whether material is transported by diapirism or porosity waves. In this thesis we study the transition from diapiric rise to solitary porosity waves by systematically changing the size of a porosity perturbation from 1.8 to 120 times the compaction length. In case of a perturbation of the size of a few times the compaction length a single porosity wave will emerge, either with a positive or negative vertical matrix flux and if melt is not allowed to move relative to the matrix a diapir will emerge. In between these physical end members a regime can be observed where the partially molten perturbation will split up into numerous solitary waves, whose phase velocity is low compared to the Stokes velocity and the swarm of solitary waves will ascend jointly as a diapir, slowly elongating due to a higher amplitude main solitary wave.
Solitary waves will always emerge from a melt perturbation as long as two-phase flow is enabled, but the time for a solitary wave to emerge increases non-linearly with the perturbation radius in terms of compaction length. In nature, in many cases this time might be too long for solitary waves to emerge.
Another important feature when it comes to two-phase flow is the transport of trace elements in melt. Incompatible elements prefer to go into the melt, which eventually enriches the area where it crystallizes again. In order to model this redistribution, the code FDCON was extended to allow for fully consistent transport of elements in melt, including melting, freezing and re-equilibration with time. A 2D model, a simple representation of a volcanic back arc, is set up to investigate the behavior of trace elements. The influence of retention number and re-equilibration time is examined. Lava-lamp like convection can be observed in the lower part of the model, producing melt, that eventually leads to enrichment in trace elements in the upper high-viscous layer. The total enrichment in this layer approaches an asymptotic value and a 0D model is introduced to recreate this behavior.