ALBERT

Description: SUMMARY Self-consistent modelling of magmatic systems is challenging as the melt continuously changes its chemical composition upon crystallization, which may affect the mechanical behaviour of the system. Melt extraction and subsequent crystallization create new rocks while depleting the source region. As the chemistry of the source rocks changes locally due to melt extraction, new calculations of the stable phase assemblages are required to track the rock evolution and the accompanied change in density. As a consequence, a large number of isochemical sections of stable phase assemblages are required to study the evolution of magmatic systems in detail. As the state-of-the-art melting diagrams may depend on nine oxides as well as pressure and temperature, this is a 10-D computational problem. Since computing a single isochemical section (as a function of pressure and temperature) may take several hours, computing new sections of stable phase assemblages during an ongoing geodynamic simulation is currently computationally intractable. One strategy to avoid this problem is to pre-compute these stable phase assemblages and to create a comprehensive database as a hyperdimensional phase diagram, which contains all bulk compositions that may emerge during petro-thermomechanical simulations. Establishing such a database would require repeating geodynamic simulations many times while collecting all requested compositions that may occur during a typical simulation and continuously updating the database until no additional compositions are required. Here, we describe an alternative method that is better suited for implementation on large-scale parallel computers. Our method uses the entries of an existing preliminary database to estimate future required chemical compositions. Bulk compositions are determined within boundaries that are defined manually or through principal component analysis in a parameter space consisting of clustered database entries. We have implemented both methods within a massively parallel computational framework while utilizing the Gibbs free energy minimization program Perple_X. Results show that our autonomous approach increases the resolution of the thermodynamic database in compositional regions that are most likely required for geodynamic models of magmatic systems.

Description: Quantifying the hydraulic properties of single fractures is a fundamental requirement to understand fluid flow in fractured reservoirs. For an ideal planar fracture, the effective flow is proportional to the cube of the fracture aperture. In contrast, real fractures are rarely planar, and correcting the cubic law in terms of fracture roughness has therefore been a subject of numerous studies in the past. Several empirical relationships between hydraulic and mechanical aperture have been proposed based on statistical variations of the aperture field. However, often, they exhibit non-unique solutions, attributed to the geometrical variety of naturally occurring fractures. In this study, a non-dimensional fracture roughness quantification scheme is acquired, opposing effective surface area against relative fracture closure. This is used to capture deviations from the cubic law as a function of quantified fracture roughness, here termed hydraulic efficiencies. For that, we combine existing methods to generate synthetic 3-D fracture voxel models. Each fracture consists of two random, 25 cm2 wide self-affine surfaces with prescribed roughness amplitude, scaling exponent, and correlation length, which are separated by varying distances to form fracture configurations that are broadly spread in the newly formed two-parameter space (mean apertures in submillimeter range). First, we performed a percolation analysis on 600 000 synthetic fractures to narrow down the parameter space on which to conduct fluid flow simulations. This revealed that the fractional amount of contact and the percolation probability solely depend on the relative fracture closure. Next, Stokes flow calculations are performed, using a 3-D finite differences code on 6400 fracture models to compute directional permeabilities. The deviations from the cubic law prediction and their statistical variability for equal roughness configurations were quantified. The resulting 2-D solution fields reveal decreasing cubic law accordance down to 1 % for extreme roughness configurations. We show that the non-uniqueness of the results significantly reduces if the correlation length of the aperture field is much smaller than the spatial extent of the fracture. An equation was provided that predicts the average behavior of hydraulic efficiencies and respective fracture permeabilities as a function of their statistical properties. A model to capture fluctuations around that average behavior with respect to their correlation lengths has been proposed. Numerical inaccuracies were quantified with a resolution test, revealing an error of 7 %. By this, we propose a revised parameterization for the permeability of rough single fractures, which takes numerical inaccuracies of the flow calculations into account. We show that this approach is more accurate compared to existing formulations. It can be employed to estimate the permeability of fractures if a measure of fracture roughness is available, and it can readily be incorporated in discrete fracture network modeling approaches.

Description: We apply three-dimensional (3-D) thermo-mechanical numerical simulations of the shortening of the upper crustal region of a passive margin in order to investigate the control of 3-D laterally variable inherited structures on fold-and-thrust belt evolution and associated nappe formation. We consider tectonic inheritance by employing an initial model configuration with basement horst and graben structures having laterally variable geometry and with sedimentary layers having different mechanical strength. We use a visco-plastic rheology with a temperature-dependent flow law and a Drucker–Prager yield criterion. The models show the folding, detachment (shearing off) and horizontal transport of sedimentary units, which resemble structures of fold and thrust nappes. The models further show the stacking of nappes. The detachment of nappe-like structures is controlled by the initial basement and sedimentary layer geometry. Significant horizontal transport is facilitated by weak sedimentary units below these nappes. The initial half-graben geometry has a strong impact on the basement and sediment deformation. Generally, deeper half-grabens generate thicker nappes and stronger deformation of the neighbouring horst, while shallower half-grabens generate thinner nappes and less deformation in the horst. Horizontally continuous strong sediment layers, which are not restricted to initial graben structures, cause detachment (décollement) folding and not overthrusting. The amplitude of the detachment folds is controlled by the underlying graben geometry. A mechanically weaker basement favours the formation of fold nappes, while stronger basement favours thrust sheets. The model configuration is motivated by applying the 3-D model to the Helvetic nappe system of the Central Alps of France and Switzerland. Our model reproduces several first-order features of this nappe system, namely (1) closure of a half-graben and associated formation of the Morcles and Doldenhorn nappes, (2) overthrusting of a nappe resembling the Wildhorn and Glarus nappes, and (3) formation of a nappe pile resembling the Helvetic nappes resting above the Infrahelvetic complex. Furthermore, the finite strain pattern, temperature distribution and timing of the 3-D model is in broad agreement with data from the Helvetic nappe system. Our model, hence, provides a 3-D reconstruction of the first-order tectonic evolution of the Helvetic nappe system. Moreover, we do not apply any strain softening mechanisms. Strain localization, folding and nappe transport are controlled by initial geometrical and mechanical heterogeneities showing the fundamental importance of tectonic inheritance on fold-and-thrust belt evolution.

Description: The evolution of crustal magmatic systems is incompletely understood, as most studies are limited either by their temporal or spatial resolution. Exposed plutonic rocks represent the final stage of a long-term evolution punctuated by several magmatic events with different chemistry and generated under different mechanical conditions. Although the final state can be easily described, the nature of each magmatic pulse is more difficult to retrieve. This study presents a new method to investigate the compositional evolution of plutonic systems while considering thermal and mechanical processes. A thermomechanical code (MVEP2) extended by a semi-analytical dike/sill formation algorithm, is combined with a thermodynamic modelling approach (Perple_X) to investigate the feedback between petrology and mechanics. Melt is extracted to form dikes while depleting the source region. The evolving rock compositions are tracked on markers using a different phase diagram for each discrete bulk-rock composition. The rock compositional evolution is thus tracked with a high precision by means of a database with more than 58 000 phase diagrams. This database describes how density, melt fraction, chemical composition of melt and solid fractions and mineralogical assemblages change over crustal to uppermost mantle P–T conditions for a large range of rock compositions. Each bulk rock composition is composed of the 10 major oxides (SiO2–TiO2–Al2O3–Cr2O3–MgO–FeO–CaO–Na2O–K2O–H2O) including an oxygen buffer. The combined modelling approach is applied to study the chemical evolution of the crust during arc magmatism and related melt extraction and magma mixing processes. Basaltic sills are periodically injected into the crust to model heat/magma influx from the mantle. We find that accumulated sills turn into long-lived mush chambers when using a lower rock cohesion or assuming a higher intrusion depth. Associated partial melting of crustal host rocks occurs around densely distributed dikes and sills. High silica rocks (e.g. granites) are generated by partial melting of the host rocks, melt segregation within dikes, and from fractional crystallization of basalts. Although the volume of these rocks is relatively small in our models compared to rocks with a mafic to intermediate composition, they provide important information about the processes of magma differentiation within arc continental crust.