Zebra pattern in rocks as a function of grain growth affected by second-phase particles

Alternating fine grained dark and coarse grained light layers in rocks are often termed zebra patterns and are found worldwide. The crystals in the different bands have an almost identical chemical composition, however second-phase particles (e.g., fluid filled pores or a second mineral phase) are concentrated in the dark layers. Even though this pattern is very common and has been studied widely, the initial stage of the pattern formation remains controversial. In this communication we present a simple microdynamic model which can explain the beginning of the zebra pattern formation. The two dimensional model consists of two main processes, mineral replacement along a reaction front, and grain boundary migration affected by impurities. In the numerical model we assume that an initial distribution of second-phase particles is present due to sedimentary layering. The reaction front percolates the model and redistributes second-phase particles by shifting them until the front is saturated and drops the particles again. This produces and enhances initial layering. Grain growth is hindered in layers with high second-phase particle concentrations whereas layers with low concentrations coarsen. Due to the grain growth activity in layers with low second-phase particle concentrations these impurities are collected at grain boundaries and the crystals become very clean. Therefore, the white layers in the pattern contain large grains with low concentration of second-phase particles, whereas the dark layers contain small grains with a large second-phase particle concentration. The presence of the zebra pattern is characteristic for regions containing Pb-Zn mineralization. Therefore, the origin of the structure is presumably related to the mineralization process and might be used as a marker for ore exploration. A complete understanding of the formation of this pattern will contribute to a more accurate understanding of hydrothermal systems that build up economic mineralization

Reaction-induced porosity fingering: replacement dynamic and porosity evolution in the KBr-KCl system

In this contribution, we use X-ray computed micro-tomography (X-CT) to observe and quantify dynamic pattern and porosity formation in a fluid-mediated replacement reaction. The evolution of connected porosity distribution helps to understand how fluid can migrate through a transforming rock, for example during dolomitization, a phenomenon extensively reported in sedimentary basins. Two types of experiment were carried out, in both cases a single crystal of KBr was immersed in a static bath of saturated aqueous KCl at room temperature and atmospheric pressure, and in both cases the replacement process was monitored in 3D using X-CT. In the first type of experiment a crystal of KBr was taken out, scanned, and returned to the solution in cycles (discontinuous replacement). In the second type of experiment, 3 samples of KBr were continuously reacted for 15, 55 mins and 5.5 hours respectively, with the latter being replaced completely (continuous replacement). X-CT of KBr-KCl replacement offers new insights into dynamic porosity development and transport mechanisms during replacement. As the reaction progresses the sample composition changes from KBr to KCl via a K(Br,Cl) solid solution series which generates porosity in the form of fingers that account for a final molar volume reduction of 37% when pure KCl is formed. These fingers form during an initial and transient advection regime followed by a diffusion dominated system, which is reflected by the reaction propagation, front morphology, and mass evolution. The porosity develops as fingers perpendicular to the sample walls, which allow a faster transport of reactant than in the rest of the crystal, before fingers coarsen and connect laterally. In the continuous experiment, finger coarsening has a dynamic behaviour consistent with fingering processes observed in nature. In the discontinuous experiment, which can be compared to rock weathering or to replacement driven by intermittent fluid contact, the pore structure changes from well-organized parallel fingers to a complex 3D connected network, shedding light on the alteration of reservoir properties during weathering

Zebra dolomites of the Spessart, Germany: implications for hydrothermal systems of the European Zechstein Basin

Zebra dolomites have a distinctive texture and are a peculiar structural variety of dolostones often encountered in the vicinity of base metal deposits commonly in the Mississippi Valley-Type (MVT). We investigate origin and evolution of the zebra dolomites found in the region of the Spessart, northwestern Bavaria, Germany, through diagenetic and petrogenetic analysis using SEM, CL microscopy, O–C isotopes, and fluid inclusion micro-thermometry. Here, we aim to shed light on the nature of the fluids that altered the zebra dolomite of the Zechstein formation. We distinguish the geochemical signatures of two different fluid flow regimes post-dating texture formation, each characterized by specific homogenization temperatures and oxygen–carbon isotope ratios (Event 1: Th = 120 °C; δ18Ofluids = [0 to 2‰]; Event 2; Th = 300 °C; δ18Ofluids = 18‰). Comparison of these fluids and the associated mineralization with published regional fluid flow data support that the zebra dolomites in the Spessart most likely coincided with the Permian large-scale fluid flow event that occurred throughout the European Zechstein Basin

Pattern formation in Mississippi valley-type deposits - identifying one of nature's fundamental processes in geologic systems

Nature has a range of distinct mechanisms that cause initially heterogeneous systems to break their symmetry and form patterns. The study of pattern formation and the behaviour of non-linear systems have interested scientists across many disciplines from physics, chemistry, biology, and economics to geosciences. In study, a new mechano-chemical process that leads to the formation of complex periodic wave- or stripe-like zebra patterns in rocks will be presented. The genesis of periodically banded dolostones, which host lead-zinc mineralization, has been studied for several years, because an evolutionary relationship between the banded dolomites and mineralized areas is highly likely. To date, a complete generic model has not been formulated for the formation of these zebra rocks and there is an ongoing debate on the exact processes leading to the genesis of the pattern. In the first part of this work, new analytical findings obtained from zebra dolomites from Peru and Germany will be presented. The zebra dolomites from Germany have never been described before and represent the first known zebra dolomite deposit in Germany. Based on the analytical finding, a numerical and an analytical model were developed in the second part of this thesis. The combination of the numerical and the analytical model yields a new approach to the zebra pattern formation based on one of nature’s fundamental processes for wave-like pattern formation in geological systems. This approach also includes a new inversion routine based on the spacing of the respective pattern

Relative rates of fluid advection, elemental diffusion and replacement govern reaction front patterns

Replacement reactions during fluid infiltration into porous media, rocks and buildings are known to have important implications for reservoir development, ore formation as well as weathering. Natural observations and experiments have shown that in such systems the shape of reaction fronts can vary significantly ranging from smooth, rough to highly irregular. It remains unclear what process-related knowledge can be derived from these reaction front patterns. In this contribution we show a numerical approach to test the effect of relative rates of advection, diffusion, and reaction on the development of reaction fronts patterns in granular aggregates with permeable grain boundaries. The numerical model takes (i) fluid infiltration along permeable grain boundaries, (ii) reactions and (iii) elemental diffusion into account. We monitor the change in element concentration within the fluid, while reactions occur at a pre-defined rate as a function of the local fluid concentration. In non-dimensional phase space using Péclet and Damköhler numbers, results show that there are no rough fronts without advection (Péclet<70) nor if the reaction is too fast (Damköhler>10−3). As advection becomes more dominant and reaction slower, roughness develops across several grains with a full microstructure mimicking replacement in the most extreme cases. The reaction front patterns show an increase in roughness with increasing Péclet number from Péclet 10 to 100 but then a decrease in roughness towards higher Péclet numbers controlled by the Damköhler number. Our results indicate that reaction rates are crucial for pattern formation and that the shape of reaction fronts is only partly due to the underlying transport mechanism

Cross-diffusion waves resulting from multiscale, multi-physics instabilities:Theory

We propose a multiscale approach for coupling multi-physics processes across the scales. The physics is based on discrete phenomena, triggered by local thermohydro-mechano-chemical (THMC) instabilities, that cause cross-diffusion (quasi-soliton) acceleration waves. These waves nucleate when the overall stress field is incompatible with accelerations from local feedbacks of generalized THMC thermodynamic forces that trigger generalized thermodynamic fluxes of another kind. Cross-diffusion terms in the 4 × 4 THMC diffusion matrix are shown to lead to multiple diffusional P and S wave equations as coupled THMC solutions. Uncertainties in the location of meso-scale material instabilities are captured by a wave-scale correlation of probability amplitudes. Cross-diffusional waves have unusual dispersion patterns and, although they assume a solitary state, do not behave like solitons but show complex interactions when they collide. Their characteristic wavenumber and constant speed define mesoscopic internal material time-space relations entirely defined by the coefficients of the coupled THMC reaction-cross-diffusion equations. A companion paper proposes an application of the theory to earthquakes showing that excitation waves triggered by local reactions can, through an extreme effect of a cross-diffusional wave operator, lead to an energy cascade connecting large and small scales and cause solid-state turbulence.</p

Cross-diffusion waves resulting from multiscale, multiphysics instabilities: Application to earthquakes

Theoretical approaches to earthquake instabilities propose shear-dominated source mechanisms. Here we take a fresh look at the role of possible volumetric instabilities preceding a shear instability. We investigate the phenomena that may prepare earthquake instabilities using the coupling of thermo-hydro-mechano-chemical reaction-diffusion equations in a THMC diffusion matrix. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves known as cross-diffusion or quasi-soliton waves. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a stationary wave focus from large to small scale. We show that the rich solution space of the reaction-cross-diffusion approach to earthquake instabilities can recover classical Turing instabilities (periodic in space instabilities), Hopf bifurcations (spring-slider-like earthquake models), and a new class of quasi-soliton waves. Only the quasi-soliton waves can lead to extreme focussing of the wave energy into short-wavelength instabilities of short duration. The equivalent extreme event in ocean waves and optical fibres leads to the appearance of "rogue waves"and high energy pulses of light in photonics. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike. This spike is likely to cause unstable slip on a pre-existing (near-critically stressed) fault acting as a trigger for the ultimate (shear) seismic moment release.</p