Daniel Koehn

Development of crystal morphology during unitaxial growth in a progressively widening vein: II. Numerical simulations of the evolution of antitaxial fibrous veins

The development of fibrous morphology and capability of fibres for tracking the opening trajectory were investigated using numerical simulations of a natural antitaxial fibrous vein. Starting from a non-unique best case, variation of fracture opening velocity, grain size, wall roughness, growth anisotropy and crystal growth velocity shows that these parameters differ in importance for crystal morphology and tracking capability. Fibrous veins can be simulated using crack–seal opening of the fracture. Grain boundaries track the opening trajectory if the wall roughness is high, opening increments are small and crystals touch the wall before the next crack increment starts.

Growth of stylolite teeth patterns depending on normal stress and finite compaction

Abstract Stylolites are spectacular rough dissolution surfaces that are found in many rock types. They are formed during a slow irreversible deformation in sedimentary rocks and therefore participate to the dissipation of tectonic stresses in the Earths upper crust. Despite many studies, their genesis is still debated, particularly the time scales of their formation and the relationship between this time and their morphology. We developed a new discrete simulation technique to explore the dynamic growth of the stylolite roughness, starting from an initially flat dissolution surface. We demonstrate that the typical steep stylolite teeth geometry can accurately be modelled and reproduce natural patterns. The growth of the roughness takes place in two successive time regimes: i) an initial non-linear increase in roughness amplitude that follows a power-law in time up to ii) a critical time where the roughness amplitude saturates and stays constant. We also find two different spatial scaling regimes. At small spatial scales, surface energy is dominant and the growth of the roughness amplitude follows a power-law in time with an exponent of 0.5 and reaches an early saturation. Conversely, at large spatial scales, elastic energy is dominant and the growth follows a power-law in time with an exponent of 0.8. In this elastic regime, the roughness does not saturate within the given simulation time. Our findings show that a stylolites roughness amplitude only captures a very small part of the actual compaction that a rock experienced. Moreover the memory of the compaction history may be lost once the roughness growth saturates. We also show that the stylolite teeth geometry tracks the main compressive stress direction. If we rotate the external main compressive stress direction, the teeth are always tracking the new direction. Finally, we present a model that explains why teeth geometries form and grow non-linearly with time, why they are relatively stable and why their geometry is strongly deterministic while their location is random.

Numerical simulation of fibre growth in antitaxial strain fringes

A two-dimensional computer model (‘Fringe Growth’) is used to simulate the incremental growth of crystal fibres in undeformed antitaxial strain fringes. The user can define the shape of a core-object (e.g. a pyrite crystal), the growth velocity and anisotropy of growing crystals, the rotation of fringes and core-object with respect to a horizontal datum and with respect to each other, and the opening velocity of fringes. Growth is simulated by movement of nodes connecting line segments that define the grain boundaries. Modelling results predict that face-controlled strain fringes will grow around smooth core-objects and strain fringes with displacement-controlled and face-controlled fibres around core-objects with rough surfaces. The surface roughness of the core-object determines if fibres in the fringes track the opening trajectory, since fibres follow asperities on the surface of the core-object. Rotation of the core-object and the fringes with respect to an external reference frame and with respect to each other influences the geometry of the fibres. Our modelling results indicate that fibre growth direction is not directly dependent on the orientation of the extensional instantaneous stretching axes or the finite maximum strain axes.

Shear sense indicators in striped bedding-veins

Striped bedding-veins are veins that lie subparallel to bedding and have an internal layering or lineation at a small angle to the veins’ long axis. They form during bedding-parallel slip and can be used as shear sense indicators. Solid inclusion trails produce the visible internal layering or lineation and track the opening direction of the veins. Elongate quartz crystals however can be oriented at an angle of up to 80° to the opening direction, are non-tracking, and contain almost no information on the shear sense. The striped bedding-veins can be separated into three types according to the geometry of their internal segmentation. Veins of type B opened parallel to jogs oriented at a low angle to bedding, veins of type J opened parallel to jogs oriented at a high angle to bedding and veins of type O opened orthogonal to bedding and jogs. Striped bedding-veins of types B and J contain crack–seal inclusion bands and displacement parallel inclusion trails. Striped bedding-veins of type O feature only crack–seal inclusion bands. The example of striped bedding-veins presented in this paper from the Orobic Alps of Italy belongs to type B. The lineation in the veins and the orientation of the inclusion bands and inclusion trails, as well as the orientation of steps in the vein wall, can be used to determine the sense of shear and the direction and amount of vein opening or bedding-parallel slip.

Disequilibrium melt distribution during static recrystallization

Melt migration and segregation, and the rheology of partially molten rocks in the upper mantle and lower crust, strongly depend on the grain-scale distribution of the melt. Current theory for monomineralic aggregates predicts a perfectly regular melt framework, but high-temperature experiments with rock-forming minerals + melt show considerable deviations from this predicted geometry. Disequilibrium features, such as fully wetted grain boundaries and large melt patches, have been described; these were mainly attributed to surface-energy anisotropy of the minerals. We present static analogue experiments with norcamphor + ethanol that allow continuous in situ observation of the evolving liquid distribution. The experiments show that all previously reported disequilibrium features can form during fluid-enhanced static recrystallization when small grains are consumed. There is no need to invoke surface-energy anisotropy, although this might enhance the effect. All disequilibrium features are transitory and evolve back toward equilibrium geometry. However, because the system undergoes continuous static recrystallization, disequilibrium features are always present in a partially molten polycrystalline aggregate and therefore control its properties.

Modeling the growth of stylolites in sedimentary rocks

Stylolites are ubiquitous pressure-solution seams found in sedimentary rocks. Their morphology is shown to follow two self-affine regimes: analyzing the scaling properties of their height over their average direction shows that at small scale, they are self-affine surfaces with a Hurst exponent around 1, and at large scale, they follow another self-affine scaling with Hurst exponent around 0.5. In the present paper we show theoretically the influence of the main principal stress and the local geometry of the stylolitic interface on the dissolution reaction rate. We compute how it is affected by the deviation between the principal stress axis, and the local interface between the rock and the soft material in the stylolite. The free energy entering in the dissolution reaction kinetics is expressed from the surface energy term, and via integration from the stress perturbations due to these local misalignments.The resulting model shows the interface evolution at different stress conditions. In the stylolitic case, i.e. when the main principal stress is normal to the interface, two different stabilizing terms dominate at small and large scales which are linked respectively to the surface energy and to the elastic interactions. Integrating the presence of small scale heterogeneities related to the rock properties of the grains in the model leads to the formulation of a Langevin equation predicting the dynamic evolution of the surface. This equation leads to saturated surfaces obeying the two observed scaling laws. Analytical and numerical analysis of this surface evolution model shows that the cross-over length separating both scaling regimes depends directly on the applied far-field stress magnitude. This method gives the basis for the development of a paleostress magnitude marker. We apply the computation of this marker, i.e. the morphological analysis, on a stylolite found in the Dogger limestone layer located in the neighborhood of the Andra Underground Research Laboratory at Bure (Eastern France). The results are consistent with the two scaling regimes expected, and the practical determination of the major principal paleostress, from the estimation of a cross-over length, is illustrated on this example.

The Jabal Akhdar dome in the Oman Mountains: Evolution of a dynamic fracture system

The Mesozoic succession of the Jabal Akhdar dome in the Oman Mountains hosts complex networks of fractures and veins in carbonates, which are a clear example of dynamic fracture opening and sealing in a highly overpressured system. The area underwent several tectonic events during the Late Cretaceous and Cenozoic, including the obduction of the Samail ophiolite and Hawasina nappes, followed by uplift and compression due to the Arabia-Eurasia convergence. This study presents the results of an extensive tectonic survey, and correlates subseismic-scale structures in Jabal Akhdar (faults, fractures, veins and stylolites) with the main tectonic events in the Northeastern Arabian plate. As some of the studied formations host large oil reserves in neighboring areas, determining the relative timing of these events in the exhumed rocks is important to understand hydrocarbon distribution and fracture patterns in these reservoirs. The formation of early veins and stylolites in the Oman Mountains is followed by top-to-the-South layer-parallel shearing that may be associated with the obduction of the Samail and Hawasina nappes. This compressional tectonic event is followed by normal (dip-slip) to oblique-slip faults and veins. Top-to-the-Northeast layer-parallel shearing, which corresponds to the first stage of exhumation of the autochthonous rocks offsets these structures. Our new data indicate that this first phase of events is overprinted by complex strike-slip networks of veins and fractures, as well as by the reactivation and onset of seismic-scale faults. Strike-slip structures belong to three distinct events. The first one (NW-SE-oriented compression) is probably associated with the oblique collision of the Indian plate against the Arabian platform during the Late Campanian to the Mid Eocene. The second event (E-W-oriented compression) is likely to have been formed during the Late Oligocene-Middle Miocene during uplift. The last event (NE-SW-oriented compression) probably took place during the Miocene-Pliocene. Structures of the first two strike-slip events have the same orientation as seismic-scale faults observed in the subsurface of Oman and Abu Dhabi. In addition, increasing vein intensity towards the top of the autochthonous formations in the Oman mountains, as well as the small angle between conjugate vein sets, indicate that high fluid pressures that are thought to be present during strike-slip deformation.

Dynamic Development of Hydrofracture

Many natural examples of complex joint and vein networks in layered sedimentary rocks are hydrofractures that form by a combination of pore fluid overpressure and tectonic stresses. In this paper, a two-dimensional hybrid hydro-mechanical formulation is proposed to model the dynamic development of natural hydrofractures. The numerical scheme combines a discrete element model (DEM) framework that represents a porous solid medium with a supplementary Darcy based pore-pressure diffusion as continuum description for the fluid. This combination yields a porosity controlled coupling between an evolving fracture network and the associated hydraulic field. The model is tested on some basic cases of hydro-driven fracturing commonly found in nature, e.g., fracturing due to local fluid overpressure in rocks subjected to hydrostatic and nonhydrostatic tectonic loadings. In our models we find that seepage forces created by hydraulic pressure gradients together with poroelastic feedback upon discrete fracturing play a significant role in subsurface rock deformation. These forces manipulate the growth and geometry of hydrofractures in addition to tectonic stresses and the mechanical properties of the porous rocks. Our results show characteristic failure patterns that reflect different tectonic and lithological conditions and are qualitatively consistent with existing analogue and numerical studies as well as field observations. The applied scheme is numerically efficient, can be applied at various scales and is computational cost effective with the least involvement of sophisticated mathematical computation of hydrodynamic flow between the solid grains.

Fingerprinting stress: Stylolite and calcite twinning paleopiezometry revealing the complexity of progressive stress patterns during folding—The case of the Monte Nero anticline in the Apennines, Italy

In this study we show for the first time how quantitative stress estimates can be derived by combining calcite twinning and stylolite roughness stress fingerprinting techniques in a fold-and-thrust belt. First, we present a new method that gives access to stress inversion using tectonic stylolites without access to the stylolite surface and compare results with calcite twin inversion. Second, we use our new approach to present a high-resolution deformation and stress history that affected Meso-Cenozoic limestone strata in the Monte Nero Anticline during its late Miocene-Pliocene growth in the Umbria-Marche Arcuate Ridge (northern Apennines, Italy). In this area an extensive stylolite-joint/vein network developed during layer-parallel shortening (LPS), as well as during and after folding. Stress fingerprinting illustrates how stress in the sedimentary strata did build up prior to folding during LPS. The stress regime oscillated between strike slip and compressional during LPS before ultimately becoming strike slip again during late stage fold tightening. Our case study shows that high-resolution stress fingerprinting is possible and that this novel method can be used to unravel temporal relationships that relate to local variations of regional orogenic stresses. Beyond regional implications, this study validates our approach as a new powerful toolbox to high-resolution stress fingerprinting in basins and orogens combining joint and vein analysis with sedimentary and tectonic stylolite and calcite twin inversion techniques.

Brittle reactivation of ductile shear zones in NW Namibia in relation to South Atlantic rifting

Rifting has occurred worldwide along preexisting mobile belts, which are therefore thought to control rift orientation on a large scale. On a smaller scale, shear zones within mobile belts are reactivated as rift faults. In NW Namibia, shear zones of the Neoproterozoic Kaoko Belt run subparallel to the present-day continental passive margin and are inferred to have been reactivated during the opening of the South Atlantic Ocean. However, the extent of this reactivation and the influence of the reactivated shear zones on South Atlantic rifting are largely unknown. A combined remote sensing and field study was conducted to quantify offsets that are a direct function of shear zone reactivation. The shear zones of the Kaoko Belt are partly overlain by the Parana-Etendeka volcanic rocks, which were emplaced shortly before or simultaneously to the Atlantic rifting. Faulting within these volcanic rocks can be linked to synrift or postrift movements. Along the shear zones, downfaulting of the basalts is widespread along listric faults where half-graben form in the hanging wall. At three sites we could determine vertical offsets of ~1180 m, ~470 m, and ~70 m. Although many shear zones were reactivated as faults, these are isolated, and offsets are small, suggesting that reactivation occurred only as a side effect of the rifting and that the Kaoko Belt shear zones have not exerted a significant influence on the rift orientation.