Finite Strain Variation Research Articles

Monazite as a monitor of shear strain in orogenic crust

The Ramsay-Graham heterogeneous simple shear zone model revolutionized our understanding of finite strain variation in orogenic belts. Many deeply exhumed (>20 km depths) shear zones in orogenic continental crust are a consequence of sub-simple shear strain accumulation during contraction and displacement at high temperature. Here we explore the micro-scale record of this process using syn-kinematic monazite in two shear zones in a >20,000 km2 terrane of exhumed lower continental crust. Field observations combined with high-spatial resolution X-ray mapping, Th–U-Pb electron microprobe petrochronology, and electron backscatter diffraction analysis demonstrate that monazite grains can provide an important textural and temporal record of shear strain in mylonite and ultramylonite gneisses. Monazite grains exhibit aspect ratios of 1.7–4.6 parallel to the stretching lineation and parallel or oblique (<30°) to the penetrative foliation. Monazite EBSD data for grain orientation spread, i.e., average misorientation relative to the mean, are consistent with no significant dislocation-accommodated internal deformation. We conclude that dissolution precipitation creep of monazite produced compositionally-defined geometries compatible with the dextral sense of shear observed in outcrop and thin section. Syn-kinematic rims on monazite grains that develop in low strain domains during accumulation of shear strain can provide absolute ages for μm-to km-scale kinematics in continental orogens.

Spontaneous generation of ductile shear zones by thermal softening: Localization criterion, 1D to 3D modelling and application to the lithosphere

The generation of ductile shear zones is essential for the formation of tectonic plate boundaries, such as subduction or strike-slip zones. However, the primary mechanism of ductile strain localization is still contentious. We study here the spontaneous generation of ductile shear zones by thermal softening using thermo-mechanical numerical simulations for linear and power-law viscous flow in one-dimension (1D), 2D and 3D. All models are velocity-driven. The 1D model exhibits bulk simple shear whereas the 2D and 3D models exhibit bulk pure shear. The initial conditions include a small temperature perturbation in otherwise homogeneous material. We use a series of 1D simulations to determine a new analytical formula which predicts the temperature evolution inside the shear zone. This temperature prediction requires knowledge of only the boundary velocity, flow law and thermal parameters, but no a priori information about the shear zone itself, such as thickness, stress and strain rate. The prediction is valid for 1D, 2D and 3D shear zones in bulk pure and simple shear. The results show that shear heating dominates over conductive cooling if the relative temperature increase is >50°C. The temperature variation induced by the shear zone is nearly one order of magnitude wider than the corresponding finite strain variation so that no significant temperature variation occurs between shear zone and wall rock. Applying typical flow laws for lithospheric rocks shows that shear zone generation by thermal softening occurs for typical plate tectonic velocities of few cm.yr−1 or strain rates between 10−16 and 10−14 s−1. Shear stresses larger than 200 MPa can already cause strain localization. The results indicate that thermal softening is a feasible mechanism for spontaneous ductile shear zone generation in the lithosphere and may be one of the primary mechanisms of lithospheric strain localization.

Finite strain variation across the Mahabharat Thrust in central Nepal Himalaya

This paper deals with the three-dimensional strain across the Mahabharat Thrust (MT) in the Malekhu area in central Nepal. The MT served as a glide plane for the Kathmandu Nappe. Its footwall is made up of phyllites, quartzites, and amphibolites, whereas the hanging wall contains garnetiferous schists, biotite schists, and quartzites with a few lenses of augen gneiss. A three-dimensional strain analysis reveals that Nadai’s amount of strain intensity (€s ) ranges from 0.396 to 0.575 in the footwall indicating an increasing trend towards the proximity of the MT. In contrast, the hanging wall shows an increase in (€ s) magnitude away from the MT and its value varies between 0.556 (at the basal part) and 0.795 (upper part). Microtextures and structures revealed dynamic recrystallisation of the footwall and static recrystallisation of the hanging wall rocks. The shape of three dimensional strain ellipsoids, types of microstructures, and mechanisms of grainscale deformation indicated that the footwall was dominantly affected by simple shear deformation at lower temperatures while the hanging wall suffered from pure shear with minor sub-simple shear deformation at relatively higher temperatures.

Tectonic implications of finite strain variations in Baraboo-interval quartzites (ca. 1700 Ma), Mazatzal orogen, Wisconsin and Minnesota, USA

Variably deformed Baraboo-interval quartzites (1750–1630 Ma) are now correlated by detrital zircon ages [Holm, D., Schneider, D., Coath, C.D., 1998. Age and deformation of Early Proterozoic quartzites in the southern Lake Superior region: implications for extent of foreland deformation during final assembly of Laurentia. Geology 26, 907–910] and were analyzed using finite strain techniques which document a SE–NW tectonic shortening orientation from the Baraboo syncline (south) to the Flambeau syncline (north). Fabric interpretations using bedding and the principal strain axis orientations indicate there was a mix of layer-parallel and layer-normal (synfolding) shortening in the plane of tectonic transport (SE–NW) in the thrust belt. Finite strain magnitudes increase from the foreland Barron–Sioux quartzites south toward the Baraboo syncline. Electron backscatter device (EBSD) fabric diagrams (pole figures) of quartz optic axes also demonstrate an increasingly penetrative strain to the south. Anisotropy of [low-field ac] magnetic susceptibility (AMS), as a strain proxy, preserve K min measurements in the Baraboo syncline quartzites that are sub-horizontal, E–W and intersect bedding. AMS measurements in underlying rhyolite on opposite limbs of the Baraboo syncline are clean, appear to be primary (magmatic) as K max intersects bedding, but require a complex folding interpretation that is inconsistent with field kinematic indicators. The flat-lying foreland Barron and Sioux Quartzites preserve a mix of results: quartzites with no strain (finite strain and EBSD measurements) or small strains that preserve vertical shortening. AMS measurements in the foreland preserve K min axes that are sub-horizontal and parallel to the regional shortening orientation in the adjacent thrust belt. The Mazatzal orogen produced a thrust belt that is orders of magnitude wider (∼500 km) and of higher metamorphic grade, than most thrust belts, where both the thrust belt and foreland are quartzites.

Finite strain variations along strike in mountain belts

Abstract In order to quantify finite strain from displacement fields derived from structural restorations in mountain belts, a simple technique using triangular elements (based on the finite element technique) is presented. This adequately describes the discontinuous displacement of a fold-thrust belt, whilst overcoming the difficulties posed by discontinuities which are integrated across appropriate elements for the purpose of strain calculation. The technique has been applied to two fold-thrust belts at contrasting scales, the Central Andes and the Neuchâtel region of the Jura mountains (Switzerland). In both cases, structural restorations have produced the finite displacement fields thought to be involved in their generation. Subsequent calculation of strain variation along strike shows that there is a strong relationship between first-order structure (the scale of major fold axes) and the trends of axis orientations. In spite of the contractional setting of both belts, strong along-strike extension is predicted but this is always in the context of a generally parallel to slightly convergent displacement field, and such extensions are generally related to differential shear accommodated on strike-slip or tear faults. Most elements showing along-strike extension are nevertheless predicted to undergo tectonic thickening. Second-order structures (faults necessary to accommodate local predicted deformation) are also calculated and the enormous difference between slip directions on small-scale faults and the regional ‘far field’ displacement direction is demonstrated. This is thought to be important when trying to infer large-scale tectonic information from very small-scale structures found in the field.

A spatial statistics approach to the quantification of finite strain variation in penetratively deformed thrust sheets: an example from the Sheeprock Thrust Sheet, Sevier Fold-and-Thrust belt, Utah

Strain is an important component of the total displacement field in the emplacement of a thrust sheet. The finite strain tensor in a penetratively deformed thrust sheet is a spatial variable. I describe a method for quantitative estimation of the finite strain variation in thrust sheets by applying spatial statistics analysis on strain data collected from a part of the Sheeprock thrust sheet, in the southern Sheeprock Mountains and the West Tintic Mountains, north-central Utah. Strain was measured in the quartzites of the Sheeprock thrust sheet and the spatial statistics method is illustrated using the XZ strain axial ratios.The Sheeprock thrust sheet was penetratively deformed during Sevier-age fault propagation folding. I quantified finite strain from quartzites using the modified normalized Fry method and calculated the three-dimensional strain ellipsoid from the quartzites using three orthogonal thin-sections from each oriented field sample. The variation of finite strain in the Sheeprock thrust sheet was best represented by an exponential semivariogram model, which I used to predict values of strain from unsampled locations by ordinary kriging. Cross-validation showed that, in general, the predicted and measured values show good agreement (within 1% of each other). The sampled space was contoured using the measured and predicted strain values to obtain a detailed finite strain variation pattern in a part of the Sheeprock thrust sheet.

A theory of finite strain variation through contrasting layers, and its bearing on cleavage refraction

A theory of finite strain variation in contrasting viscous layers is presented. The theory is applicable to layers which are oblique to two principal strains, but parallel to the third, and is not restricted to plane strain. Results may be obtained algebraically or by use of the Mohr diagram for strain. Solutions are given for various examples of layering attitude and viscosity ratio, measured with respect to a reference layer. It is shown that the finite strain ellipsoid changes in shape and orientation across contrasting layers, and in some cases the principal axes may be exchanged. Low strain is indicated in relatively more viscous layers, and high strain with extension at a smaller angle to the layering, in less viscous layers; the latter may approximate simple shear parallel to layering if the strain is sufficiently high. The geological implications of the theory are strong strain variations in layered rock sequences. It is suggested that, in general, strain will be inhomogeneous from layer to layer both in orientation and amount. The relationship of strain and cleavage are reviewed in the Introduction to establish the validity of predicting cleavage patterns from strain data. Qualitative comparisons between the theoretical results of strain variation and natural cleavage refraction in layered rocks would appear to justify the assumption that cleavages of varied morphologies are sub parallel to the XY planes of strain. With this assumption, some three-dimensional features of planar and linear fabric refraction in contrasting rocks are predicted.

Constraints on geological strain rates: Arguments from finite strain states of naturally deformed rocks

A summary of known finite strain states is presented; longitudinal strains (1 + e) as measured in many rocks often range from 1 to 40 and 1 to 0.025. The time span available to produce such measurable strains in young orogenic zones seems to be less than 10 m.y., possibly less than 1 m.y., which constrains conventional strain rates into the range of 10−13 s−1 to 10−15 s−1. For both pure and simple shear (the most efficient way and a much less efficient way to accumulate incremental strains, respectively) the ellipticity of the finite strain ellipse increases in a nonlinear manner. Finite strain variations in adjacent layers, which give rise to features such as cleavage refraction, arise with only slight differences in the strain rates within these layers.

Experiments on superimposed buckle folding

The geometry of experimentally developed superimposed buckle folds with internal tangential longitudinal strain in a single competent layer embedded in an incompetent host is analysed. It has been found that the first-generation folds are not refolded in the same way as a lineation. On the contrary, they have a great influence on the development and geometry of the second-generation folds. Outcrop patterns quite similar to those occurring in natural rock complexes were formed in the experiments in a way which is not in agreement with the explanation usually given to such patterns. When the layer developed folds only in a zone, and not throughout the layer, and the bulk of material was only able to expand upward, it was found that the layer became bent in such a way that the folds are situated on the top of a broad antiformal structure. Fold-zone intersections are situated on broad domal structures. Within the upper surface of the competent layer, the finite strain variation is complicated within the fold areas while no strain is taken up by the unfolded parts of the layer. The possibility of finding similar structures in nature is considered.

Hot high-nitrogen gas in a metal mine

Strain is an important component of the total displacement field in the emplacement of a thrust sheet. The finite strain tensor in a penetratively deformed thrust sheet is a spatial variable. I describe a method for quantitative estimation of the finite strain variation in thrust sheets by applying spatial statistics analysis on strain data collected from a part of the Sheeprock thrust sheet, in the southern Sheeprock Mountains and the West Tintic Mountains, north-central Utah. Strain was measured in the quartzites of the Sheeprock thrust sheet and the spatial statistics method is illustrated using the XZ strain axial ratios.The Sheeprock thrust sheet was penetratively deformed during Sevier-age fault propagation folding. I quantified finite strain from quartzites using the modified normalized Fry method and calculated the three-dimensional strain ellipsoid from the quartzites using three orthogonal thin-sections from each oriented field sample. The variation of finite strain in the Sheeprock thrust sheet was best represented by an exponential semivariogram model, which I used to predict values of strain from unsampled locations by ordinary kriging. Cross-validation showed that, in general, the predicted and measured values show good agreement (within 1% of each other). The sampled space was contoured using the measured and predicted strain values to obtain a detailed finite strain variation pattern in a part of the Sheeprock thrust sheet.