William M. Dunne

Circular scanlines and circular windows: new tools for characterizing the geometry of fracture traces

Abstract We introduce new estimators for fracture trace intensity, trace density and mean trace length that exploit the use of circles as efficient sampling tools. A fracture trace is the commonly observed surface expression of a fracture, i.e. the intersection of a fracture with an exposed surface such as a rock pavement or a mine drive wall. Trace intensity, trace density and mean trace length estimators are derived and shown to form a self-consistent set of two-dimensional fracture abundance measures. The intensity estimator n/4r uses the number, n, of intersections between fracture traces and a circular scanline of radius r. The density estimator m/2πr2 uses the number, m, of trace endpoints inside a circular window. The mean trace length estimator (n/m)πr/2 uses the ratio of the number of trace intersections on the circle to the number of endpoints in the circle. The circular sampling tools and estimators described here eliminate most sampling biases due to orientation and also correct many errors due to censoring and length bias that plague established scanline and areal measurement techniques. Performance of the estimators is demonstrated by comparison with areal samples of a synthetic fracture trace population with known intensity, density and mean trace length. The estimators are also applied successfully to a natural rock pavement with two orthogonal fracture sets, one of which is severely censored. Because the new circle-based estimators only require counts of trace–circle intersections and/or trace endpoints, they are more time-efficient than current methods for estimating geometric characteristics of fracture traces.

Strain factorization and partitioning in the North Mountain thrust sheet, central Appalachians, U.S.A.

Abstract By examining finite strain distribution and partitioning strain among deformation mechanisms, a model of thrust sheet deformation is established. The model takes into account kinematic history and environmental conditions. In the North Mountain thrust sheet of northern Virginia, factorizing finite strain into pure and simple shear components shows that the thrust sheet experienced 6–13% pure shear shortening parallel to the transport direction. Thrust-parallel simple shear strains increase slightly from the top of the thrust sheet toward the base. Within 500 m of the floor thrust, however, simple shear values increase markedly toward the basal thrust. This strain pattern occurs throughout the thrust sheet, overprinting earlier imbricate structures. Therefore, the finite strain in the thrust sheet may be modelled as a transport-parallel pure and simple shear applied during the major transport episode, and after thrust sheet imbrication. This transport-related strain overprints a weak layer-parallel shortening that is probably related to earlier passage of the thrust tip. Rocks in the thrust sheet with X / Z strain ratios greater than 1.35 have a slight crystallographic preferred orientation and are therefore tectonites in a strict sense. The distribution of tectonites within the thrust sheet defines a ‘tectonite front’ that is inclined toward the foreland. In the North Mountain thrust sheet the ‘tectonite front’ also generally coincides with the transition to high-temperature deformation mechanisms, and ultimately may parallel a paleo-isotherm within the thrust wedge. Strain partitioning indicates that approximately 70% of the finite strain results from intragranular mechanisms (i.e. dislocation glide, dislocation creep and diffusion mechanisms); 25% results from calcite twinning; and less than 5% resulted from transgranular mechanisms such as pressure solution. In non-tectonites, approximately 50% of the finite strain results from pressure solution and intragranular mechanisms, with the remaining strain due to twinning in calcite.

Blind thrust systems

Blind faults are documented from 20 thrust systems throughout the world. They occur as single faults, sets of faults, or entire thrust systems. The overlying cover responds to the formation of the blind system by backthrusting, coupling, forethrusting, and deposition. The relative importance of the first three responses for pretectonic cover is represented in a ternary backthrusting-coupling-forethrusting diagram. Pretectonic cover of blind systems deforms by either a combination of coupling and forethrusting or a combination of backthrusting and coupling.

Origin of a thrust-related fold: geometric vs kinematic tests

Abstract Geometric tests to determine the origin of fault-related folds are common, but as is typical in structural geology, more than one fold origin may yield the final natural geometry. Thus, the results of geometric tests are usually non-unique. In contrast, kinematic tests of origin, which employ both geometry and data about deformation, commonly yield more constrained, if not unique, results. Unfortunately, the necessary data collection requires much more work than for a geometric test. In this study, the thrust-related Barclay anticline is analyzed both geometrically and kinematically to determine which test is more effective. Geometric tests, using angular relationships, indicate three possible origins: fault-bend, fault-arrest, and break-thrust. For the kinematic test, predicted deformations for interlayer and flexural slip, flexural flow, simple shear, and bending strains are compared to micro- and mesostructural distributions, solution strain, and finite strain from the anticline. Strain measurements indicate that microscale deformation is uniformly distributed through the structure and is lithification-dominated. The microscale deformation does not match kinematic predictions, and did not accommodate fold formation. Fold growth was achieved primarily through layer-parallel slip restricted mostly to the forelimb and absent in the hinge, which eliminates fault-bend and fault-arrest origins that require material transport from forelimb to backlimb. The Barclay anticline is therefore interpreted to be a break-thrust structure. Interestingly, a suite of contraction faults in the forelimb and hinge indicates material transport from forelimb to backlimb. Such transport has been discounted for break-thrust folds. The most important result of this study is that a kinematic test was a necessary step for distinguishing fold origin. Geometric testing alone was insufficient. Given that the Barclay anticline has geometric characteristics typical of many thrust-related folds, kinematic testing appears necessary to determine their structural origin

Cover deformation above a blind duplex: An example from West Virginia, U.S.A.

Abstract Pretectonic cover above blind thrust systems responds to underlying thrusting by combinations of forethrusting, backthrusting and coupling. The role of these responses was examined in the Hanging Rock-Cacapon Mountain anticlinorium of the central Appalachians. This cover fold consists of Middle Ordovician and younger sedimentary rocks above a blind horse of Cambro-Ordovician carbonates. The cover has abundant folding and subsidiary faulting. Cover cleavage in carbonate and fine-grained clastic rocks formed before regional folding in response to layer-parallel shortening (LPS). This 15% LPS also produced grain-suturing and fluid-inclusion trails in quartzarenites. The LPS formed during cover forethrusting, accommodating older blind horses in the hinterland. With the formation of the underlying horse, cover coupling occurred with bending-folding, additional secondary buckling and cleavage rotation by flexural flow with perhaps minor flattening. This cover coupling was insufficient to accommodate horse formation. No evidence exists for backthrusting, but forelandwards, abundant subsurface evidence exists for cover forethrusting with imbricate thrusting. This thrusting accommodates horse formation and differs in style from the LPS of the older forethrusting event. So, for this blind system, the cover responded with a combination of coupling and forethrusting.

Orthogonal fracture systems at the limits of thrusting: an example from southwestern Wales

Abstract A well-developed orthogonal vein system is located in the autochthonous foreland just beyond the limits of Variscan thrusting in southwestern Wales. The two vein sets trend 200° and 290°, perpendicular and parallel, respectively, to Variscan structures. The veins contain stretched quartz fibers indicating horizontal extensions of between 0.3 and 2.5%. The 200° set has greater extension with a distinctive morphology, including shorter more curvilinear fractures that have components of normal offset. Vein intersections are simple, indicating episodic growth by alternating regional propagation of each set. During propagation, maximum compression was subvertical and the horizontal principal stresses switched direction with the alternation of set growth. The system formed during waning Variscan compression when the directions of horizontal principal stresses were still controlled by the tectonic compression. The differential stress may have been greater during propagation of the 200° set. This example indicates that orthogonal fracture systems in forelands beyond thrusting: (1) are initiated by fracturing parallel to tectonic compression; (2) form in a few stages that are controlled by changes in regional stress; and (3) form during waning tectonic compression that controls fracture orientations.

Fractal characterization of fracture networks: An improved box‐counting technique

given by N / rD , where N is the number of boxes containing one or more fractures and r is the box size, then the network is considered to be fractal. However, researchers are divided in their opinion about which is the best box-counting algorithm to use, or whether fracture networks are indeed fractals. A synthetic fractal fracture network with a known D value was used to develop a new algorithm for the box-counting method that returns improved estimates of D. The method is based on identifying the lower limit of fractal behavior (rcutoff) using the condition ds/dr ! 0, where s is the standard deviation from a linear regression equation fitted to log(N) versus log(r) with data for r < rcutoff sequentially excluded. A set of 7 nested fracture maps from the Hornelen Basin, Norway was used to test the improved method and demonstrate its accuracy for natural patterns. We also reanalyzed a suite of 17 fracture trace maps that had previously been evaluated for their fractal nature. The improved estimates of D for these maps ranged from 1.56 ± 0.02 to 1.79 ± 0.02, and were much greater than the original estimates. These higher D values imply a greater degree of fracture connectivity and thus increased propensity for fracture flow and the transport of miscible or immiscible chemicals.

The problem of strain-marker centers and the fry method

Abstract The Fry method and its variants will underestimate finite strain when applied to strain markers deformed heterogeneously at marker scale, despite homogeneous behavior at a population scale. This difference results from the post-deformation centers not coinciding with the original pre-deformation centers. The amount of error may rapidly approach 50% for small strains in ideal cases, but is likely to be in the range of 20–30%.

Conditions of vein formation in the southern Appalachian foreland: constraints from vein geometries and fluid inclusions

Abstract The Nolichucky Shale in the Whiteoak Mountain thrust sheet of the southern Appalachian foreland contains four coeval bed-normal calcite vein sets that trended 015°, 055°, 090° and 320° before thrusting. The pretectonic veins were displaced by syn-tectonic bed-parallel slickensided calcite veins during local Alleghanian thrusting. Fluid inclusion thermometry indicates precipitation of both bed-normal and bed-parallel veins from NaCl-CaCl2 brines (27 wt% NaCl-equiv. salinity), at 80–110°C for bed-normal veins and 110°C for bed-parallel veins. These temperatures correspond to burial depths of 2.4–3.6 km, which were attained after the middle Mississippian. These pressure-corrected homogenization temperatures are comparable to time-temperature indicators, such as CAI and illite crystallinity, and indicate that inclusions were trapped near-maximum burial conditions and were not deformed after trapping. This conclusion is supported by the absence of petrographic evidence for inclusion failure and a worst-case mechanical analysis that indicates a lack of brittle deformation to inclusions after trapping. The four coeval bed-normal vein sets could not be formed by one simple stress field, nor by the development of a single structure, but required the interaction of at least two stress components or structures. It is proposed that the interaction of the Alleghanian and Ouachita orogenic stress components, beyond the limits of thrusting, produced the sets as coeval Alleghanian orthogonal (055°,320°) and Ouchita sub-orthogonal (015°, 090°) mode I fractures.

Variation in quartz arenite deformation mechanisms between a roof sequence and duplexes

Abstract Microstructural abundances and histories in quartz arenite of the Lower Silurian Tuscarora Sandstone were used to determine the nature and role of microscale deformation in a cover sequence and underlying thrust system, and to assess the degree to which the cover sequence accommodated emplacement of the thrust system. Sandstone samples are located across the transition from the central to southern Appalachian foreland thrust system where the thrusts change from blind to emergent southwards and where southern deformation of early Alleghanian age has been previously shown to be overprinted by central deformation of Alleghanian age. Microstructures observed with transmitted light and cathodoluminescence microscopy indicate that grain-scale deformation occurred by dislocation flow, pressure solution, and microfracturing, with the last being generally the most important. The sequence of deformation mechanisms is the same for the cover sequence and the thrust system: pressure solution during sedimentary compaction; dislocation flow during layer-parallel shortening; and localized microfracturing with limited pressure solution near major thrust ramps and in steep fold limbs. A greater abundance of dislocation flow microstructures in the cover sequence from layer-parallel shortening indicates grain-scale accommodation in the Tuscarora Sandstone of some shortening associated with emplacement of the thrust system. The transition zone between the central and southern Appalachians contains the greatest occurrence of every microstructure which is consistent with the area having been affected by diachronous central and southern Alleghanian deformations.