Fold-Related Faults Track Progressive Fold Development from Layer-Parallel Shortening to Subsequent Orthogonal Extension within an Appalachian Buckle Fold System: Bear Valley Mine, Shamokin, PA, USA

Folds in sedimentary strata are one of the most fundamental, instructive, and compelling geologic structures on Earth, and they have long been studied to better understand deformation processes (e.g. [1-6]). The orientations, geometric relationships, strain patterns, and microstructures within folded strata provide important records of folding mechanisms, rheology, and links to broader-scale tectonic processes. As such, various existing mechanical, theoretical, kinematic, and conceptual models have been developed to predict the distribution of strain and secondary structures associated with folding (e.g. [2, 5, 7-11]). While many folds are secondary structures produced as a result of faulting (“fault-related folds”) (e.g. [12]), buckle folds are primary structures and a direct expression of the rock properties and deformation conditions during fold evolution (e.g. [3, 6, 8]).

Buckle folds form by end-loading of a strong layer (or layers) in a weaker matrix. Idealized buckle folding is understood to occur through the progression of three phases: (1) initial layer-parallel shortening (LPS) and fold nucleation, (2) fold amplification, and (3) limb rotation and late-stage modification (e.g. [2, 13-17]). Final shapes, wavelengths, and strain distributions in buckle folds are controlled by layer and matrix strength contrast, layer thicknesses, layer spacing, layer slip, and mechanical anisotropies (e.g. [2, 18-23]). At each stage, the distribution of strain within the folded layer, and thus, the structures that record that strain, vary. Although many buckle fold models assume power-law viscous deformation, deformation of strata at shallow crustal levels is mostly accommodated by fracturing, frictional sliding, pressure solution, and related low-temperature processes (e.g. [24]). Mesoscale faults that record internal strain of a buckled layer are herein considered “fold-related faults.”

In this contribution, we report observations of a fold train in an abandoned coal mine within the Appalachian Valley-and-Ridge tectonic province of northeastern United States (Figure 1). Mid-nineteenth-century strip mining for coal exposed a series of mesoscale folds [25] in exquisite detail within the Bear Valley mine (Figure 2). The outstanding exposure permits examination of the three-dimensional form of the folded surfaces and the structures that accommodated folding at multiple scales of observation (Figure 2). Nickelsen [26] documented several generations of structures within the mine that record strain before and during folding (Figure 3). Our new structural analyses of these faults are intended to illuminate strain accommodation during progressive fold growth and are compared to existing end-member conceptual models for buckle folds.

The Bear Valley Strip mine is located on the south limb of the Western Middle Synclinorium of the Pennsylvania anthracite region, approximately 3.5 km SW of the town of Shamokin (Figure 1). The Pennsylvanian Llewellyn Formation forms the core of the synclinorium and is intensely folded at an average wavelength of 170 m (Figure 1(b)) [27, 28]. Sandstone, siltstone, mudstone, and coal are well exposed throughout the abandoned mine and are generally organized in fining upward cycles (Figure 4) [29]. We measured stratigraphic sections at six localities distributed throughout the mine [30] and made a composite stratigraphic section based on these data as well as measurements from the local area by Arndt et al. [27] (Figure 4). The floor of the mine follows the layers that immediately underlie the Mammoth coal: a 30 +/− 15-cm-thick carbonaceous silty shale and an underlying 4.3- to 5.2-m-thick sandstone (hereafter referred to as the Whaleback sandstone) [30]. The silty shale has tabular beds that are finely laminated and contain abundant plant and trace fossils [30]. The Whaleback sandstone is a well-cemented litharenite [26, 31] that contains tangential cross stratification, thick tabular to lenticular beds, distinctive ironstone concretions, and abundant plant and trace fossils [30].

The Whaleback sandstone and overlying silty shale are folded to form two E-W trending anticlines exposed in the mine (Figure 4). The anticlines (referred herein as the North anticline and Whaleback anticline) host aerially extensive bedding surfaces with patches covered by mine tailings, while the intervening synclinal hinge zones are partially filled by tailings. The north-dipping, south limb of the southern syncline forms the south wall of the mine. The Whaleback anticline and south wall are predominantly capped by the Whaleback sandstone with limited exposures of the overlying silty shale, whereas the opposite is true for the North anticline. The east wall of the mine exposes a disharmonically folded sedimentary sequence that overlies the Mammoth coal seam (Figure 2(b)). At the west end of the Whaleback, the anticline is partially exposed in profile. There, the Whaleback sandstone is at least 3.4 m thick, indicating that the sandstone bed profile is nearly complete. Elsewhere, erosion and minor faults that offset bedding allow for observation of the upper contact of the sandstone as well as the interior of the sandstone bed. Based on the disharmonic nature of the folds in the Bear Valley mine (Figures 2(b) and 3(a)), we conceptualize the exposed folds in the floor of the mine to be a buckle-fold train in the Whaleback sandstone that is bound above and below by a weak matrix (coal and silty shale).

The Bear Valley folds developed during (very) low-grade metamorphism. The coals are semi-anthracite rank, and studies of vitrinite reflectance, two-phase fluid inclusions in syntectonic quartz veins, and clay mineralogy suggest the rocks experienced deformation at approximately 185 °C to >200°C and as much as 293 MPa [32-34]. Vitrinite reflectance anisotropy measured across the Western Middle Anthracite Field indicates that coalification began prior to folding and continued during folding [35].

The folds in Bear Valley host a range of mesoscale and microscale structures including faults, folds, cleavage, joints, and grain-scale strain interpreted to record deformation during the Alleghenian Orogeny. The 100 m wavelength-scale of the folds at Bear Valley is at a critical scale between regional-scale structures (e.g. [36-38]) and the outcrop scale (e.g. [39, 40]) in studies of fold-related strain. Bedding surface preservation becomes less common at longer length scales, leading researchers working on larger, regional-scale structures to rely on surface reconstructions for meaningful results (e.g. [37]). At finer scales, the diversity and population size of secondary structures are reduced. In this sense, the Bear Valley folds present a rare opportunity to quantitatively characterize multiscale structures associated with folding.

A well-documented relative chronology of mesoscale structures [26] permits us to distinguish structures and their temporal context with respect to fold evolution (Figure 3). The general chronology of progressive deformation in the mine (Figure 3) was originally described by Nickelsen [26, 41] as: a pre/early LPS phase, which includes (i) NE-striking, pre-Alleghenian extension joints, and (ii) NW-striking, early-Alleghenian joint sets (this earliest phase is not the focus of this study); an LPS phase, which includes (iii) spaced cleavage and cm-scale folds that clearly predate the (iv) propagation of conjugate thrust and strike-slip faults; (v) a folding phase, which produced the third-order (100 m) folds in the mine; and (vi) a fold modification phase, which includes axis-parallel and transverse extensional faults associated with fold growth and tightening. The sequence of Alleghenian events preserved in the structures at Bear Valley is observed throughout the Valley-and-Ridge province (e.g. [42, 43]).

Previous finite strain studies in the central Pennsylvania Valley-and-Ridge document initial compaction strain, overprinted by NW-directed LPS strain of up to 50% in fine-grained lithologies (e.g. [25, 32, 44, 45]). Sandstones and siltstones in the central Pennsylvania Valley-and-Ridge have LPS strains of approximately 20% [46]. These prior studies demonstrate that the regional LPS strain is heterogeneous and that the strain patterns vary in magnitude depending on lithology and position within Alleghenian folds.

End-member kinematic models for buckle folds include orthogonal flexure (neutral surface folding) and flexural slip or flexural flow (Figure 5). These two models each predict distinctly different distributions of strain and associated secondary structures (see [11] and references therein); thus, folds with comparable shapes may have different internal strain distributions that reflect variable kinematics and mechanisms (e.g. [5, 11]). Folds that form from orthogonal flexure experience instantaneous tangential extension of the outer arc and contraction of the inner arc (Figure 5(a)) separated by a neutral surface that undergoes no tangential longitudinal strain. Maximum strain occurs where curvature is greatest: at the hinge. Strain diminishes to zero at the inflection points between folds and along the neutral surface. In orthogonal flexure, strain is dominated by pure shear with no appreciable slip between layers. Representative minor structures associated with orthogonal flexure include veins and fractures perpendicular and parallel to bedding along the outer and inner arc (respectively), minor faults oblique to layering that accommodate layer-parallel extension (LPE) in the outer arc and shortening in the inner arc, and spaced cleavage perpendicular to bedding along the inner arc (Figure 5(c)). In comparison, folds that form by flexural slip or flexural flow accommodate slip on layer-parallel sliding surfaces or through distributed shear within the folding layer (Figure 5(b)). In flexural-slip/flow models, strain increases with limb dip and is maximum at inflection points between fold hinges. Strain varies according to layer dip and is uniform normal to layering. Although flexural flow is a common conceptual end-member for fold-related strain, Huddleston et al. [47] suggest that the anisotropy of competent rock layers is insufficient for flexural flow folding to occur in natural single-layer folds, but is possible in highly anisotropic rocks or composite layers of alternating high and low viscosity material. Minor structures expected in shallow crustal rocks associated with flexural-slip folding include bedding-plane faults with slip lineations perpendicular to the fold hinge, and en echelon vein sets and spaced cleavage at oblique angles to bedding (e.g. [48-50]) (Figure 5(c)).

Natural multilayer folds may combine orthogonal flexure and flexural slip/flow, along with differential volume loss and superimposed shortening (e.g. [51]). Which folding mechanisms are active is related to varying rheologies (e.g. [52]), changing deformation conditions during fold growth [53], and increasing limb dip over time. For example, at low to intermediate limb dips, bed-parallel slip may occur between competent layers, but when fold limbs become steeply dipping, slip on bedding surfaces may stop as layer-parallel shear stress decreases and layer-perpendicular normal stress increases [54, 55]. Such “fold lock up” effectively reduces the number of mechanical layers (increases effective layer thickness), thus driving a shift in strain patterns.

As noted, buckle folds grow in three stages. At shallow crustal levels, common structures produced during the initial LPS stage include minor faults, fracture/vein sets, spaced cleavage and tectonic stylolites, calcite twins, and subtle shape-preferred fabrics (e.g. [56, 57]) (Figure 5(c)). Higher deviatoric stress during folding favors the development of minor faults, whereas higher fluid pressure and lower deviatoric stress favor development of tensile fractures and veins [21]. Minor faults that accommodate LPS may include conjugate thrust faults at acute angles to layers and conjugate strike-slip faults at a high angle to bedding, reflecting interchange of the intermediate stress/strain axis between horizontal and vertical. Eventually, loading exceeds the buckling strength of the layer(s) leading to fold nucleation and limb rotation. The relative amount of LPS a competent layer undergoes before buckling increases with decreasing strength contrast between the layers and matrix (e.g. [2]).

For a single-layer buckle fold, the fold amplification stage begins when limb dips reach ~15^o with respect to the enveloping surface (fold amplitude reaches ~5% of the wavelength) [17]. During early fold amplification, the competent layer(s) may function as a stress guide with local principal stresses remaining about parallel and perpendicular to bedding [58]. When limb dips reach ~45°, buckle folds grow principally by limb rotation driven by bulk shortening. During this stage, the fold axial surface becomes a plane of flattening, with thickening of the hinge and thinning of the limbs expected [7, 56, 59, 60]. As fold limbs rotate into high angles with the bulk shortening direction, they may experience LPE with overprinting minor faults and veins [61, 62]. Mitra [63] argued that late-stage faults within a fold may initiate due to the inability of flexural slip to accommodate additional fold tightening at high limb dips.

Natural fold forms and their associated mesoscale to microscale structures display large variations, reflecting differences in mechanical stratigraphy (layer thicknesses, viscosity, anisotropy), stress state, environmental conditions (P, T, fluids), and deformation paths (e.g. [11, 64]). Interpreting what combination of folding models (if any) best matches natural fold characteristics thus requires robust datasets from well-exposed structures, preferably across all three dimensions of a fold. In particular, minor faults that form during progressive folding can yield a critical means to evaluate the appropriateness of fold mechanism models and the stress state during folding.

In this contribution, we illustrate how secondary brittle faults can be analyzed to track progressive deformation during fold initiation, growth, and modification for a set of well-exposed folds at an ideal scale. To date, most work on fold-associated fracture sets focused on their geometric relationships, in which agreement is shown between fracture orientation and style, and the predicted changes in stress field during folding (e.g. [58, 65-75]). That said, it is well documented that fractures within folded strata can be generated by multiple drivers, including tectonics (e.g. faulting and folding), diagenesis, high fluid pressure, exhumation and erosion, high strain rates, changes in the local state of stress, and fracture events caused by regional stresses (e.g. topography-induced stress gradients) (e.g. [22, 72, 76-80]), all of which adds complexity to any interpretation. It is most certainly the case that the geologic record of the local stress field during buckle folding is incomplete and only represents snapshots of the stress field during fold growth. The presence of multiple styles and orientations of fracture sets in a folded rock layer requires that the orientation and relative magnitudes of the principal stresses change throughout the history of folding (e.g. [60, 70, 71]). Consequently, it is imperative to document relative timing for the various observed fracture sets. Importantly, fractures that form prior to fold amplification can introduce local anisotropies that will likely change the strength of the rock and affect the subsequent distribution of stresses and their orientations. Such changes consequently influence the development of additional fracture sets and/or the reactivation of existing sets during fold development.

What follows is a kinematic analysis of over 900 outcrop-scale faults exposed within adjacent folds in an abandoned coal mine within the Appalachian Valley-and-Ridge tectonic province that, when coupled with clearly established relative age relationships, allows delineation of distinctive fault sets and their strain accommodation during fold evolution. Based on this analysis we suggest that LPE, including fold-axis-parallel and -transverse extension, is an underappreciated component of three-dimensional buckle folding–induced strain and that models for minor fault sets that accommodate three-dimensional strain during fold formation are currently incomplete.

All field observations and measurements for this study were made within the Bear Valley mine. The structural geology basemap of Nickelsen [26] and our new orthophotomosaics were used as references and to locate our observations. The bulk of our data were collected from the North anticline, the centrally exposed Whaleback anticline, and the south wall of the mine (Figure 2). All planar and lineation data were measured using Brunton pocket transit compasses and field protractors. Where possible, a 15-m ladder was used to access features. In some cases, exposures were improved by using a broom or whisk.

Due to the excellent exposure (Figure 6), structures are clearly and easily observed, permitting thorough characterization of their geometry, spatial distribution, kinematics, and cross-cutting relationships. The relative ages of these features are interpreted from cross-cutting relationships, their orientations relative to primary bedding, and through stereonet analysis of fault orientations on opposing limbs of folds, which are thoroughly described in the following sections. All structural data were plotted in their in situ coordinates as well as their orientation relative to bedding (with local bedding restored to horizontal). Due to the low plunge of the fold axes (Figure 7), simple rotation about local strike was used to restore bedding to horizontal. All stereonet analyses were performed using the Stereonet 10 software package [81, 82].

The faults measured in this study are characterized by shear displacements ranging from a few decameters (with rare offsets on the order of meters) to millimeters (as evidenced by a combination of shear sense indicators, slip lineations, and offset markers). Individual fault kinematics were established, when possible, by recording the orientation of the slip surface, the trend and plunge of the observed slip vector (or rake depending on dip of slip surface), and shear sense. Shear sense was interpreted based on quartz slickenfiber steps, Riedel shears, drag folds, and gash veins. For kinematic analysis, we assume slip lineations form in the direction of the maximum resolved shear stress on a fault surface (e.g. [83, 84]). The data were separated into discrete kinematic populations based on the orientations of slip surfaces and their slip vectors relative to bedding. Slip on minor faults is assumed to represent infinitesimal strain for which the strain axes are parallel to principal stress axes at the time the faults slipped. Interpreted principal paleo-stress axes were determined using FaultKin v.8 software (algorithm explanation for this software package can be found in [81, 82]). The average P- and T-axes (maximum shortening and maximum stretching axes, respectively) were determined using the Linked Bingham distribution analysis tool, which provides an objective directional maximum of the extension and shortening axes [85] and are contoured for visual inspection using the Kamb technique [86] with a 2-sigma contour interval (when the number of observations were sufficient).

To quantify linear strain due to minor faulting during fold modification, we examined faults interpreted to be active during fold modification (Nickelsen’s [26] stage VI, Figure 3) along nine scanlines on the North anticline and thirteen scanlines on the Whaleback anticline (Figure 6). The locations of the scanlines were selected to maximize spatial distribution across the folds and were oriented in two principal directions: transverse and axis-parallel with respect to the fold (Figure 6). The distribution of the scanlines was also limited to areas safely accessible on foot or by ladder. The scanlines range in length from approximately 4 to 24 m. For each fault that intersected a scanline, we measured: shear sense, fault orientation, orientation of slip lineation, amount of displacement, bedding orientation, and heave parallel to bedding (to calculate LPE).

To examine grain-scale deformation mechanisms, we prepared 190 oriented thin sections from 41 oriented hand samples and 84 oriented cores from sample localities distributed throughout the mine. Samples included both the silty shale that underlies the Mammoth coal and the Whaleback sandstone. The examination of thin sections was conducted using both light microscope and backscatter scanning electron microscopy. Internal grain structures that appeared to be randomly oriented and do not extend into adjacent grains or were incongruous with the deformation conditions of the Llewellyn Formation were interpreted to be inherited features, whereas internal grain structures were recognized based upon their localization at grain boundary point contacts, and/or their parallelism with internal structures in adjacent grains.

The steep dip of bedding and the large amplitude of the Whaleback and North anticlines posed physical limitations in measuring bedding orientations over the whole fold surface. To obtain an even distribution of bedding measurements throughout the strip mine for fold-form analysis, a point cloud was generated using structure-from-motion photogrammetry with photographs taken from a compact remote-controlled aircraft (drone) [87]. The point cloud was manually reduced to solely the sandstone and shale surfaces and subsequently subsampled to 1 m spacing. A surface of nonuniform rational basis splines (NURBS) was applied to the point cloud to interpolate a smooth, continuous surface of the folds (Figure 7(c); [88]). Converting the NURBS surface to a polygonal mesh enabled the extraction of vertex normals associated with individual polygons. These normals represent poles to bedding and are used to generate π-diagrams for a wholistic fold-form analysis (Figure 7(c)).

In general, the exposed folds in the mine are approximately cylindrical with planar limbs and a broadly periclinal shape (Figures 2 and 6). The North anticline is a slightly east-plunging, upright, open fold that becomes more box shaped in profile to the west. Field-measured poles to bedding for the North anticline reveal a strongly girdled distribution in stereographic projection that is best-fit by a great circle, indicating, at least locally, a general cylindrical form with a fold axis that plunges very slightly (5^o) toward 072^o (Figure 7(a)). The Whaleback anticline is a tight upright fold with planar limbs, partially overturned on the north limb, and has a broad, rounded hinge zone. Field-measured poles to bedding for the Whaleback anticline also show a girdled distribution best-fit by a great circle, indicating a general cylindrical form with a fold axis that is essentially horizontal and trends toward 080^o (Figure 7). The Whaleback decreases in amplitude to the east and west creating a pericline (e.g. [89]).

To test for variations in orientation of the fold axis and fold shape, we sectioned the meshed NURBS model into four, 50 m, axis-parallel segments and plotted a π-diagram [90] for each using on-the-vertex-normals to the mesh polygons (Figure 7(c)). The plots by segment illustrate the periclinal shape: the stereonet for the western-most section yields an axis that plunges slightly west; the stereonets for the two eastern-most sections show that the axis in the eastern half steepens to ~11° E. The trend of the fold axis calculated for the eastern half of the Whaleback axis appears to be 4° counterclockwise from the western half. Recognizing that the measured orientations may be influenced by the sampling of polygon populations, the NURBs interpolation, and the fraction of the folded surface exposed, the difference in fold axis trend is not significant.

All measured faults were segregated into sets based on the orientation of the slip surfaces and slip lineations relative to local bedding (Figure 8). Broadly, our classification of fault sets and their relative ages conforms to that of Nickelsen [26]. Four sets of faults related to early LPS and two additional sets that record subsequent LPE were identified on the basis of cross-cutting relationships as described in detail in subsequent sections.

Three groups of faults maintain a consistent relationship to bedding regardless of bedding dip or their position on the folds. Cross-cutting relationships, folded fault surfaces, and folded slip lineations indicate that these fault sets formed prior to folding [26]. As a result, their fault kinematics are more readily interpreted when bedding is structurally restored to paleo-horizontal. One group is a conjugate set, roughly perpendicular to bedding with slip lineations approximately parallel to bedding (hereafter referred to as strike-slip faults) (Figures 8(a)–8(c) and 9). Another group is a conjugate set at acute angles to bedding with slip vectors normal to the strike of the faults in a restored coordinate frame (hereafter referred to as thrust faults) (Figures 8(c) and 8(d) and 10). Finally, a group of minor faults is localized by ironstone concretions at the top of the Whaleback sandstone (Figures 8(e) and 10). In all cases, the slip surfaces associated with concretions (hereafter referred to as concretion thrust faults) are found in conjugate sets that define the boundary between the stiff concretions and the underlying weaker sandstone (Figure 8(e)). The concretion thrust faults display slip vectors that generally trend parallel to the dip directions of the faults, have reverse shear sense when bedding is restored to horizontal, and have opposite sense of vergence on either side of the concretion-sandstone contact (Figures 10(a) and 10(b)). Based on the kinematics of the conjugate early strike-slip faults, thrust faults, and concretion thrusts, all three fault sets are interpreted to have accommodated LPS prior to folding. We describe the kinematic analysis of each set in more detail in the following subsections.

We identified strike-slip faults based on bed-parallel slip lineations and bed-normal fault planes regardless of bedding dip (Figure 9). All strike-slip faults have at least some slip vectors parallel to bedding, indicating that the strike-slip faults initiated prior to folding and were subsequently reoriented during fold limb rotation. Structurally restored faults represent a conjugate set with opposite slip sense (Figure 9). The dihedral angle of the conjugate strike-slip faults decreases overall from approximately 55^o in the west to 40^o in the east across the mine (Figure 9) and seems to cluster into two distinct spatial populations within the mine. Strike-slip faults, for bedding restored to paleo-horizontal, have subhorizontal maximum shortening axes that trend approximately 151^o–331^o (Figure 9(b)) in the eastern side of the mine and 153^o–333^o (Figure 9(d)) in the western end.

Both conjugate sets of strike-slip faults exhibit evidence of reactivation. Where exposed on the limbs of the folds, several of these faults show overprinting or curving slip lineations on their surfaces. In the latter case, the sense of curvature of the slickenfibers on the strike-slip fault mimics the sense of curvature of the fold limb. The shear sense of each strike-slip fault is maintained throughout a continuous arc of slickenfibers or through a series of overprinting slickenfibers. Slickenfiber rakes can vary by as much as 90^o, from bed-parallel to bed-normal, on a single fault surface. These relationships indicate that while the strike-slip faults initially formed when bedding was horizontal, the faults continued to slip as fold limbs rotated during fold growth. The role of strike-slip fault reactivation during folding is discussed further in Section 4.2.2.

Thrust faults range in scale from small intra-bed thrusts with cm-scale displacements, to faults that cut through the exposed sandstone and have meter-scale displacements (Figures 8(c) and 8(d)). Thrust faults are best exposed along the south wall of the mine and the limbs of the Whaleback anticline. None are observed in the silty shale on the North anticline. All measured faults within this group show uniform geometry with respect to bedding regardless of position around the exposed folds, suggesting they initiated prior to folding (Figures 10(a) and 10(b)). In addition, some of the larger thrust faults clearly demonstrate that the fault surface is folded with bedding as both surfaces similarly change their dips near the crest of the Whaleback anticline. When these data are structurally restored, they display a consistent pattern of shallow to moderately north- and south-dipping slip surfaces with slip vectors that are near parallel to dip and have kinematic indicators that suggest thrust motion (Figure 10(b)). Kinematic analysis of 44 thrust faults in their restored coordinate frame indicates the thrust faults accommodated layer-parallel maximum shortening that trended approximately 172^o–352^o, with near vertical extension (Figure 10(b)). Similar to observations made by Nickelsen [41], at least two of the thrust faults exposed on the limbs of the Whaleback anticline exhibit a minor component of inverted (normal) slip sense as evidenced by a pull-back of the thrust tip and exposure of the underlying thrust surface.

Concretion thrusts are found on the limbs of the Whaleback anticline and along the south-wall exposure (Figure 8(e)). We measured 102 conjugate concretion thrust faults at the contact between concretions and the underlying sandstone (Figures 10(c) and 10(d)). When these data are structurally restored, they display a consistent pattern of shallow to moderately north dipping and south dipping slip surfaces with slip vectors that are near parallel to fault dip. Slickenfibers suggest thrust motion of the concretion relative to the underlying sandstone (Figure 10(d)). Concretion thrusts have a distinctive spatial distribution of parallel slickenfibers, with the concretion being thrust in opposite directions on opposing sides of its contact with bedding, and no slickenfibers found in the nadir of the concretion. Nickelsen [26] concluded that these slip surfaces reflect a difference in bulk strain between the overlying stiff ironstone concretion and the less-stiff sandstone beneath. Relative slip occurred when the sandstone shortened more than the concretions during LPS. In the restored coordinate frame, a maximum shortening direction is estimated to be approximately 171^o–351^o, with near vertical extension (Figure 10(d)).

Two sets of faults accommodate later LPE of the sandstone and overlying silty shale. One set strikes parallel to the fold axes (axial LPE faults); the other set strikes at high angles to the fold axes (transverse LPE faults). Both sets have moderate to high dip with respect to bedding and slip vectors that are normal to the fault-bedding intersection (Figures 11 and 12). Cross-cutting relationships indicate the transverse LPE faults are predominantly younger than axial LPE faults. In most cases, both sets are found as conjugate pairs with opposite shear sense, producing decameter-scale horst and graben structures with respect to bedding (Figures 8(f)–8(l)). Both sets of conjugate LPE faults are well exposed and ubiquitous within the limbs and hinge zones of all exposed anticlines. LPE faults are less common on the south wall of the mine.

To view the spatial distribution of faults in the sandstone, we produced an image of an “unfolded” Whaleback anticline surface (Figure 13). We used Blender, an open-source three-dimensional modeling software, to digitally “unbend” a three-dimensional model of the anticline so that it is approximately planar. The unbending axis of the model is slightly offset from the Whaleback fold axis to facilitate a view of the slightly overturned north limb and to evenly distribute the bending distortion. The resulting image illustrates the distribution of the largest faults on the anticline, showing geometrical coherence across the limbs (Figure 13). At this scale, more faults are apparent on the north limb of the Whaleback than on the south. On the north limb, transverse LPE faults are more abundant in the west, and axial LPE faults are more abundant in the east (Figure 13).

Many of the LPE faults contain only one set of slickenfibers, suggesting that those faults ruptured and slipped exclusively during LPE (Figures 8(f)–8(l)). However, some LPE faults exhibit multiple slickenfiber orientations suggesting fault reactivation (Figures 8(f) and 8(i)). LPE faults that exhibit evidence of reactivation characteristically lie subperpendicular to bedding, share similar orientation with some LPS strike-slip faults, and have at least one set of slickenlines parallel to the fault-bedding intersection lineation, suggesting these faults originated as LPS strike-slip faults (similar to the interpretation of Nickelsen [26]). Additional fault displacement is evidenced by overprinting and/or continuously curved slip lineations that vary in rake by as much as 90^o on individual fault surfaces, resulting in bedding-plane throw (Figures 8(f) and 8(i)). Fault reactivation occurred on both sets of LPS strike-slip faults, although the set with left-lateral shear sense is more commonly reactivated. The sense of curvature of the original strike-slip fault slickenfibers as they transform to those formed during LPE matches the trajectory consistent with a fault that maintained its shear sense (rather than reversed it) during reactivation.

We measured 723 unique LPE faults (Figures 12-15). Of these, 400 are on the Whaleback anticline (Figures 12(a)–12(h)) and 323 are on the North anticline (Figures 12(i)–(k)). Contoured stereoplots of in situ shortening axes show a strong single maximum everywhere around the folds; however, the orientation of the maximum varies with position on the folds (Figures 14 and 15). When viewed in aggregate, the calculated shortening axes are scattered along a great-circle girdle that strikes NNW-SSE. Contoured stereoplots of in situ extension axes predominantly exhibit two maxima that are subperpendicular to each other (Figures 12(g) and 12(j)). Although the extension axes change orientation with position on the folds, the angular relationships between the two extension maxima remain nearly constant. The extension axes related to transverse LPE faults are associated with the ESE-WNW maximum on both folds (Figure 12(b)) and those associated with axial LPE faults are associated with nearly vertical maximum (Figure 12(d)). In situ transverse LPE fault shortening axes on the fold limbs (>20^o limb dip on the North anticline and >25^o on the Whaleback) correspond with mean maximum shortening direction that trend approximately N-S. In aggregate, axial LPE shortening axes define a NNW-SSE girdle ranging from subhorizontal on fold hinges (Figure 12(f) and (j)) to vertical on the steeply dipping fold limbs of the Whaleback (Figures 12(g) and 12(h)).

To evaluate the relationships between the geometry of extensional faults and their position around the folds, the kinematic data were binned into bedding dip domains (Figures 14 and 15). When bedding dip domains are rotated to horizontal with their respective LPE fault populations, a remarkably uniform pattern of faulting emerges. Shortening axes associated with all LPE faults lie subperpendicular to bedding (i.e. near “vertical”) and both sets of extension axes lie in or near the plane of bedding (i.e. near “horizontal”). The NNW-SSE extension maxima are associated with axis-parallel LPE faults and the E-W extension maxima are associated with transverse LPE faults. The hinge zone of both folds includes both LPE fault populations, with consistently vertical in situ shortening axes and extensional axes that are shallow and either N-S or WNW-ESE oriented (Figures 12-15).

We examined faults along 22 axis-parallel and transverse scanlines to quantify linear strain produced by LPE fault displacements (Figure 6). The magnitudes of horizontal, axis-parallel extension produced by transverse LPE faults on the north limb, south limb, and crest of the Whaleback anticline are remarkably similar (2.67%, 2.52%, and 2.94%, respectively), despite their uneven spatial distribution (Figures 6 and 13). The North anticline shale exhibits 1.80% axis-parallel extension. The average extension perpendicular to the fold axis due to axial LPE faults on the Whaleback is 3.43%. The North anticline has an average of 4.14% transverse extension.

Due to differences in exposure level on the two folds, measured LPE faults on the Whaleback anticline are predominantly within the Whaleback sandstone and measured LPE faults on the North anticline are exclusively within the overlying silty shale. However, both folds expose LPE faults in both lithologies. Although the LPE data are similar for both folds, we observe differences in fault expression between the two lithologies that are independent of their position on the folds.

Scanline surveys reveal the transverse LPE fault density on the Whaleback anticline is 0.8 faults per meter, whereas the North anticline silty shale exhibits 1.8 transverse LPE faults per meter. Axial LPE fault density on the Whaleback anticline is 2.0 faults per meter, whereas the North anticline silty shale has an average 4.2 faults per meter. The approximately twice as dense LPE fault arrays in the shale compared with the sandstone do not correspond with a similar scale increase in extensional strain. Rather, LPE faults in the shale tend to have smaller displacements, ranging from 0.1 to 15 cm [30]. LPE faults in the sandstone have displacements that typically range from decimeters to more rarely meters. In contrast to the Whaleback sandstone, none of the faults examined in the silty shale contained more than one set of slickenfibers or any other evidence of fault reactivation.

In aggregate, the acute angle between conjugates of both types of LPE faults to the estimated maximum shortening axis within the Whaleback sandstone averages ~60^o (Figure 12) and is bisected by the direction of maximum shortening that is subperpendicular to bedding. The overlying silty shale exhibits axial and transverse LPE faults with substantially larger dihedral angles (Figures 8(k), 8(l) and 16). The direction of maximum shortening, subperpendicular to bedding, bisects an average obtuse angle of 110^o between LPE faults in the silty shale (Figures 12(i) and 15). The observed difference in dihedral angles between lithologies is consistent with experimental findings by Gomez-Rivas and Griera [91], who demonstrated that faults form with unusually large dihedral angles (~115^o) in highly anisotropic analog materials. For the Bear Valley system, the degree of anisotropy would naturally be more pronounced in the carbonaceous silty shale compared to the underlying Whaleback sandstone. At a few localities, individual LPE faults are observed to refract from a moderate to high angle to bedding as they pass from the silty shale into the sandstone; however, most LPE faults in the silty shale do not penetrate the sandstone.

The maximum shortening axes in the silty shale of the North anticline do not fan as much as the normals to bedding (Figure 15). On the limbs of the fold, the shortening-axes are slightly skewed toward the hinge of the fold. The effect is best illustrated on the contoured kinematic axes stereoplots where bedding has been returned to horizontal (Figure 15). Relative to bedding, the mean maximum shortening axis plunges steeply north on the north limb, is vertical at the crest, and plunges steeply south on the south limb.

Fold-related strain is also recorded at the grain scale. Given the low temperatures of metamorphism, detrital grain mineralogy is largely preserved with the detrital clay fraction likely having undergone an increase in crystallinity. Observed noninherited microstructures range from discontinuities (e.g. cleavage, fibrous and blocky veins, healed microfractures, faults and boudins), features indicative of crystal plasticity (e.g. deformation lamellae, crenulations), and grain-boundary diffusion-related structures (e.g. pressure solution indentation, stylolites at grain boundary, and preferentially oriented grain overgrowths). Oriented thin sections cut in mutually perpendicular planes from oriented hand samples, allowed for the interpretation of extension and contraction orientations for each microstructure, cross-cutting relationships between microstructures, and ultimately correlation with stages of deformation observed at the mesoscopic scale.

The Whaleback sandstone manifests evidence of LPS at the grain-scale by pressure solution indentation and sutured grain contacts at a high angle to bedding (Figure 17(a)) and kinked detrital micas (Figure 17(b)). Quartz grains commonly contain deformation lamellae and dense arrays of healed microfractures marked by planes of fluid inclusions (Figure 17(a)). The grain-scale LPS is associated with a localized bedding-plane lineation that is near parallel to the fold axes in the mine. Bed-normal shortening and corresponding bed-parallel extension are manifested by blocky quartz veins at a high angle to bedding (both parallel to bedding strike and bedding dip direction) and normal microfaults (Figure 17(c)) and sutured grain contacts that are parallel to bedding (Figure 17(a)).

The overlying silty shale exhibits a host of microstructures that indicate a complex history of noncoaxial deformation that apparently involved swapping orientations of contraction and extension axes with progressive deformation. LPS is evidenced by a primary crenulation and associated localized cleavage [92] in authigenic and detrital micas (Figure 17(d)) and stylolites at a high angle to bedding. Veins parallel to bedding with quartz fibers at a high angle to bedding (Figures 17(d) and 17(e)) and bed-normal fibrous grain overgrowths correspond to vertical extension during LPS (Figure 17(f)). Microscopic thrust faults with quartz slickenfibers are also present. Copious evidence of LPE includes quartz veins with fibers parallel to bedding (Figure 17(g)), microscopic extensional faults with quartz slickenfibers (Figure 17(h)), and bedding-parallel pressure fringes on organic and mineral grains (Figure 17(i)). Stylolites at a high angle to bedding contain quartz mineral fibers suggesting a progression of LPS followed by LPE. Organic particles and coal-rich layers show evidence of boudinage with bed-parallel quartz fibers filling the gaps between boudins (Figures 17(e)–17(g)). The apparent brittle extensional deformation of coaly laminae is consistent with the mesoscopic observations of joints in the coal seams at Bear Valley and regionally [93]. Sutured grain contacts within the plane of bedding and bed-parallel stylolites indicate bed-normal contraction. Features indicative of LPE (and associated bed-normal contraction) are found in bed normal thin sections that are cut both parallel and normal to the fold axes (e.g. Figure 17(i)).

Monfort [31] presented normalized fry analysis of the sand grains in Whaleback sandstone that yielded highly variable, small finite grain-scale strain (R = 1.05–1.24 +/−0.03 in the bedding plane and R = 1.04–1.21 +/−0.03 in a vertical plane normal to the Whaleback fold axis). Generally, the finite strain ellipse is elongated at high angles to bedding in cross-sectional view and along the fold axis within the plane of bedding. These strain patterns most likely reflect LPS prior to folding, consistent with finite strain studies in sandstone elsewhere in the region (e.g. [32, 46, 81, 94]). The finer grained lithologies in Bear Valley have higher grain-scale finite strain (R > 2.0 in some cases) in the plane of bedding based on fossil and trace fossil distortions [26].

In summary, grain-scale features indicative of LPS and LPE are found in the Whaleback sandstone and overlying silty shale. The deformation microstructures corroborate the deformation sequence interpreted from the mesoscale fault data. Grain-scale deformation in the Whaleback sandstone is dominated by brittle fracture, pressure solution, and low-temperature crystal plasticity. The silty shale microstructures are dominated by low-temperature crystal plasticity, dissolution-reprecipitation at grain boundaries, and brittle microfaulting. The quartz fibers at a high angle to bedding in the silty shale suggests fluid overpressures during LPS (e.g. [95]).

There are few well-documented field examples that illustrate the three stages of fold development. Kinematic analysis of more than 900 individual minor faults from the Bear Valley mine, PA provides a framework for constructing an evolutionary model of buckle folding for the Bear Valley folds (Figure 18) from LPS, through fold initiation and limb rotation, and finally to fold tightening/flattening and late-stage modification (Figures 10-15). At the Bear Valley mine, fault sets formed and underwent displacement (in some cases continuously) during fold development providing insights on fold growth and modification that challenge existing two-dimensional and three-dimensional buckle fold models.

Stage 1: LPS and fold initiation: In his seminal work, Nickelsen [26] documented an early strain history in the vicinity of the Bear Valley mine that occurred prior to Alleghenian LPS (Figure 3(b)). Based on cross-cutting relationships, he identified pre-Alleghenian tensile fractures in coal that consisted of a systematic joint set that trends ~NE-SW. This phase was followed by an early Alleghenian NW-striking systematic joint set that is well expressed in the ironstone concretions and sandstone layers in the Bear Valley mine. The early deformation phase also produced small-scale folds and spaced cleavage that were later rotated during larger-scale folding [26] and now lie oblique to the larger folds found in the mine.

Continued Alleghenian LPS, which ultimately led to large-scale fold initiation, progressed from initial bulk-rock horizontal compaction to brittle shear failure. In the Bear Valley mine, Alleghenian LPS produced conjugate strike-slip faults that accommodated ~NW-SE shortening and ~NE-SW extension. This initial phase was largely followed, based on cross-cutting relationships, by continued ~N-S shortening, but locally vertical extension as evidenced by initiation of conjugate thrust faults and concretion thrusts. For the population of concretion thrusts, the differential slip between the ironstone concretions and the underlying sandstone likely occurred due to differential LPS between the sandstone and more rigid concretions. The fracture and fault systems that formed prior to and during earliest fold amplification likely introduced intrinsic heterogeneities and weaknesses into the sandstone. We infer that buckle folding nucleated around these local structural perturbations in the competent Whaleback sandstone. These early structures also affected the subsequent development and reactivation of future fault sets associated with fold growth (e.g. [96]).

Stage 2: Fold amplification: As buckling initiated, bedding dips increased. As argued by [56, 57], LPS-related strain likely decreased substantially when the limb dips reached ~10^o to 20^o. At lower limb dips the folding layer was essentially everywhere parallel to the maximum compression direction (i.e. LPS), but once limb dips became sufficiently steep, shortening was mainly accommodated by buckling and growth of the fold (e.g. [61]), with a minor contribution from ongoing strike-slip fault displacements. We discuss evidence for the mechanism that enables folding of the layer in the next section.

Stage 3: Fold tightening and modification: In the Bear Valley mine, continued limb rotation and fold amplification resulted in a dramatic change in the local strain within the folds, which ultimately resulted in a transition from LPS and development of fold curvature to widespread LPE and the development of new axis-parallel and transverse extensional faults. These brittle structures likely affected fluid flow and local pore pressure (as evidenced by observed veins in thin section (Figures 17(e), 17(g), 17(h), and 17(i)), slickenfibers on fault surfaces, and gash veins within the Whaleback sandstone), and consequently the relative strength of the competent layers (e.g. [97]).

The axial LPE faults record a single slip vector, with no evidence of overprinting slip lineations or reactivation of older structures, indicating that they likely formed during a single phase of deformation associated with fold limb rotation and fold tightening. This contrasts with the transverse LPE faults in the Whaleback sandstone, some of which record multiple overprinting slip vectors, or curved slip vector traces, indicating activity penecontemporaneous with fold development. The transverse LPE faults with multiple slip lineations are all oriented parallel to existing LPS strike-slip faults (when bedding is restored to horizontal) (compare Figures 9 and 13(a)). Furthermore, all transverse LPE faults with multiple slip lineations are planar, lie nearly normal to bedding (similar to the strike-slip faults that formed during LPS), and include slip lineations that are subparallel to bedding and/or display bed-normal gash veins and drag folded bedding lineations indicative of bed-parallel slip. These observations lead to the interpretation that transverse LPE faults with multiple slip lineation trends are reactivated LPS strike-slip faults. Where reactivated strike-slip faults are part of a conjugate pair of transverse LPE faults, their partner fault tends to be oblique to bedding and dips toward the reactivated strike-slip fault (when bedding is restored to horizontal). In addition, the partner faults tend to contain one slip lineation that is approximately normal to the fault-bedding intersection lineation and have a more corrugated slip surface. The different origins of transverse LPE faults (reactivated versus newly formed) likely explain the more scattered distribution of orientations of transverse LPE faults compared to the axial LPE populations (compare Figures 12(a) and 12(c)).

While mesoscale faults clearly illustrate strain during all stages of fold development in Bear Valley (e.g. continuously curving slickenfibers on transverse LPE’s), the mechanisms that accommodated buckling of the layer are less evident. Here we consider the contributions of orthogonal flexure, flexural slip and flexural flow, and/or fold modification by flattening as potential mechanisms for the Bear Valley folds.

The traditional orthogonal flexure fold model predicts outer arc extension with vanishing outer arc finite LPE with proximity to the inflection points of the fold (Figure 5(a)). In Bear Valley mine folds, axial LPE faults are present at all positions on the exposed folded surfaces and there is no change in LPE finite strain from hinge to limbs (Figure 13; [88]). Exposures do not permit examination of the entire Whaleback sandstone profile at all positions on the fold. Where exposed in cross section, there is no discernable depth at which LPE vanishes (i.e. the position of the finite neutral surface). In the silty shale that caps the Whaleback sandstone on the North anticline, the unusual open angle between conjugate LPE faults in the carbonaceous silty shale suggests that the shale may have undergone penetrative pure shear following formation of the LPE faults. If it is assumed that these faults originally formed as Andersonian conjugate sets, subsequent bed-normal shortening in the shale during orthogonal flexure may have rotated faults to shallower angles with respect to bedding, opening the dihedral angle between conjugate faults. Alternatively, the axial LPE faults in the carbonaceous silty shale may have originally formed with a large dihedral angle due to the strong anisotropy in this lithology (compatible with experimental results of [91]), as reflected in the microstructures. Regardless, while a classical two-dimensional orthogonal flexure model can explain the extensional strain at the fold hinges, it does not fully account for the extensional strain produced by mesoscopic axial LPE faulting at all the fold positions where they are observed in Bear Valley.

In recent finite-element models of two-dimensional orthogonal flexure, Frehner [96] compares incremental and finite strain distributions, revealing a more complex and varying position of the incremental neutral surface between incremental LPE and shortening strains during fold growth and limb rotation. In these models, the incremental neutral surface is never found to be continuous along the arc length of the fold (in contrast to the classic kinematic model of Ramsay [5]). Instead, the incremental neutral surfaces migrate from the outermost arc of the fold toward the inner arc with increasing shortening, resulting in a strain history of LPS followed by LPE over a larger cross-sectional area of the folded layer. In particular, the Frehner [96] models with high viscosity contrasts (as we infer for Bear Valley folds) predict incremental LPE that extends from a fold’s hinge zone down along portions of the fold limbs during fold growth. This interpretation implies axial LPE faults near the hinge formed earlier than LPE faults on the limbs; our observations neither support nor refute this interpretation. Nevertheless, based on the distribution of axial LPE faults, it is likely that orthogonal flexure was an important mechanism during Bear Valley fold growth.

Flexural flow/slip models for folding predict strains produced by layer-parallel slip (flexural slip) and/or distributed shear (flexural flow) within the limbs of the folding layer. In this model, the highest strain is proximal to the inflection area of fold limbs and is oblique to the layers, and strain diminishes to zero at the hinge (Figure 5(b)). In the early stages of folding, flexural slip on bedding surfaces could have become favorable as fold amplification caused bedding dip to become sufficiently inclined to the regional horizontal compression to resolve shear. Thus, flexural slip could provide a frictional mechanism to accommodate fold amplification. There are a few bedding-plane surfaces observed in the mine that show slickenfibers with shear sense consistent with flexural slip (Figures 8(o) and 8(p)), and there is evidence that early LPS thrust faults experienced a minor phase of inverted slip (normal slip) during folding [41]. However, with the exception of the pull-back observed on some thrusts, the timing of slip is ambiguous and could have occurred prior to folding due to LPS-related low-angle thrust faulting.

The LPE faults in the silty shale may give additional clues regarding the contribution of flexural flow to the development of Bear Valley folds. While the shortening kinematic axes of axial LPE’s in the Whaleback sandstone maintain their bed normal orientation and fan around the Whaleback anticline (Figure 14), the shortening kinematic axes for the axial LPE faults in the silty shale on the North anticline are normal to bedding at the hinge zone, but slightly oblique to the limbs, forming a subtly convergent fan (Figure 15). Assuming an initial phase of orthogonal flexure extended the outer surface of the folds and generated axial LPE faults that continued down to the limbs, favorably oriented axial LPE faults in the relatively weak silty shale might have undergone slight rotation toward the fold axial plane during subsequent flexural flow. Additionally, Nickelsen [26] argued that the angular relationships between bedding, cleavage, and a vertical fossil tree trunk on the south limb of the North anticline (~6.8 m below the base of the Whaleback sandstone in the northwest corner of the Bear Valley mine) are best explained by flexural shear of the limbs during folding.

Late-stage fold modification occurs by flattening a fold perpendicular to the fold axis (e.g. [5]). Flattening models explain limb extension but also predict contraction and thickening in the hinge of the fold [5, 21], which is not seen in Bear Valley. Though the recent finite-element models of orthogonal flexure by Frehner [96] provide a plausible explanation for the observed distribution of axial LPEs away from the hinge zone, the concentration of these faults within and across the inflection points of the fold imply fold flattening as an additional driver of axial LPE fault growth during late-stages fold development. Modern three-dimensional numerical models of buckle folds show that LPE during fold amplification and tightening can occur in both the fold-axis parallel and perpendicular direction depending on the model boundary conditions (e.g. [66, 98]). The predicted LPE structures in these models are spatially limited and concentrate along the inflection lines of the fold limbs. Though there is no discernable localized concentration of axial LPE faults in the Bear Valley fold limb inflections, the distribution of these faults over the entire fold profile suggests that fold flattening alone cannot explain the presence of axial LPE’s on Bear Valley folds. However, fold flattening may have played a role in the development of axial LPE faults on the fold limbs.

In summary, axial LPE faults in the hinge areas are most likely evidence of orthogonal flexure during limb rotation, whereas the distribution and orientation of axial LPE faults on the limbs and across the fold profile are likely the result of a combination of folding mechanisms potentially including incremental extension due to a migrating neutral surface during continued orthogonal flexure and fold flattening, with potential late-stage modification of axial LPEs by flexural flow.

Although classical two-dimensional strain models can explain the initiation of at least some of the observed axial LPE faults, none explain the transverse LPE faults that accommodate strain in the third dimension. Late-stage fold flattening could produce the observed transverse LPE faults, as in the chocolate-tablet boudinage of [98], but on the Whaleback anticline, cross-cutting relationships suggest that most transverse LPE faults are younger than axial LPE faults. If axial LPE faults formed by outer arc extension during orthogonal flexure, and if we assume Andersonian faulting, the intermediate principal stress (σ2) is initially parallel to the fold axis, which is typical. In this scenario, the maximum compressive principal stress (σ1) is parallel to bedding at fold initiation and then at progressively higher angles to bedding as the limbs rotate during folding. We infer that formation and slip of axial LPE faults during fold amplification reduced the total energy of the system by decreasing the differential stresses that brought about failure and fault activation in the first place (e.g. [21]). Consequently, the relative value of σ3 may have increased and eventually exceeded that of σ2, causing σ2 and σ3 to swap orientations leading to a phase of extensional faulting normal to the fold axis. This proposed sequence is supported by a preponderance of transverse LPE faults that cross-cut axial LPE faults (Figure 13). The two fault sets ultimately resulted in a similar LPE fault-related strain across the fold (Figure 18), characterized by overall biaxial extension parallel and transverse to the fold axes within the layer (Figures 13 and 14).

Structures at other scales are kinematically consistent with the LPS and LPE accommodated by mesoscopic faults. At the scale of the mine, the folds record approximately 33% horizontal shortening. Fault-related strain due to LPS faults is unknown; however, as much as 50% LPS bulk rock shortening is recorded by distorted macrofossils in the mine [26]. Despite their abundance, linear strain produced by LPE faults during folding is relatively minor (ranging from 1.80 to 4.14%) at this locality. Grain-scale finite strain in the Whaleback sandstone is widely variable in magnitude and orientation and generally small, likely complicated by overprinting of LPE on LPS and possibly earlier compaction fabrics [31]. Microstructural analyses show that microfaulting and solution mass transfer evidenced by sutured grain contacts, fibrous overgrowths, and veins accommodated both LPS and LPE strain. Primary crenulations in the silty shale and crenulated detrital micas in the Whaleback sandstone provide additional evidence of LPS, while normal microfaults, boudinaged organics with quartz vein fill in between boudins, and bed-parallel quartz fiber filled veins and overgrowths are additional evidence of LPE. Despite the differences in expression of LPS and LPE, the grain-scale structures and mesoscale fault sets are compatible with each other and reinforce the importance of LPE deformation during growth of these folds.

The rare three-dimensional exposure of the Bear Valley mine fold surface allows for a perspective not often accessible from most localities, which are inevitably limited to cross section or map view perspectives or discontinuous surface outcrop exposures, in which the three-dimensional form of the fold(s) is by necessity inferred. Such constrained and limited observations likely underrepresent the importance of LPE during general buckle folding. That said, important axis-parallel extension has been documented in various orogenic systems by multiple researchers (e.g. [99-103]) and has been modeled using analogue experiments by Grujic and Mancktelow [104]. Previous buckle fold studies have identified extension either parallel or perpendicular to the fold axis (e.g. [22, 99, 105]) but are often limited to specific regions of the folded surface (e.g. hinge zone or fold limbs). These reports have been especially relevant in transpressive zones in which the maximum extension direction is shown to transition from vertical to fold-axis-parallel (e.g. [106]). In a nontranspressive example, Friedman and Stearns [69] observed fracture sets in the Teton Anticline of Montana that indicate extension parallel to the fold axis, and where found, were concentrated in regions where the rate of dip change is highest, thus hinting at a correlation to fold curvature, which is not observed in the Bear Valley folds. In addition to the Bear Valley folds, other Alleghenian fold-belt outcrops across the region are also known to display LPE faults interpreted to be caused by late-stage fold tightening (e.g. [42, 107]). Alternative models for extensional faults associated with fold outcrops in contractional mountain belts argue that they do not initiate during buckling, but rather during erosional unroofing of the fold, and are therefore post-folding in nature [66]. Due to the geometric relationships of the extensional faults with respect to bedding around the Bear Valley folds and the evidence of progressive slip vector change during folding, a post-folding model for fault formation in the Bear Valley mine is not considered viable.

The orientations, geometric relationships, and distributions of minor structures in folded strata provide important insights into the folding process, its kinematics, the accommodating deformation mechanisms within and between folded layers of rocks, and the controlling factors on a fold’s ultimate form. Field observations of microscale and macroscale structures within buckle fold systems indicate that the dominant strain produced by folding in contractional systems is due to compression parallel to the primary layering and perpendicular to the resultant fold axis [108]. What is less understood is the importance of extensional strain during fold amplification and tightening, and whether our classic conceptual models for folds (orthogonal flexure, flexural slip/flow, fold flattening) adequately predict observed strains within natural fold systems, and especially the spatial distribution, timing, and formation of fold-related minor fault systems (e.g. [109]).

The outstanding three-dimensional exposure of fold-related faults at the decameter scale in Bear Valley permits observation of progressive deformation through all stages of folding, as well as the response to folding of different lithologies at shallow crustal levels. The multiple populations of minor faults documented from the Whaleback and North anticlines in the Bear Valley mine indicate that folding developed through a complex interplay of LPS and LPE. Faults that largely predate folding (conjugate strike-slip and thrust faults) helped accommodate LPS. Faults that formed during fold tightening resulted in LPE and bed-normal shortening, regardless of position around exposed folds. Some of the LPE faults originated as LPS strike-slip faults that underwent continued slip during folding, though most LPE faults initiated during later stages of folding. All axial LPE faults were initiated during fold amplification and post-amplification flattening. Most transverse LPE faults post-date axial LPE faults and reflect changes in the local stress field during fold flattening. LPE faults formed on two adjacent folds and in contrasting lithologies. Despite difference in fault expression in the carbonaceous shale and Whaleback sandstone, both lithologies experienced LPE during fold growth and tightening and appear to have accommodated similar extensional strain in the plane of bedding along and across the folds.

No simple existing model of buckle folding and resulting strain distribution is consistent with the pattern of observed strain in Bear Valley; thus, a combination of folding mechanisms is required for its development. Especially well exposed at Bear Valley is the transition from LPS to LPE leading up to and during the folding process; a similar magnitude of linear strain produced by LPE faults during fold growth across all positions on the folds; and longitudinal and transverse bedding-parallel extension that developed during fold growth and tightening. Together, these observations lead to a more nuanced model of fold growth that involves early LPS, bulk shortening by limb rotation, and fold tightening that led to LPE (Figure 18). At Bear Valley, fold-related LPE faulting likely formed through a combination of folding mechanisms that began with limb rotation and orthogonal flexure in the outer arc of the exposed folds. This initial phase created axial LPE faults across the anticlinal hinge zones. Over time, as fold limbs reached higher dip angles, bedding-plane (or low-angle fault) slip may have aided folding, and axial-parallel LPE fault growth expanded onto the fold limbs and across the entire fold profile due to a combination of neutral surface migration and fold flattening. During fold-flattening, changes in the local stress state resulted in axial-parallel extension, which promoted growth of cross-cutting transverse LPE faults. A minor component of flexural flow/slip contributed additional strain across the fold limbs.

Without the unique three-dimensional exposure from the Bear Valley mine, the significance of fold-related LPE might not be recognized, leading to misinterpretation of regional folding mechanisms (e.g. hinge zone extension in orthogonal flexure folding versus strain free hinges in flexural fold models). Moreover, not accounting for observed LPE has implications for the proper assessment of extensional structures for cross-sectional balancing and characterization of the complete three-dimensional deformation field, as well as potential implication for fold-modified rock permeability due to growth of faults both parallel and perpendicular to the fold axes. Our study further reinforces the need for representative strain documentation at multiple scales to properly estimate net shortening from a cross-sectional perspective (e.g. [110]). Additionally, if axis-parallel extension is an important aspect of strain accommodation during folding, then end-member fold models that rely on plane strain (e.g. neutral surface folding) are limiting and need to be modified, when describing the mechanisms for folding.

Derived data supporting the findings of this study are available from the corresponding author on request.

None declared.

Arlo Brandon WEIL: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Validation, Visualization, Writing – original draft, Writing – review and editing

Mary Beth GRAY: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Validation, Visualization, Writing – original draft, Writing – review and editing

Kylie CUSH: Investigation, Methodology

Mattathias NEEDLE: Formal analysis, Methodology, Visualization, Writing – review and editing

Juliet CRIDER: Formal analysis, Funding acquisition, Writing – review and editing

This project was funded by the NSF EAR – Tectonics division, grants EAR-1523955 to Arlo Weil, EAR-1523958 to Mary Beth Gray, and EAR-1523909 to Juliet G. Crider.

This research was supported in part by the National Science Foundation grant EAR 152395. We are grateful for access to computer programs Faultkin and Stereonet (Allmendinger and Cardozo) and to Reading Anthracite Company and the Anthracite Outdoor Adventure Area for giving us permission to access and work in the mine. Bucknell undergraduate students Eric Monfort, Ali Reach and Ben Finley, Bryn Mawr undergraduates Helen Whitty and Ankitha Kannad, and University of Washington’s Keith Hodson assisted with field and laboratory analyses. We thank the Lithosphere journal editor, Elizabeth Petrie, and two outside reviewers, Elena Druguet and Alvar Braathen, for their very constructive comments and criticisms, which led to a much improved manuscript.