We present a kinematic model for the evolution of the central Appalachian fold-thrust belt (eastern United States) along a transect through the western flank of the Pennsylvania salient. New map and strain data are used to construct a balanced geologic cross section spanning 274 km from the western Great Valley of Virginia northwest across the Burning Spring anticline to the undeformed foreland of the Appalachian Plateau of West Virginia. Forty (40) oriented samples and measurements of >300 joint orientations were collected from the Appalachian Plateau and Valley and Ridge province for grain-scale bulk finite strain analysis and paleo-stress reconstruction, respectively. The central Appalachian fold-thrust belt is characterized by a passive-roof duplex, and as such, the total shortening accommodated by the sequence above the roof thrust must equal the shortening accommodated within duplexes. Earlier attempts at balancing geologic cross sections through the central Appalachians have relied upon unquantified layer-parallel shortening (LPS) to reconcile the discrepancy in restored line lengths of the imbricated carbonate sequence and mainly folded cover strata. Independent measurement of grain-scale bulk finite strain on 40 oriented samples obtained along the transect yield a transect-wide average of 10% LPS with province-wide mean values of 12% and 9% LPS for the Appalachian Plateau and Valley and Ridge, respectively. These values are used to evaluate a balanced cross section, which shows a total shortening of 56 km (18%). Measured magnitudes of LPS are highly variable, as high as 17% in the Valley and Ridge and 23% on the Appalachian Plateau. In the Valley and Ridge province, the structures that accommodate shortening vary through the stratigraphic package. In the lower Paleozoic carbonate sequences, shortening is accommodated by fault repetition (duplexing) of stratigraphic layers. In the interval between the duplex (which repeats Cambrian through Upper Ordovician strata) and Middle Devonian and younger (Permian) strata that shortened through folding and LPS, there is a zone that is both folded and faulted. Across the Appalachian Plateau, slip is transferred from the Valley and Ridge passive-roof duplex to the Appalachian Plateau along the Wills Mountain thrust. This shortening is accommodated through faulting of Upper Ordovician to Lower Devonian strata and LPS and folding within the overlying Middle Devonian through Permian rocks. The significant difference between LPS strain (10%–12%) and cross section shortening estimates (18% shortening) highlights that shortening from major subsurface faults within the central Appalachians of West Virginia is not easily linked to shortening in surface folds. Depending on length scale over which the variability in LPS can be applied, LPS can accommodate 50% to 90% of the observed shortening; other mechanisms, such as outcrop-scale shortening, are required to balance the proposed model.

The Appalachian Mountains, extending along the eastern side of North America from Newfoundland (Canada) to Alabama (USA), are among the most recognizable and well-studied orogenic belts. However, the deformation mechanisms and fault kinematics that accommodated the shortening in this iconic range remain unresolved after more than 150 years of investigations (e.g., Rogers and Rogers, 1843; Dana, 1866; Rodgers, 1949; Herman, 1984; Faill, 1998, Evans 2010). The central Appalachian fold-thrust belt has been described as a blind fold-thrust belt with few emergent faults (Gwinn, 1964; Herman, 1984; Spraggins and Dunne, 2002). Shortening is accommodated through a series of duplexes that repeat a lower Paleozoic stiff sequence and an overlying cover sequence that displays the classic map-scale folds of the Appalachian Valley and Ridge province (Dunne and Ferrill, 1988). Within the cover sequence, deformation manifests as folding and layer-parallel shortening (LPS). Axial traces of map-scale folds trend at a high angle to the maximum shortening direction, and measured LPS is oriented at small angles to the maximum shortening direction (Rutter, 1976; Herman, 1984; Sak et al., 2012, 2014).

Over the past several decades, studies have sought to evaluate the structure of the Appalachians using balanced cross sections (e.g., Gwinn, 1970; Herman, 1984; Dunne, 1996, Evans, 2010; Sak et al., 2012; Ace et al., 2020). When drafting a kinematically viable and balanced cross section, shortening must be conserved across the system, with unfaulted units accommodating strain through folding and LPS (Elliott, 1983; Geiser, 1988a; Woodward et al., 1989). Early attempts to construct sections through the central Appalachians highlighted a significant discrepancy between the shortening described by faulted lower Paleozoic rocks and the overlying folded upper Paleozoic rocks (Herman, 1984; Hatcher 1989). These and other studies (e.g., Nickelsen, 1988; Mount et al., 2017; Ace et al., 2020) argued for a passive-roof duplex solution, where the structural response to shortening varies with stratigraphic position. Within the Cambrian–Ordovician carbonate sequence, shortening is accommodated through fault repetition (Herman, 1984; Evans, 2010; Sak et al., 2012; Ace et al., 2020), and in the overlying cover sequence, shortening is accommodated via map-scale folds and LPS. Proposed magnitudes of LPS required to reconcile discrepancies in the restored line length of the cover and carbonate sequences range from 28% in Pennsylvania (USA) (Herman, 1984; Hatcher, 1989) to as much as 50%–60% in West Virginia (USA) (Evans, 1989, 2010) (Fig. 1). Although the restored line lengths of the cover and carbonate sequences were equal in these studies, the LPS values were not measured. Instead, they reflect the magnitude required to balance the differences in line lengths of the restored cross sections.

In contrast, Sak et al. (2012) independently measured LPS and used the measured values to reconcile shortening magnitudes in the faulted and cover sequences. They showed that along the Susquehanna River valley, folding in Silurian and younger rocks combined with 20% LPS in the Valley and Ridge and 13% LPS in the Appalachian Plateau accommodated the same amount of shortening as the duplex in Cambrian through Ordovician strata. In addition, they demonstrated that quantifying both the distribution and magnitude of bulk grain-scale strain is imperative in order to determine the magnitude of shortening and the geometry of subsurface structures of the central Appalachians (Sak et al., 2012). More recently, seismic surveys at the Appalachian structural front have further constrained the kinematics of how shortening is transferred from the Valley and Ridge to the Appalachian Plateau (Mount et al., 2017; Ace et al., 2020).

The goal of this study is to quantify grain-scale LPS along the length of an orogen-scale transect through the central Appalachians in Virginia and West Virginia and integrate these measurements into a balanced geologic cross section that shows permissible geometries and shortening distributions of folds and faults. Integration of grain-scale strain into fold-thrust belt reconstructions elucidates whether grain-scale shortening is a significant component of the overall shortening magnitude (e.g., Mitra, 1994; Yonkee and Weil, 2010; Sak et al., 2012) or negligible (Eichelberger and McQuarrie, 2015). Inclusion of grain-scale strain can alter the kinematic path proposed in balanced cross sections (e.g., Mitra, 1994; Sak et al., 2012), and the magnitude and orientation of grain-scale strain has been shown to systematically vary across curved orogens (Yonkee and Weil, 2010). Marked differences in how and why grain-scale strain varies in fold-thrust belt systems (e.g., Eichelberger and McQuarrie, 2015) highlight the importance of spatially quantifying and integrating estimates of grain-scale strain into orogen-scale geologic cross sections.

Deformation that accompanied the Alleghany orogeny affected Cambrian to Permian strata throughout the central Appalachian region. Faulting initiated along a basal décollement in shales at the base of the Cambrian Waynesboro Formation (Fig. 2) (Kulander and Dean, 1986; Mitra, 1986), leading to shortening preserved at the surface as predominantly folded Silurian through Permian strata (Gray and Mitra, 1991, 1993). North and south of the study area, regional-scale fold axes trend ∼070° (Fig. 1) (Whitaker and Bartholomew, 1999; Sak et al., 2012). However, through the central Appalachians of West Virginia, fold axes trend 030°–035° (Fig. 1).

Deformation styles vary between the Valley and Ridge and Appalachian Plateau physiographic provinces, although both provinces are composed of unmetamorphosed foreland basin sequences resting on passive-margin sedimentary rocks and crystalline basement. In West Virginia, the boundary between the Valley and Ridge and the Appalachian Plateau (the Alleghanian structural front) is delineated by the Wills Mountain anticline (Fig. 1) (Perry, 1978; Mitra, 1987). To the east, in the Valley and Ridge, map-scale folds have 5–10 km wavelength and 70–140 km axial traces (Cardwell et al., 1968). In contrast, the Appalachian Plateau is characterized by broad 10–20-km-wavelength folds with 20–100 km axial traces. The abrupt change in structures exposed at the surface is attributed to a series of horses of Cambro-Ordovician strata (Kulander and Ryder, 2005; Ryder et al., 2008; Evans, 2010), defining the amplitude and wavelength of the regional-scale folds within the Valley and Ridge province (Dunne and Ferrill, 1988; Herman, 1984; Evans, 2010; Sak et al., 2012). These faults form a passive-roof duplex system beneath the Reedsville Formation. Although the Wills Mountain anticline is the western edge of this duplex system, faults through the Cambro-Ordovician strata are also present under the Elkins Valley anticline in the Appalachian Plateau (Ryder et al., 2008) (Fig. 3; Plate 1).

The stratigraphy consists of four structural tiers: (1) a sedimentary and crystalline Neoproterozoic basement, (2) faulted Cambrian to Lower Ordovician carbonates, (3) Middle Ordovician to Silurian faulted shales and sandstones, and (4) an upper Silurian to Pennsylvanian folded siliciclastic cover sequence (Fig. 2). While basement is separated from the fold-thrust belt along a décollement found within the Waynesboro Formation (Kulander and Dean, 1986; Mitra, 1986; Ryder et al., 2008), décollements are also identified within the Ordovician Reedsville Formation, Silurian Salina Formation salt, and Middle Devonian shales. The Ordovician Reedsville Formation (0.5 km thick) transitions and thickens to the east into the Martinsburg Formation (1–4 km thick), is the major décollement horizon in the Valley and Ridge (Drake and Epstein, 1967), and remains a key detachment horizon in West Virginia east of the Elkins Valley anticline (Fig. 1). The Silurian Salina Formation (Salina salt) and the Middle Devonian shales become major décollement horizons on the Appalachian Plateau, separating different packages of faulted and folded strata (Perry, 1978; Davis and Engelder, 1985; Nickelsen, 1988; Ryder et al., 2008; Sak et al., 2012; Mount, 2014; Ace et al., 2020).

This study presents a new balanced cross section along an east-west–trending transect across the central Appalachians of Virginia and West Virginia. The cross section is constrained by pre-existing well data, seismic interpretations, and geologic mapping. These data are supplemented by detailed geologic mapping in the immediate vicinity of the transect and bulk finite strain estimates of grain-scale strain on samples spanning from the Great Valley of Virginia to the Appalachian Plateau in West Virginia.

Geologic Mapping

Bedrock geology maps of West Virginia and Virginia were obtained through the U.S. Geological Survey National Map Database, the West Virginia Geological and Economic Survey, and the Virginia Department of Mines, Minerals and Energy, with scales ranging from 1:500,000 to 1:24,000 (Cardwell et al., 1968; Orndorff et al., 1993; Rader and Evans, 1993; McDowell, 1995; Dean et al., 2000, 2001; Dean and Kulander 2006a, 2006b, 2011). These were then compiled within ArcGIS software and georeferenced using digital elevation models (DEMs) published by the West Virginia GIS Data Clearinghouse and the Radford University (Radford, Virginia) GIS center. Field work targeted areas of limited coverage.

Through the course of our field work, we collected >500 structural measurements, including joint measurements and measurements of bedding orientation. The ∼300 joint measurements were collected using the selection method (Engelder and Geiser, 1980; Hancock, 1985; van der Pluijm and Marshak, 2004), where three to five joint orientations were collected from visually identified joint sets. For each station, coordinates were obtained using GPS. Bedding orientation measurements at these reference points provide the bulk of the structural measurements used to constrain the balanced cross section. Within the hinterland portions of the transect, road cuts are less abundant; and field data were supplemented by digitizing strike and dip data from published 1:24,000-scale quadrangles (Fig. 3) (Orndorff et al., 1993; McDowell, 1995).

Strain Analysis

Spatial variations in grain-scale bulk finite strain across the transect were constrained using 40 oriented samples of the cover strata. The samples came from outcrops distributed across the transect, with a single sample from the Great Valley, 22 samples from the Valley and Ridge, and the remaining 17 samples from the Appalachian Plateau (Fig. 1; Table 1). Three mutually perpendicular thin sections were cut: parallel to strike of bedding (A plane), normal to strike of bedding (B plane), and in the plane of bedding (C plane) (Figs. 4A and 4B). For each plane, three photomicrographs were taken with cross-polarized light: horizontal, −30°, and +30°. The three micrographs were merged into one image to highlight (primarily quartz) grain boundaries (Fig. 4C). Each compiled image was analyzed using the normalized Fry method (Erslev, 1988). The strain analyses were conducted using a normalized Fry method script for Matlab (Eichelberger and McQuarrie, 2015). Using this script, grain center locations were marked along with the long and short axes for ∼150–250 individual grains for each sample (Fig. 4C). The normalized plotted grain centers define a ring of high-density points surrounding a vacancy field representing the shape and orientation of the strain ellipse (Figs. 4D and 4E). Axial lengths were used to normalize the distance between grain centers, which are plotted through multiple iterations to reveal a central vacancy field defined by the minimum distance between centers. The normalized Fry method assumes that each sample had an anti-clustered, isotropic distribution before deformation, consequently the central vacancy field represents the bulk finite strain ellipse. The best-fit ellipse is then generated through a bootstrapping approach (Eichelberger and McQuarrie, 2015). Using this two-dimensional (2-D) evaluation, the ellipticity (Rs), or the axial ratio of the long to short axes, as well as the angle of inclination (φ), or the angle between the long axis and a horizontal reference, can be calculated for each image (Table S1 in the Supplemental Material1).

The 2-D strain data calculated using the normalized Fry method for the A, B, and C planes (Fig. 4F) of the sample was then input into the Mathematica program Best-Fit Ellipsoid with Statistics (Mookerjee and Nickleach, 2011) to determine the best-fit strain ellipsoid using the least-squares approach. Measured axial ratios and angular orientation data are subtracted from the axial ratio and angular orientation of a general ellipsoid defined in terms of six unknown matrix elements. The differences are squared and summed, with the sum minimized to calculate the best-fit ellipsoid (Figs. 4G and 4H). Error for each ellipsoid is obtained through the simulation of 1000 best-fit ellipsoids drawn randomly within the standard deviation of 2-D input data (Rs, φ, and orientation) (Mookerjee and Nickleach, 2011; Mookerjee and Peek, 2014). The resulting three-dimensional (3-D) strain ellipsoid can then be used to calculate the final orientation of principal strain axes. Best-Fit Ellipsoid then rotates the calculated ellipsoids into the geographic reference frame and gives the trend and plunge of the three principal axes (Fig. 4I; Table S2 [footnote 1]).

In 3-D space, because each sample has three mutually perpendicular cuts, any given plane shares an axis with another, allowing the comparison of axial ratios along the shared axis. For example, because the “C” plane is cut parallel to bedding, this plane quantifies the bulk finite strain between the along-strike and the dip directions. In the majority (32) of the 40 samples, the longest axes of measured strain ellipsoids (and therefore of the grains) parallel the strike of the bedding. The axial ratio in the bedding-parallel section (C plane) records the magnitude of LPS due to volume loss in the B direction assuming there are no overgrowths on grains and no filled fractures within grains that increase the length of the A plane (parallel to strike of bedding). These features were not observed in the 40 samples evaluated for this study. We resolve the 3-D ellipsoid onto the C (bedding) plane to quantify the amount of LPS (Table S2 [footnote 1]). The rest of this paper discusses the axial ratio obtained from this projection onto the C plane as the ellipticity ratio (Rs), and assumes that the loss of material in the shortening (B) direction indicates a percent shortening that can be applied over the distance the sample is assumed to represent. This distance over which the strain measurement is valid is unknown, as is the true variability in LPS. We attempted to quantify the length scale over which a strain measurement is applicable by taking multiple samples from the same outcrop. Where outcrop-scale folds were present, we collected samples in the core and along the limbs of a fold. These samples indicated no change in principal strain orientation or significant change in magnitude. These data are shown in the Valley and Ridge portion of Plate 2 as two or more strain measurements tied to the same location. In these areas, the range in measured LPS is 0%–3%. However as seen in Plate 2, LPS values can change by 9%–12% over a distance of 1–2 km.

Cross-Section Methodology

The 274-km-long transect for the geologic cross section was selected to bisect field data collected along an east-west–trending corridor through West Virginia and Virginia (Fig. 1). The transect extends from the Great Valley of Virginia in the hinterland to a pin line in the foreland northwest of the Burning Springs anticline (Figs. 1 and 3) (Cardwell et al., 1968; Davis and Engelder, 1985). The line of section is offset 30 km along the axis of the Whip Cove syncline (Figs. 1 and 3) to more closely align with field observations.

The basal décollement for the central Appalachians is gently dipping (∼1°), constrained from the depth to basement, in well log data, of 6200 m in the Wills Mountain anticline and 6600 m at the Arches Fork anticline (Fig. 1) (Ryder et al., 2008). All unit thicknesses are based upon stratigraphic columns, well logs, and previously published geologic cross sections of the region (Cardwell et al., 1968; Patchen et al., 1985; Ryder et al., 2008; Evans, 2010). The topographic profile was extracted from a 30 m DEM using MOVE software (Midland Valley) with surficial geology based upon the composite map. All structural data were then transposed from the map to the cross section using apparent-dip calculations. The cross section was drafted and balanced by hand at a 1:100,000 scale, and then digitized (Plate 1). As a result, this cross section focuses upon the first-order features of the orogen, with insufficient resolution to capture outcrop-scale features, which for the purposes of this study are defined as 0.01–100-m-scale features in competent rocks including mesoscale folds and outcrop-scale faults, particularly wedge faults (Fig. 5). The effect of outcrop-scale shortening may be significant. For example, Hogan and Dunne (2001) demonstrated that outcrop-scale shortening may account for as much as 10% shortening along local transects in Valley and Ridge of West Virginia. Similarly, Sak et al. (2012) documented 13% outcrop-scale shortening along an 11.5 km section of the transect C-C′ (Fig. 1) in the north-central portion of the Valley and Ridge of Pennsylvania. We assume that there is a potential for as much as 10% shortening by outcrop-scale structures east of the Elkins Valley anticline and through the Valley and Ridge. While spaced cleavage is a ubiquitous hand sample– to outcrop-scale structure within incompetent shale and siltstone lithologies throughout the central Appalachians (Engelder and Geiser, 1979; Geiser and Engelder, 1983; Sak et al., 2014), it is not present in competent sandstone to quartzite lithologies where equivalent shortening is accommodated through quartz dissolution along grain boundaries (LPS) and wedge faulting (Sak et al., 2012, 2014; Eichelberger and McQuarrie, 2015; Ace et al., 2020).

As with previously published cross sections of the Valley and Ridge province in the central Appalachians, a passive-roof duplex solution is invoked to fill space beneath the first-order folds (Herman, 1984; Sak et al., 2012; Ace et al., 2020). The passive-roof duplex deformation model assumes that the Cambrian to Ordovician carbonates are a stiff layer that shortens through fracturing and faulting without additional grain-scale shortening (Herman, 1984; Hatcher, 1989; Evans 2010), consistent with the low values of LPS (<5%) measured in these carbonates (Evans and Dunne, 1991; Sak et al., 2012). The overlying Ordovician to Pennsylvanian cover strata accommodate shortening through folding and LPS. We also assume that the major décollement horizons on the Appalachian Plateau (Salina Formation) and in the Valley and Ridge (Reedsville and Martinsburg Formations) have mobility to flow and deform ductilely. Significant thickness changes in the Salina Formation on the plateau are imaged in industry seismic data (Mount, 2014; Ace et al., 2020). In general, locally thick zones of strata that are ductilely thickened along décollement horizons have been imaged in seismic data through the Appalachians, emphasizing the importance of the ductile duplexes in accommodating deformation (e.g., Thomas, 2001, 2007).

In the hinterland, the southeasternmost 23 km of the cross section are in the Great Valley at the front of the Blue Ridge Mountains. The exposed strata in the Great Valley have undergone extensive pressure solution (Wright and Platt, 1982). We collected one strain sample from the Great Valley (Fig. 1; Plate 2), however Wright and Platt (1982) collected 14 samples from 10 localities through the Martinsburg Formation in Pennsylvania, Maryland, and West Virginia that show high variability in strain (7%–56%), with nine out of 14 samples showing >28%. The three samples closest to our study area vary from 16% to 50% LPS. The extensive and variable LPS complicates applying these LPS estimates to our cross section. Because of this, we focus on applying our measured strain data to 251 km of the cross section that extends through the Valley and Ridge and across the Appalachian Plateau; the northern 23 km of the 274 km cross section shows a geometry of faulted Cambrian through Ordovician strata in the Great Valley that is balanced by 35% LPS, the mean value of the recorded strain through the region.

As mentioned in the previous section, we use the ellipticity ratio (Rs) of the 3-D strain resolved onto the C plane (bedding plane) to determine a percent shortening of the strata before folding and faulting. The lack of overgrowths and fracture-filled veins in the long-axis (strike-parallel) direction supports our assumption that the LPS was accommodated by grain dissolution, while consistent LPS orientations that do not fan after folds are restored indicate that dissolution preceded folding. Due to the high variability in measured LPS values (Table 1), the balanced cross section was divided into 16 intervals (Plate 2). Intervals were chosen to group spatially related LPS data together and optimize the amount of shortening accommodated by measured LPS values. For each interval, an average LPS is calculated from the range in measured values, producing an estimate of the measured shortening accommodated through LPS in the overlying cover sequence over the specified distance. This value was subtracted from the percent shortening described by the geometry of faulting in the stiff Cambrian through Ordovician section to obtain the net value representing the difference between shortening amounts in the folded and LPS strata and the faulted strata. For simplicity, we assume that shortening due to duplexing is locally accommodated in the overlying strata within the cover sequence. If the difference between LPS and cross section shortening is positive, then the magnitude of LPS is greater than that needed to balance shortening by folding and faulting as shown on the cross section, and indicates that the net positive value (within that specific interval) can be used to accommodate shortening elsewhere in the section. In contrast, if the value is negative, it indicates that there is missing shortening in the cover sequence that must be accommodated by either excess LPS from other intervals or other contributions to shortening such as outcrop-scale deformation. After this method is applied across all 16 intervals, a total net balance of measured and proposed LPS can be used assess whether the strain data set across this portion of the Appalachians can account for the magnitude of LPS needed to balance the proposed cross section.

Joint Orientations

Raw joint orientations across the transect show a wide scatter with two dominant joint sets trending 321° and 227°. A narrower subset of data (n = 132) that includes both joint orientation and bedding orientation at the same location allows for the data to be restored to an original orientation with respect to horizontal bedding (Fig. 6). Restored data show a dominant joint orientation of 035° ± 5°, parallel to fold axis orientations of 030°–035°, suggesting outer-arc extension or post-tectonic unloading or release joints (Engelder, 1985). The next most-dominant joint set fans from 300°–350° with a dominant orientation between 300°–330°. This joint set is interpreted as cross joints, which are broadly parallel to the shortening direction and consistent with measured joint orientations through this portion of the Appalachian orogen (Nickelsen and Hough, 1967; Engelder, 1985, 2004).

Strain Measurements

Calculated bulk finite strain values (Rs) for a total of 40 oriented samples collected from siliciclastic cover-sequence rocks range from 1.02 to 1.23 (Fig. 1; Table 1) with an average of the 10% LPS. The errors in strain magnitude are ≤0.01 (Table S1 [footnote 1]), and the error in ellipsoid orientation is provided in Table S2. The samples display strain ellipsoids with scattered orientations. However, axial orientations in the bedding-parallel (C) plane, which directly compare strain along the strike and dip directions, exhibit a predominant west-northwest mean trend of short axes (Fig. 6). The calculated 3-D strain ellipsoids show a maximum shortening direction axis with low-angle (<40°) plunge magnitudes and 25 of 40 samples with plunge magnitudes ≤20° with respect to horizontal bedding (Table S2). Low angles between the plunge of the short axis and bedding strongly support LPS preceding folding. The 3-D ellipsoids show 68% of maximum shortening directions falling between 250° and 330° (Fig. 6). The mean preferred shortening direction is 304° ± 5° (Fig. 6). The mean maximum shortening direction is perpendicular to the general 030°–035° structural trend of map-scale structures and similar to the findings of Whitaker and Bartholomew (1999) who documented 10% LPS parallel to a 308° preferred shortening direction (Fig. 6) based upon deformed crinoid ossicles, ooids, and chert nodules preserved on bedding surfaces in southern West Virginia.

Grain-scale bulk finite strain is highly variable, ranging from 2% to 23% (Table 1). Eleven (11) of the 40 samples produce LPS values between 10% and 15%, and 17 out of 40 samples have LPS values of 5%–9%. Although the largest percentage of LPS values are similar to previous Appalachian strain studies, the measured variability is significantly different than previously found. Sample variability does not correspond with stratigraphic position (Table 1), geographic location (Fig. 1), or position with respect to map-scale structures in the fold-thrust belt (Fig. 1; Plate 2A). The high variability of LPS complicates incorporation of grain-scale bulk finite strain into the geologic cross section.

The average amount of LPS determined from the axial ratio (Rs) of bedding-plane surfaces is 10% along the entire transect. Average LPS values are slightly lower through the Valley and Ridge (9%) and higher across the Appalachian Plateau (12%). These values are significantly lower than the ∼50% LPS previously proposed as necessary to balance cross sections through the region (Evans, 1989, 2010). Average LPS measurements in the Appalachian Plateau (12%) compare favorably with the 13% LPS measured to the north and east in the Appalachian Plateau of Pennsylvania and New York (Engelder and Engelder, 1977). Average LPS measurements in the Valley and Ridge (9%) are notably lower than the 20% reported by Sak et al. (2012) in Pennsylvania (Fig. 1).

A balanced cross section must be both viable and admissible. Embedded in viability is the assumption that little or no motion has occurred into or out of the plane of the section (Dahlstrom, 1969; Elliott, 1983; Woodward et al., 1989). In addition, for a section to be viable, the displacement path of each structure must be known such that the structures can be restored to an unstrained state, and that fault slip is conserved through the entire fault system (Dahlstrom, 1969; Boyer and Elliott, 1982; Geiser, 1988b; Woodward et al., 1989). In an admissible cross section, structural styles depicted in the cross section are the same as those observed in the field (Elliott, 1983). For fold-thrust belts characterized by blind thrusts and LPS, this requires that as the fault displacement decreases toward the fault tip in the direction of transport, equivalent amounts of shortening are accommodated by folding or LPS.

The balanced cross section presented here (Plate 1) was constructed using the sinuous bed method (Dahlstrom, 1969). In the Valley and Ridge province of Pennsylvania and West Virginia, previous workers have documented that most of the folds are flexural-slip kink folds with planar limbs and narrow hinges (Faill, 1969, 1973; Orndorff et al., 1993; Sak et al., 2012, 2014). We observe both narrow anticlinal hinges adjacent to broad synclines as well as narrow synclinal hinges adjacent to broad-topped anticlines (Plate 1). Concentric folding is maintained on the Appalachian Plateau portion of the cross section, consistent with field observations. The low-magnitude dips measured in the Appalachian Plateau do not create significant space problems between the surface exposures and the mobile salt accommodating the folding (Wiltschko and Chapple, 1977; Mount, 2014).

The process of balancing the cross section begins in the foreland by restoring the folded and faulted bed lengths to horizontal, including shortening in Cambrian through Silurian rocks between the Elkins Valley anticline and the Appalachian structural front (Plate 1). For our proposed model, the total amount of shortening experienced by the cover strata of the Appalachian Plateau is 24 km (11%), with ∼2 km (1%) accommodated through the gentle folding of the Upper Devonian rocks. This suggests that the 22 km difference in shortening between the folded Upper Devonian strata and Lower Devonian strata needs to be accommodated through 10% LPS. Applying the same approach through the Valley and Ridge province, the faulted Cambro-Ordovician section accommodates 31 km (33%) of shortening, and folding in the Silurian through Devonian strata accounts for 8 km (4%) of shortening. This 23 km discrepancy would need to be reconciled by 25% LPS, or smaller values of LPS combined with permissible outcrop- or smaller-scale shortening features (Plate 1).

Across the Appalachian Plateau, the deformation within strata overlying the Cambrian–Ordovician carbonate sequence is intrinsically linked to the transfer of 24 km of slip from faults in the Valley and Ridge and faults coring the Elkins Valley anticline into décollements found in the Ordovician Reedsville Formation, Silurian-aged Salina salt, and the Mahantango Formation (Ace et al., 2020). Of this slip, 16 km originates from horses 3–5 (Plate 1), directly east of the Wills Mountain anticline. The remaining 8 km is transferred onto the Appalachian Plateau through horses 1 and 2 within the Elkins Valley anticline. The Appalachian Plateau is dominated by broad, gentle folds with 10–20 km wavelengths and 500 m of structural relief. West of the Elkins Valley anticline, these folds do not have sufficient amplitudes or structural relief to indicate the presence of underlying Cambrian–Ordovician horses. Instead, we infer that these folds result from detachments at the base of the Tully Limestone within the Mahantango Formation and at the top of the Salina salt, combined with wedge-style faulting of the Middle Devonian shale and carbonate rocks between these detachment horizons. Repetition of the Middle Devonian shale and carbonates along individual faults with offsets <1 km is recognized in seismic lines straddling the Alleghanian front in central Pennsylvania (Ace et al., 2020) and in well cores at the western limit of the Appalachian Plateau (Ryder et al., 2008). East of the Elkins Valley anticline, the structural relief of the overlying cover sequence indicates that wedge faulting in the Middle Devonian shales alone is insufficient to fill space below the cover strata, and available seismic lines through the region do not support faulting of the underlying Ordovician–Cambrian section. Instead, we suggest that this space is filled by faulting in the Williamsport through Reedsville Formations (Plate 1). Similar duplexing of the correlative stratigraphic interval is recognized in seismic lines in the Valley and Ridge in central Pennsylvania (Ace et al., 2020). These two systems, inferred within the Appalachian Plateau, accommodate 24 km of shortening and need to be matched by equal amounts of shortening within the cover rocks for the cross section to balance.

At the Appalachian structural front, the structural relief increases to ∼3 km, and well log data from the core of the Wills Mountain anticline indicate the presence of a fault-propagation fold originating from a basal décollement within the Waynesboro Formation (Ryder et al., 2008). We propose that the Wills Mountain anticline represents the western extent of the passive-roof duplex system where the Ordovician Reedsville Formation separates faulted Cambro-Ordovician rocks from the overlying folds of the Valley and Ridge province (Perry, 1978; Evans, 2010). East of the Wills Mountain anticline (Fig. 1), first-order folds are inferred to be a result of Cambro-Ordovician horses in order to fill space below the cover strata. The geometry of these horses is inferred to follow a fault-bend-fold geometry (Suppe, 1983). Above the horses of the duplex system, smaller second-order folds with 5 km wavelengths and 100–300 m amplitudes observed in the cover strata are a result of deformation-induced thickness variations within the weak and deformable Reedsville Formation. While thickness variations in the Reedsville Formation are not directly observed in outcrops along the transect, variation in thickness is assumed only where necessary to fill space. The Reedsville Formation serves as the upper detachment for the underlying passive-roof duplex, and thickness variations have been observed along weak décollement horizons in other regions of the Appalachians, including within this formation (e.g., Thomas 2001, 2007; Ace et al., 2020). The importance of the Reedsville-Martinsburg Formations in accommodating shortening and filling space increases to the east in the Great Valley region; here, an additional 15 km of shortening is accommodated by Cambro-Ordovician horses and is balanced by 35% LPS (Wright and Platt, 1982).

The shortening required by the proposed cross section through the Appalachian Plateau and Valley and Ridge can be compared to that calculated by measurements using the normalized Fry method (Table 2). As stated previously, measured LPS across this portion of the Appalachians is highly variable. To compare measured values to the values needed to balance the cross section, we have averaged spatially related LPS samples across the transect, producing 16 intervals ranging in length from 4 to 46 km for which an average LPS is calculated (Plate 2). These intervals were chosen to represent structural domains and to maximize the applied amount of LPS shortening. The average of the measured LPS values defined for each interval is then compared to the magnitude of LPS required to balance the shortening accommodated by faulting and folding. Net positive LPS values indicate that the measured grain-scale LPS is greater than the magnitude of LPS needed to balance the shortening in the duplexed strata. Net positive values are calculated for seven of the 16 subdivisions (Plate 2, sections 7, 8, 11, 12, 14, 15, and 16), while the remaining nine domains yield net negative results. Without accounting for other mechanisms of shortening, our model suggests that including our calculated LPS values, the proposed cross section solution requires an additional 12.66 km of shortening that is 4% greater than the measured LPS values (Table 2). However, if an average of 10% outcrop-scale shortening (Hogan and Dunne, 2001) is applied to the portion of the transect between the Elkins Valley anticline (interval 10), where outcrop-scale shortening becomes significant, eastward to the boundary of the Great Valley (interval 16) (Plate 2), the proposed model would have an deficit of only 0.7 km. Thus 10% outcrop-scale shortening combined with shortening accommodated by folding and layer-parallel dissolution is necessary to balance the proposed geometry and resulting shortening of the faulted Cambrian through Ordovician section.

The cross section that we present assumes that slip transferred from horses 1–5 (Plate 1) in the Ordovician–Cambrian strata to the Appalachian Plateau is accommodated in the strata exposed at the surface solely through folding and LPS. However, the Middle Devonian organic-rich shales and the Silurian–Ordovician siliciclastics are decoupled from this cover sequence and accommodate slip through faulting within the two separate packages. It is commonly assumed that the detachment at the base of the Salina Formation on the Appalachian Plateau separates the unstrained units (below the detachment) from those deformed via LPS and folding above the detachment (Evans, 2010; Sak et al., 2012). However, newly acquired high-resolution 3-D seismic data across the Alleghanian structural front in central Pennsylvania (Ace et al., 2020) combined with pre-existing well data from the core of the Burning Springs anticline (Ryder et al., 2008) reveal wedge-style faulting within the Middle Devonian organic-rich shales, forming the cores of the low-amplitude folds of the Appalachian Plateau. We incorporate these geometries in the balanced cross section (Plate 1) and propose that the cover strata of the Appalachian Plateau are detached from the underlying stiff sequence along a décollement at the base of the Devonian Tully Limestone.

In a previous study, Evans (2010) invoked a double stack of Cambrian to Ordovician carbonate thrust sheets directly east the Wills Mountain anticline to explain the higher structural elevations between the Wills Mountain anticline and the Whip Cove syncline (Plate 2). However, the proposed 32.5% to 63% shortening magnitudes required to balance these sections (Evans, 2010) are not compatible with the strain values obtained through this study or previous studies of grain-scale bulk finite strain in the central Appalachian Mountains (e.g., Dunne, 1996; Whitaker and Bartholomew, 1999; Sak et al., 2012). Even using the more conservative geometries proposed here, the calculated shortening budgets indicate more shortening than is accounted for by the measured grain-scale LPS. Consequently, the model we propose does not assume a “double stack”, but instead proposes a series of faults all originating from the detachment at the base of the Waynesboro Formation. Furthermore, the 18% shortening required to balance the section is plausible only when the maximum permissible measured LPS values for each interval (Plate 2A) are combined with the maximum permissible outcrop-scale shortening (Hogan and Dunne, 2001).

In order to balance the cross section, this study relies upon 10% outcrop-scale shortening over a 125 km portion of the eastern Appalachian Plateau and the Valley and Ridge. This is equal to the upper limit (10%) of outcrop-scale shortening documented along the 18.6 km transect of Devonian-aged strata in the western Valley and Ridge of northeastern West Virginia (Hogan and Dunne, 2001). Our proposed model’s reliance upon outcrop-scale shortening can be minimized if 2.2 km and 2.8 km less displacement is assumed for horses 6 and 9, respectively (Plate 2B), resulting in 5 km less LPS to balance the section. This, in turn, reduces the magnitude of outcrop-scale shortening required to balance the section from 10% to 6.5%. Reductions in outcrop-scale shortening require greater variations in the thickness of the ductile Reedsville Formation through the Valley and Ridge. Additionally, the incorporation of outcrop-scale shortening can further be reduced from 6.5% to 5% if 2.2 km less displacement is assumed on horse 4 (Plate 2B), adjacent faults in the Ordovician to Silurian packages, and wedge faulting of the Middle Devonian shales east of the Elkins Valley anticline. The 5% outcrop-scale shortening is consistent with estimates of Hogan and Dunne (2001), where a majority of studied transects exhibit 4%–6% outcrop-scale shortening.

Integration of bulk grain-scale finite strain measurements in balanced cross sections is a critical component for documenting total amount of shortening and elucidating the kinematics of deformation. The strong variability in measured LPS values from this study suggests caution in assuming magnitudes of LPS even between transects across the same portion of an orogen. The LPS measurements we present here, when combined with other Appalachian measurements, document significant variations in both location and magnitude of grain-scale shortening within the system and provide insight into the partitioning of strain between shortening mechanisms. Although LPS is a critical component of shortening within the West Virginia portion of the Appalachian fold-thrust belt, the cross section remained unbalanced without the additional estimates of outcrop-scale shortening. The 40 siliciclastic samples collected across this transect reveal an average LPS value of 10% with a mean trend of 304° ± 5°. Complementary fracture analyses of outcrops highlight a strike-parallel joint set and cross joints that are broadly parallel to the shortening direction. We maximize the permissible LPS values by assigning measured LPS values to prescribed intervals. This approach suggests a shortening deficit of ∼13 km once measured LPS is applied. This deficit is further reduced (to 6 km) by minimizing shortening in Cambro-Ordovician rocks to ∼49 km and is completely removed by assuming 5% outcrop-scale shortening across the eastern Appalachian Plateau and Valley and Ridge. Through the cross section proposed in this study, we present a revised deformation and kinematic scenario from the simple two-part passive-roof duplex system shown in other cross sections across the Appalachian fold-thrust belt (Gwinn, 1970; Herman, 1984; Dunne, 1996; Sak et al., 2012). Our revised kinematics includes the transfer of 24 km of slip from faults in Cambrian to Ordovician units of the Valley and Ridge to décollements in the Middle Devonian shales, Salina salt, and Reedsville Shale across the Appalachian Plateau, accommodating strain through duplexes within both the Middle Devonian shales and carbonates and the Silurian to Ordovician siliciclastics. Overall, the total proposed shortening along a transect from Burning Springs anticline of West Virginia to the Great Valley of Virginia is 56 km (18%); additional shortening from the Great Valley region may increase this estimate to 71 km (Plate 1).

This research was partially funded by a Stephen Pollock Undergraduate Research Program Grant from the Northeastern Section of Geological Society of America to DL, with additional support provided by a Summer of Undergraduate Research Fellowship from the College of Arts and Sciences at the University of Pittsburgh to DL. PBS graciously acknowledges funding from U.S. Geological Survey EDMAP program and additional support from the Dickinson College Research and Development Committee. Finally, we are grateful to Mary Beth Gray, Steve Wojtal, an anonymous reviewer, and Associate Editor Mike Williams for their detailed and comprehensive reviews that greatly improved this paper.

1Supplemental Material. Supplemental Data Table S1 contains axial ratios for the best-fit vacancy field (with statistics) of grain-scale bulk finite strain from the three mutually perpendicular cuts. Supplemental Data Table S2 contains orientations of the best-fit strain ellipsoid (with statistics) and ellipticity ratios and orientations on the bedding plane. Please visit https://doi.org/10.1130/GEOS.S.12598586 to access the supplemental material, and contact editing@geosociety.org with any questions.
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Associate Editor: Michael L. Williams
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