The Mechanics of Initiation and Development of Thrust Faults and Thrust Ramps

Manuscript received October 27, 2021; Accepted February 20, 2022. 2 Department of Geosciences, Utah State University, 4505 Old Main Hill, Logan, UT 84322-4505, james.evans@usu.edu 3 INTERA Inc, 3240 Richardson Road, Suite 2, Richland, Washington 99354, sarahwigginton92@gmail.com 4 Department of Natural and Environmental Sciences, Western Colorado University, Gunnison, CO 81231, espetrie@western.edu


INTRODUCTION
The geometrical relationships and kinematic models used to explain the formation of structures in fold and thrust belts (Dahlstrom, 1970;Boyer and Elliott, 1982;Butler, 1982;Suppe, 1983;Cooper and Trayner, 1986;Suppe and Medwedeff, 1990) support a classic flat-ramp kinematic model of thrust fault propagation (Suppe and Medwedeff, 1990). The flat-ramp model is based on a thrust fault that nucleates on weak, shallowly dipping décollement horizons and propagates along décollement until the resistance to frictional slip on the flat is greater than resistance to brittle failure in rocks above the décollement. At this point faults propagate upward to form a ramp (Rich, 1934;Rodgers, 1950;Dahlstrom, 1970;Boyer and Elliott, 1982;Butler, 1982;Williams and Chapman, 1983;Mitra, 1990;McClay, 2011).
While this geometric/kinematic model is well documented in fold-and-thrust belts, it may not fully account for the mechanics and mechanisms by which thrust fault formation occurs. Integrating rock material properties and mechanical modeling with traditional field geology and kinematic analysis allows for investigations of different models for the development of thrust faults and folds (Chapple, 1970;Erickson, 1996;Underwood et al., 2003;Teixell and Koyi, 2003;Bourne, 2003;Welch et al., 2009;Roche et al., 2013;Hughes and Shaw, 2015). Merging mechanics with kinematic models can help answer questions about the conditions that promote failure at thrust ramps, how stress state variations may promote failure, and the rock properties govern the continued propagation or arrest of newly formed thrust faults (Busetti and Fang, 2018).
The mechanical stratigraphy of rocks in thrust terrains may exert a control on nascent thrust fault formation (Eisenstadt and De Paor, 1987;Ferrill et al., 2017). Stress concentrations may form at imperfections in mechanically strong layers and stress heterogeneities at these sites in the stratigraphic system may cause faults to nucleate on the ramp and arrest in mechanically weak layers above and below (Eisenstadt and De Paor, 1987;Roche et al., 2013;Ferrill et al., 2016). Field evidence of this "ramp-first" faulting style is documented in mechanically layered formations at the sub-meter scale (Fig. 1;Eisenstadt and De Paor, 1987;McConnell et al., 1997;Ferrill et al., 2016) to the 10's m scale (Ferrill et a., 2016;Alsop et al., 2021) and map scales (Onderdonk et al., 2005;Newsom, 2015;Ferrill et al., 2016). Primary indicators of the ramp-first faulting style include the presence of fault propagation folds that form at both fault tips and a displacement or slip profile in which slip is largest in the center and decreases toward both fault tips (Ferrill et al., 2016;Alsop et al., 2021). These observations indicate that mechanical stratigraphy exerts an influence on the nucleation, propagation, and arrest of developing thrust faults, but more information is needed to describe the loading conditions that promote failure.
We integrate field-based structural analysis and two-dimensional cross section reconstructions (Wigginton, 2018), with the results of mechanical finite element models to investigate the effects of mechanical stratigraphy on stress heterogeneity, rupture direction, and thrust fault geometry. We use the results of field-based studies (Petrie et al., 2018;Wigginton, 2018) and their resulting kinematic models as the foundation for finite element mechanical models of small-displacement thrust fault development in rocks with contrasting mechanical strengths across layers and fault propagation folds in the hanging wall and footwall.

Background
Mechanical stratigraphy is the stratal expression of the contrasts in the cohesive, compressive, tensile, and frictional strengths of rock, along with the thicknesses of rock units and interface properties between mechanical units (Corbett et al., 1987;Gross et al., 1995;Underwood et al., 2003;Laubach et al., 2009;Ferrill et al., 2017;Hart and Cooper, 2021). Mechanical stratigraphy affects fault nucleation and propagation (Teixell and Koyi, 2003;Underwood et al., 2003;Laubach et al., 2009;Roche et al., 2013;Ferrill et al., 2017;Bracken, 2020), fracture nucleation location (Eisenstadt and De Paor, 1987;, fault length, width, and the aperture across a slip surface (Laubach et al., 2009;McGinnis et al., 2017), fault-growth directions (King et al., 1988;Mitra and Mount, 1998), the proportions of folds and faults that form (Morley, 1994;Erickson, 1996), fold geometry (Fischer and Jackson, 1999;Gutiérrez-Alonso and Gross, 1999), fault-fold interactions (Chester, 2003), and fault shape and related fault zone deformation (Woodward and Rutherford, 1989;Pfiffner, 1993;Ferrill and Morris, 2008). Strong, competent units withstand higher stresses before deforming plastically (permanently) and they accommodate stress loads by brittle failure (Currie et al., 1962). Conversely, weak or incompetent strata deform plastically at lower stresses and may deform ductilely before fracturing in response to increased stress (Goodman, 1980). Stresses applied to mechanically layered sections with varying Young's moduli might lead to varying layerparallel stresses within the anisotropic package (Roche et al., 2013). The highest stresses are expected to form in the competent units, and this is where faulting might initiate in some mechanically layered package (Eisenstadt and De Paor, 1987;Ferrill et al., 2016). This contrast in deformation styles between competent and incompetent rocks creates strong stress heterogeneity in mechanically layered systems.
If a fault nucleates in a competent layer and propagates upward and downward, it is predicted to arrest in fault-tip folds in the more ductile layers above and below (Fig. 1). These asymmetric folds verge in the transport direction of the thrust fault. The dual-directional propagation of a thrust fault creates a hangingwall anticline associated with the upward propagating tip and a footwall syncline associated with the downward propagating fault tip (Fig. 1). Fault slip patterns along a "ramp-first" fault slip decreases in both directions along faults (Ellis and Dunlap, 1988;McConnell et al., 1997;Apotria and Wilkerson, 2002;Tavani et al., 2006;Cawood and Bond, 2020). All these features point to a potential influence of mechanical stratigraphy on the location, geometry, and direction of thrust fault development.
Previous models of the mechanics of thrust fault nucleation and fold formation used elastic dislocation models (Rodgers and Rizer, 1981), wax analogues (Odonne, 1990), two-dimensional (2D) numerical models (Reches and Eidelman, 1995), 2D numerical models of viscous flow around a fault (Grasemann et al., 2003), 2D finite element models of elasto-plastic deformation (Strayer and Hudleston, 1997), displacement field analysis (Grasemann et al., 2005), 2D kinematic plane strain models (Welch et al., 2009) and three-dimensional (3D) elastic numerical models (Roche et al., 2013). These studies produced a number of findings which bolster the ramp-first model of thrust fault propagation: 1) Odonne (1990) and Grasemann et al. (2005) found that displacement along the fault causes heterogeneous reorientation of the strain axes and the highest strains were found at the fault tips (Reches and Eidelman, 1995). Here the increased stresses were responsible for the development of fault-propagation folds, and the kinematic model of McConnell et al. (1997) for a dual edged fault propagation fold model is an excellent explanation of their results. 2) Models confined with overburden pressure produce significantly more stress heterogeneity around the fault and the degree of fault related folding likely depends partly on the depth of the fault (Odonne, 1990). 3) Low-angle faults (dips ~30°), are more likely to produce the fault-propagationfold geometry (Grasemann et al., 2003;Grasemann et al., 2005). 4) The stress conditions that create faultpropagation folds are largely insensitive to the rheology of the rock (as long as the rheology is continuous and uniform), so fault propagation folds can form in any rock type (Reches and Eidelman 1995;Grasemann et al., 2005). 5) Relatively small differences in yield strengths can make a significant change to the sequence of failure in a sedimentary package (Roche et al., 2013). Roche et al. (2013) showed that for stratigraphic sequences with little variation in strength, nucleation occurs in the stiff layers (limestone or sandstone), while failure occurs in the compliant layer (claystone) if the stiff layer has high cohesion (Roche et al., 2013).

METHODS
In order to investigate the effects of mechanical stratigraphy on stress heterogeneity, rupture direction, and fault geometry we examined the Ketobe Knob thrust fault in Central Utah. The exposed thrust system exhibits characteristics of the ramp-first faulting style with a hanging wall anticline and large footwall syncline. In this section we briefly summarize the results of fieldwork and kinematic reconstructions which are the foundation for the numerical modeling (Wigginton, 2018). We describe in detail the methodology for generating the numerical finite element models of thrust fault formation.
A range of field analyses were conducted at the Ketobe Knob outcrop to characterize the structures and lithology including: 1) documentation the fold and fault geometries, 2) measurements of displacement along the length of the fault exposed at the Ketobe Knob outcrop, 3) documentation of mesoscopic structures, (e.g. slip surfaces on faults and bedding planes), 4) collection of rock samples for thin section analysis and XRD to characterize mineralogy and 5) collection of rebound values for each rock unit using a Schmidt hammer. The methodology and results of this field work are detailed in Wigginton (2018).
Restored cross sections were created in Move™, which contains a suite of algorithms to create/restore faults including Fault Parallel Flow, Elliptical Fault Flow, and three different kinematic fold/unfold algorithms that we utilized including Flexural Slip, Simple Shear, and Line Length (Petroleum Experts). A combination of these algorithms was applied to the structures on a dip-parallel outcrop photo of the Ketobe Knob thrust. The reconstruction of a balanced cross section is a common tool to validate an interpretation of structures in the field (Dahlstrom, 1969). While a restored cross section is a non-unique solution, through trial and error, a balanced restoration can reveal possible 1) fault nucleation locations, 2) fault propagation directions 3) the cause of fold formation, and 4) a possible order of events in the structure. We use these kinematic models which satisfy geometrical constraints, to motivate the finite element modeling. The methodology and results of the kinematic reconstructions are detailed in Wigginton (2018), and the geometry and kinematics of the structure are also described in Wacker, 2001;Souque et al., 2008;and Petrie et al., 2018. We use the numerical finite element modeling program ABAQUS ™ (Dassault Systèmes, 2011) to mechanically model fault-fold structures. This finite element code allows for the creation of complex geometries, including non-planar faults to be combined with mechanical stratigraphy and load conditions (Smart et al., 2009;Smart et al., 2012). The models satisfy the equilibrium, constitutive, and compatibility relationships necessary to create a mechanically permissible model. We establish the initial boundary conditions, stress state, and constitutive relationships, consider a range of material properties to simulate rock behavior (simple elastic or elastic-plastic responses) and examine variable friction between layers (Smart et al., 2008;Petrie and Evans, 2016). Parameterization studies were performed using a simple three layer model with a coarse mesh to test for model convergence, and to examine the impact of rock properties, interlayer slip, overburden pressure, fault friction, and fault angle individually. The preliminary models enabled us to decide on reasonable input values such as the use of damping factors, non-linear algorithms, and surface contact types (Smart et al., 2009(Smart et al., , 2012. We then examined specific mechanical models with realistic stratigraphy and finer meshes in order to explore a range of questions, track the spatial and temporal distributions of magnitudes and orientations of stresses as well as elastic and inelastic strains throughout the model domain (Petrie and Evans, 2016;Smart et al., 2010Smart et al., , 2012. The finite element models have a rigid boundary condition at the base to prevent downward movement and a rigid boundary condition at the top to represent overburden material and to prevent excess distortion of the topmost layer (i.e., upward movement was restricted). These models do not incorporate pore pressure in the material properties.
The models consisted of two load steps. In step 1 we applied a downward gravitational acceleration to the model and let it equilibrate. The gravity load applied in step 1 remains on the model through step 2. In step 2 we applied the horizontal tectonic loads. The downward pressure simulates an overburden of 40 MPa as suggested from the stress orientation and magnitude inversions in 3D Stress from small fault slip data for the site (Souque et al., 2008;Morris, 2017;Wigginton, 2018). A horizontal load of 200 MPa is applied, which is more than sufficient to induce failure of all rock units in the model. Models were run with a range of mesh sizes and time increments to ensure we had achieved a convergent result -that is we tested to make sure that alteration of the time increment, and mesh size did not alter the distribution of stress and strain in the final model. We ran models with the same parameters and incrementally reduced the mesh size from 2 m to 0.5 m and altered the run time from 1 s to 10 s. Each model yielded the same pattern of stresses and very close to the same magnitudes.

Geologic Analyses
The Ketobe Knob thrust exposure is a lateral ramp in the southwestern part of the Buckhorn Flats thrust complex, in the Cedar Mountain thrust system, Utah (Figs. 2 and 3, Neuhauser et al., 1988;Wacker, 2001;Souque et al., 2008;Welch et al., 2009;Petrie et al., 2018) where moderate-displacement thrusts cut the Jurassic Entrada Formation through the Curtis Sandstone (Fig. 3). The following sections summarize the mechanical stratigraphy and cross section construction and restoration as published in Wigginton (2018).

Mechanical Stratigraphy
Rocks at the Ketobe Knob outcrop were divided into five mechanical units ( Fig. 4; Table 1) based on the distribution of mesoscopic structures, mineralogic and sedimentary petrographic analyses, and Schmidt rebound hammer field tests (Wigginton, 2018). This mechanical stratigraphy is related to, but may differ from, formally recognized stratigraphic units. Relative rock strengths were determined in the field with an N-type Schmidt rebound hammer. Rebound was used with the following relationships to estimate UCS and E values: (1)  (2016) and these variations affect the brittle failure response of a layered sequence in a range of settings (Underwood and Cooke, 2003;Petrie et al., 2014). Mesoscopic structures include slickensides on bedding surfaces at the Ketobe Knob site, that indicate that interlayer frictional slip failure occurred during deformation throughout the area (Wigginton, 2018). Other mesoscopic structures include small folds and sheared rocks in shale-siltstone sequences, all of which indicate that the rocks deformed by brittle slip and shearing.

Cross Section Construction and Restoration
Wigginton (2018) generated restored cross sections in Move™ in which several variations of initial fault geometries and structural timing were explored and tested for acceptability by their area balance and logic of restorability. We created restorations from four different initial geometries because the highly deformed region in-between the upper and the lower fault left room for multiple interpretations (Wigginton, 2018). Over 20 restorations were attempted, a selection of which are presented in Wigginton (2018, Appendix B). With each of those initial geometries we varied the order of fault failure, location of fault nucleation, and the fault and fold algorithms applied. All attempted restorations, except our preferred interpretation, were considered unsuccessful due to the following problems: 1) the algorithms of the program could not complete an unfaulting or unfolding step (due to non-concentric folding) , or 2) they required steps which are not geologically reasonable, in that they created 1) more deformation than exists present day, 2) excessive layer thickening, or 3) unreasonably tight folding (Wigginton, 2018). Based on the detailed reconstruction steps (Wigginton, 2018, Appendix B), our preferred interpretation shows that the structures at the Ketobe Knob could reasonably be created by the series of events in Figure 5. It is also important to note that we do not assign a strict absolute timeline to the reconstruction; the faults and folds could have all formed in very short succession or simultaneously as connected relays.
The preferred area-balanced restoration (Fig. 5) consists of two sub-parallel thrust faults that nucleated in the sandstone member of the Entrada Formation and propagates upward and downward into the mechanically weaker rocks (made weaker due to laminations, less calcite cementation, or overall unit thickness (Wigginton, 2018)). The displacement-distance profile or displacement-distance diagram (Fig. 6) shows the likely region of fault nucleation could be the site with the greatest displacement (Muraoka and Kamata, 1983;Williams and Chapman, 1983;Ellis and Dunlap, 1988

Mechanical Modeling
The finite element models of mechanically layered sequences in ABAQUS TM explore the ramp-first style of thrust fault propagation. These models incorporate field data and provide a mechanically-based analysis of the development of the thrust faults at the Ketobe Knob site. We examine models for intact, unfaulted layered sequences with and without frictional interlayer slip (Fig. 7a), and models of a faulted layered sequence without and with variations of mechanical properties of the rock (Fig. 7b).

Model Inputs
Analysis of rock properties and the kinematic models of the Ketobe Knob site serves as the guide for the number of layers to include in the model, their thicknesses, compressive strengths, initial stress state of the model (Table 2), and the nature of interlayer slip. We use elastic-plastic (Mohr-Coulomb) material properties to describe the bulk deformation of upper crustal rocks (Smart et al., 2012), and use a Coulomb friction model to govern slip between layers and faulted surfaces (Smart et al., 2010).
We created two model suites within this framework: 1) intact and unfaulted models to examine how the difference in mechanical stratigraphy affects the distribution of stresses in the pre-faulted state, and 2) faulted models which use the same inputs but contain a planar fault (contact surface with a coefficient of friction) to show how a recently nucleated fault alters stress in the surrounding rocks. The faulted models were run with slight variations including a) variation in mechanical stratigraphy, b) uniform mechanical stratigraphy (no variation of strength between the layers), and c) variation in mechanical stratigraphy and deformed by a horizontal displacement load.

Unfaulted Models
The unfaulted models provide the base case for the distribution of stresses and strains in an intact stratigraphic sequence. We apply horizontal far-field tectonic stresses to the strata and show how the difference in mechanical strength of each unit at the Ketobe Knob affects the distribution of stresses.
The unfaulted models reveal the dramatic variation of stresses that develop in different mechanical layers (Fig. 8a). The stresses in the modeled stratigraphic section range from ~130 MPain the weaker mechanical layers (representing properties derived from the Curtis sandstone, Curtis conglomerate, and Earthy Entrada silty member), and up to ~300 MPa in the strong mechanical layers (representing properties derived from sandstones in the Entrada Formation) (Fig. 8c). Animations of the model run show the stresses are consistently higher in the strong units (Table 1) and radiate outward through the weaker units (Wigginton, 2018). The largest contrast in layer strength is at the center of the model , and stress contrasts are pronounced at layer interfaces (Fig. 8c). A graph of stress through time (Fig. 9a) shows that during loading stresses in the mechanically layered sequence diverge rapidly with the higher stresses in strong units (Entrada sandstone) and the weaker units experience lower stresses. Graphs plotting stress vs strain show that the two strongest units (Table 1) are more resistant to deformation (i.e. for a given strain, stress is higher in the strong rock units; Fig. 8c). Stress-strain and stress-time curves (Fig. 9a and 9b) show that the weaker units depart from linear elastic behavior earlier than in the strong layer, and that ductile deformation continues through the model run. With µ of 0.85, the stresses in the stronger layers expand laterally, and are communicated broadly to the overlying layer (Fig. 10d).

Influence of Interlayer Slip
The stress-time curves (Fig. 11) for these models provide insights into the behavior of the sequence. In  (Tables   3 and 4).

No Variation in Mechanical Stratigraphy
The model of a newly formed thrust fault in uniform mechanical stratigraphy is the base case for the faulted models and shows the distribution and concentrations of stresses created by a newly formed fault without the additional impact of mechanically layered stratigraphy. All the model inputs remain the same as the previous model, except that we assign uniform material properties (those used to represent the upper Entrada sandstone) to represent a layered, mechanically uniform package of sedimentary rocks (Fig. 12).
Both fault tips show Coulomb stress perturbations with a stress increase in the compressional quadrants, a very focused stress increase at the footwall of the upper fault tip, and corresponding decreases in stress in the dilatational quadrants (Fig. 12). The hanging wall above the upper fault tip and below the lower fault tip both show an increase in stress and heterogeneous reorientation of stress axes around the fault tips (Fig.   12b). The region of increased stress below the lower fault tip is larger than the area of increased stress above the upper fault tip (Fig. 12). This result shows that without the added effect of mechanical stratigraphy, nascent thrust faults may result in increased stress increases near the faults tips and this induces deformation in the hanging wall and footwall near the fault tips. Stress magnitudes are slightly larger in the strongest units (Table 1) throughout the simulation.

Models with Variation in Mechanical Stratigraphy and a Displacement Boundary Condition
The displacement model simulates a rapid loading scenario (Smart et al., 2010(Smart et al., , 2012. This model shows the perturbed stress state directly after the loading event (Fig. 13). The displacement boundary condition necessitates additional material be added to the edges of the model to absorb material failure directly adjacent to the applied load. We add a thick base layer for the upper units to slide over to avoid edge effects of the lower boundary condition. The displacement load model parameters (Table 4) have an initial static stress state to create a pre-stressed volume of rock in a contractional stress regime. The gravitational load is applied in step 1. In step 2 an additional boundary condition is placed on the right side of the model to prevent movement in the x direction, then a horizontal displacement of 2 m was applied to the left side (Fig.   15a). The displacement models use the same material properties as previous versions except for the interlayer slip and fault coefficient of friction (Table 4). We applied a friction coefficient of µ = 0.2 to layer contacts to allow interlayer slip and prevent the layers from failing where the load was applied. of stresses in the model also indicates that the formation of a back-thrust in the Curtis sandstone (Fig. 15b).
The stress pattern shows a thin band of increased stress at ~40°. High stress concentrations on the left side of the model should be disregarded as they are a result of rock failure at the location of load application.
The distribution of stresses in each unit through time (Fig. 16) mirrors results from the unfaulted model before they level off later in the loading step (Fig. 11). Stresses are highest in the Entrada sandstone units and lower in the Curtis Formation and the earthy Entrada, as seen in all previous models.
The extreme stress concentration at the hanging wall side of the lower fault tip (Fig. 15d) exhibits the geometry of a back thrust at the lower fault tip. Principal stress orientations are significantly reoriented here. These orientations indicate that steeply dipping faults would form at the lower tip zones of the faults (see also Strayer and Hudleston, 1997).

DISCUSSION
The results of the finite element models based on field data and kinematic restorations provide insights into how the mechanical stratigraphy of rocks influences thrust fault nucleation and propagation, and we examine the ramp-first model for thrust fault development (Eisenstadt and De Paor, 1987;Ferrill et al., 2016;Alsop et al., 2021). We discuss the nature of the fault-to-fold transitions, the nature of mechanical stratigraphy and its influence on the structure, and details of the fault development.

Mechanical Stratigraphy
A number of factors contribute to determining how layered rocks respond to stresses including primary rock textures and diagenetic or metamorphic processes. Rock composition may significantly affect failure properties, but there are few universal relationships solely between lithology and rock strength in many clastic sedimentary rocks (Busetti and Fang, 2018). Instead, lithology combined with layer thicknesses, grain size, grain composition, laminae, degree and nature of cementation, burial history, and other factors affect rock strength and failure modes in these types of rocks (Corbett et al., 1987;Petrie et al., 2015;Busetti and Fang, 2018).
The numerical modeling results  show that the stress magnitudes are significantly perturbed from the uniform starting stresses in all models in response to horizontal shortening. Peak stresses are larger in the stronger horizons, whereas the weaker units have much lower stresses. The models show that the uniform stress state at the beginning of the model runs quickly deviate to produce nonuniform distributions. We also show how to use experimentally determined rock mechanics properties for the rocks exposed at Ketobe Knob in conjunction with basic Mohr-Coulomb failure analysis to show how failure might first occur in these stronger horizons (Petrie et al., 2015). Experimentally determined values for the cohesive strengths and tensile strengths of similar rocks (Petrie et al., 2014;Petrie et al., 2015) provide general constraints on the Coulomb failure envelopes in these rocks. The relatively strong Entrada Sandstone sequences tend to have lower tensile strength and higher cohesive strength than the silt-rich rocks. At the differential stresses predicted in our models, the Entrada Sandstone layers are likely to reach failure (Fig. 17). In contrast, the low stresses in the weaker rocks, combined with slightly higher tensile strengths, indicate that the weaker rocks (as determined by field measurements) may not reach failure (Fig.   17). While the yield strengths of the weak rocks are lower, the stresses in the weak rocks are also significantly reduced as the strong rocks act as a load bearing sequence. This stress imbalance and strength difference within the mechanically layered stratigraphic section reverses the anticipated order of rock failure. We note that the range of yield strengths measured at the surface may differ from the rock properties at depth. We model faulting at the overburden load of 2 km, which corresponds to the maximum burial of the rocks, and during the time frame inferred for deformation of these rocks (Neuhauser et al., 1988). he differences in mechanical strength may have been less extreme at depth, thereby dampening the observed stress partitioning in response to an applied horizontal compressive stress. However, the analyses of variations of frictional properties are sound regardless of the burial history, and the results in the mechanically layered sequence provide insight into the relative behavior of the rocks.
The strength contrast between units affects fracture propagation (Petrie, 2014). Two rock units with similar strengths are likely to have a fracture propagate through the interface. Conversely, strong layer contrasts (a weak unit next to a strong unit) are likely to arrest propagating fractures (Cooke and Underwood, 2001;Larsen et al., 2010). This relationship is demonstrated by the fault and fold formation at the Ketobe Knob where faults likely nucleated in stiff units, then formed fault propagation folds in more ductile units before they broke through.

Mechanics of Thrust Fault Development
The finite element models provide a mechanical explanation for the field observations and reconstructions of the thrust fault-fold relationships (Ferrill et al., 2016;Wigginton, 2018). The results from the faulted models show that initially uniform stresses in the sedimentary rocks quickly evolve to nonuniform distributions with high stresses concentrated in the strong layers. In the faulted models, stress becomes concentrated at fault tips in the upper and lower weaker layers (Eisenstadt and De Paor, 1987), and conjugate stresses form from the lower fault tip. Fault-propagation folds form and the faulted models show an increase in stress and strain in the unfaulted units around the fault tips (in the Curtis conglomerate and the Earthy Entrada). While the fold amplitudes are not the same as the folds seen in the field, it is easy to imagine that this model is an early snapshot in the formation history of the present-day structures at the Ketobe Knob. The increase in stress occurred in the models without variation in mechanical stratigraphy and are even more dramatic in the models with variation in mechanical stratigraphy (stress in the strong layers is more than twice the stress in the weak layers). The results also explain macroscale footwall folding that is so common; the stress and strain heterogeneities are present at both the upper and lower fault tips regardless of the direction of propagation or the mechanical stratigraphy.
The development of a high stress region in the hanging wall of the thrust, near its upper fault tip, and dipping towards the fault predicts that significant deformation should occur in the hanging wall of the thrust (Fig. 13). The stress patterns are similar to the back thrust development predicted from rock models (Morse, 1977;Chester et al. 1991;Marshak et al., 2019), analytical models (Berger and Johnson, 1982;Kilsdonk and Fletcher, 1989), field studies (Serra, 1977;McConnell et al., 1997), and kinematic models (Welch et al., 2009). Our results also suggest that high back-thrust stresses develop early in the junction of the fault tip and the lower, weaker rock contact, consistent with analog models of frontal thrust development (Morse, 1977;Marshak et al., 2019).
We based our models on mechanical stratigraphy that is distilled from the field-based measurements, and considered a single fault. This ensures that we produced tractable models that evaluated the impact of mechanical stratigraphy and rock properties on stress distributions at fault tips. The Ketobe Knob thrust consists of several faults (Figure 3) and the mechanical stratigraphy may have affected how these faults interacted as the structure evolved. Such complexity may warrant further analyses.

Fold Geometry
The Ketobe Knob thrust faults and associated hanging wall anticlines and footwall synclines reveal fault/fold geometries that are compatible with the ramp-first style of thrust fault formation. The presence of macroscale footwall deformation at the Ketobe Knob (Wigginton 2018;Petrie et al.et al., 2018) and in other studies (McConnell et al., 1997;Ferrill et al., 2017) favor ramp-first formation over flat-ramp formation. The Ketobe Knob thrust shape and position of the folds are consistent with that expected from fault propagation folds, i.e. when the fault propagates through the fault tip folds it leaves behind tight, steep to overturned anticlines and synclines adjacent to the fault surface (Suppe and Medwedeff, 1990). The elevated stress and heterogeneous reorientation of stress axes at the upper and lower fault tips in faulted models agree with analogue and analytical models (Rodgers and Rizer, 1981;Patton and Fletcher, 1995).
The region of potential failure (folding) directly above a reverse-fault is elongated parallel to the dip of the fault (Patton and Fletcher, 1995). . Rodgers and Rizer (1981) found shear stress to be the greatest at the fault tip and vertical displacement increased above the fault tip. These results and our results enforce the concept that elevated stresses may generate fault propagation folds at fault tips, regardless of lithology or propagation direction.
The folded Curtis conglomerate and Earthy Entrada silty sandstone exhibit thinner beds than the other units. The Curtis conglomerate is only 1.6 m thick and the Earthy Entrada unit is 2.9 m thick but contains extremely fine laminations (0.25 mm in thin section). The Curtis sandstone, while weaker in terms of elastic strength (low rebound) is very thickly bedded, which explains its lack of folds in the hanging wall. The upper and lower Entrada sandstones are elastically strong (high rebound) and are thickly bedded, which would make them the most competent units in the stratigraphic section. Analytical mechanical models of free slip along fault ramps (Kilsdonk and Fletcher, 1989) predict that a footwall ramp syncline may result in cases where the footwall is stiffer than the hanging wall, with thinning and extension of the footwall. Our models do not allow for free slip, and the fault tips are "pinned". Evolution of the structures from pinned to free slip may result in changes from contractional to extensional strains in the fault tipfault ramp regions.
The sizable amplitude difference between the hanging wall anticline and footwall syncline could be due to textural differences in the rocks (i.e. the degree of cementation and the thickness of bedding/laminations). The Earthy Entrada silty sandstone is weakly cemented, very finely laminated, and has smaller grain size which make it more ductile. Conversely, the Curtis conglomerate contains thicker beds, larger grain sizes, and strong cementation, making it less ductile than the Earthy Entrada.  (Link, 1949;Teal, 1983;Morley, 1994;Begin et al., 1996;McMechan, 1999;Langenberg et al., 2006), the Osen-Røa thrust sheet in Norway (Morley, 1994), and the Wyoming thrust belt (Woodward, 1986;Fischer et al., 1992). Sometimes called "sled runners" or "incipient thrusts", small-displacement thrusts form 10's of km in front of the conventionally defined fold and thrust belt (McMechan, 1999). In seismic reflection profiles these faults appear to cut stiff sandstone units and lose displacement above and below in weaker reflectors (Teal, 1983;McMechan, 1999).

CONCLUSIONS
We integrate traditional structural geology field methods, 2-dimensional cross section reconstructions, and finite element mechanical models to investigate the effects of mechanical stratigraphy on stress heterogeneity, rupture direction, and fault geometry by examining a large-scale field example of ramp-first faulting in central Utah. The results of this study provide strong support for the importance of the rampfirst faulting style in mechanically stratified systems. The mechanical stratigraphy of faulted rocks exerts a first-order control on thrust fault formation. Kinematic reconstructions and finite element models indicate that faults at the Ketobe Knob nucleated in structurally strong (stiff, low ductility) layers, then propagated upward and downward, and created fault propagation folds at both fault tips. Numerical models provided a mechanical explanation for the kinematics; strong rock units showed elevated stresses and more brittle behavior making them likely to fault first. Weak units showed lower stresses, but were more likely to respond ductilely and form folds under pressure. When a fault was nucleated in the layered system, the finite element models showed similar fold orientations to those seen in the outcrop.
We hypothesize that in some cases thrust fault nucleation occurs in the ramp-first style that then evolves to ramps that are linked by flats (slip along long angle, weak surfaces) (Eisenstadt and De Paor, 1987;Marshak et al., 2019). Many thrust systems may originate in this way, but field evidence is hard to unravel   Wacker, 2001;Witkind, 1998;Petrie et al., 2018). The Ketobe thrust structure is part of a lateral ramp structure that is part of a north-northeast trending thrust complex that cuts gently north, northeast and northwest dipping Jurassic strata at the northern end of the San Rafael Swell, central Utah.

Figure 3.
Outcrop view looking to the northwest at the Ketobe Knob thrust. Rocks in the hanging wall display a small anticline above the fault at the northeast side. The footwall is characterized by a small syncline (exposed in dip and strike views). The fault consists of several sub-parallel southward-dipping strands. The fault is exposed in the dip-section on the southeast and northwest sides of the precipice, and the lower tip region is exposed in the strike section along the lower left of this view.                (Gercek, 2007), Friction Angle (φ) (Smart et al., 2014), and Dilation Angle (ψ) (Smart et al., 2014), Cohesion yield stress (C) (Goodman, 1980) (C=UCS/(2*tan(45+.5* φ)).