1. Beasley, C., Surpless, B.E., and Wigginton, S., 2013, 2D Computer Kinematic Forward Modeling of the Stillwell Anticline Fold System: Testing Models of Fold Evolution: Geological Society of America, Abstracts with Programs, Denver, CO. 2. Cardoza, N., 2005, Trishear modeling of fold bedding data along a topographic profile: Journal Structural Geology, v. 27, p. 495-502. 3. Cobb, R., and Poth, S., 1980, Superposed deformation in the Santiago and northern Del Carmen Mountains, Trans-Pecos Texas: In Trans-Pecos Region (West Texas): New Mexico Geological Society Fall Field Conference Guide book 31, p. 71 – 75.4. Davis, G.H., Reynold, S.J., and Kluth, C.F., 2012, Structural Geology of Rocks and Regions. Ed. 3, p. 414-428.5. Ewing, T.E., 1991, The Tectonic Framework of Texas: University of Texas at Austin, Bureau of Economic Geology, p1-36.6. Hardy, S., and Ford, M., 1997, Numerical modeling of trishear fault-propaga�on folding and associated growth strata: Tectonics, v.16, p. 841-854. 7. Lehman, T.M., and Busbey, A.B., 2007, Society of Vertebrate Paleontology Fall 2007 Big Bend Field Trip Guide: Austin, Texas, Society of Vertebrate Paleontology, 117 p.8. Maler, M.O., 1990, Dead Horse Graben: A West Texas Accommodation Zone: Tectonics v.6, p. 1357–1368.9. Maxwell, R., Lonsdale, J., Hazzard, R., and Wilson, J., 1967, Geology of Big Bend National Park, Brewster County, Texas: Texas Bureau of Economic Geology, Pub. 6711, 320 p., geologic map scale 1:62,500.10. Miller, D., Nilsen, T., and Bilodeau, W., 1992, Late Cretaceous to early Eocene geologic evolution of the U.S. Cordillera: In Burchfiel, B., Lipman, P., and Zoback, M. eds., The Cordilleran Orogen: conterminous U.S., Geological Society of America, v. G-3, p. 205 – 260.11. Muehlberger, W.R., 1980, Texas Lineament Revisited: New Mexico Geological Society Guidebook, 31st Field Conference, Trans-Pecos Region, p. 113-121.12. Muehlberger, W.R., and Dickerson, P.W., 1989, A tectonic history of Trans-Pecos, Texas, in Muehlberger, W.R., and Dickerson, P.W., eds., Structure and stratigraphy of Trans-Pecos Texas: American Geophysical Union Field Trip Guidebook T315, p. 35 – 54.13. Page, W., Turner, K., and Bohannon, R., 2008, Geological, Geochemical, and Geophysical Studies by the U.S. Geological Survey in Big Bend National Park, Texas, In Gray, J., and Page, W., Eds., U.S. Geological Survey Circular 1327, 93 p.14. Poole, F.G., J.W. Perry, R.J. Madrid, and R. Amaya-Martinez, 2005, Tectonic Synthesis of the Ouachita Marathon-Sonora Orogenic Margin of Southern Laurentia—Stratigraphic and Structural Implications for Timing of Deformational Events and Plate Tectonic Model, in Anderson, T.H., Nourse, J., McKee, J.W., and Steiner, M.B., eds., The Mojave-Sonora Megashear Hypothesis—Development, Assessment, and Alternatives: Geological Society of America Special Paper 393, p. 543–596.15. St. John, B.E., 1965, Structural geology of Black Gap area, Brewster County, Texas: Ph.D. Thesis, University of Texas at Austin, Austin, Texas, 200 p.16. Suppe, J., and Medwedeff, D., 1990, Geometry and kinematics of fault-propagation folding: Eclogae Geology, v. 83(3), p. 409-454.17. Surpless, B.E., and Quiroz, K., 2010, Complex folding in the Stillwell anticline region, west Texas: American Geophysical Union, Abstracts with Programs, San Francisco, CA.

3D Move is a computer software package that uses geometrical algorithms to provide efficient and viable proxies for deformation that follow traditional modeling approaches. This approach, based on decades of research and grounded upon the physical laws of rock deformation, permits us to test and improve our structural models. With these 2D and 3D models, we can construct valid subsurface interpretations of initial fault geometries that have led to the structural geometries that we observe on the surface today. We performed our research by building a 3D model of the system through the integration of existing 2D geologic cross sections, construction of additional cross sections, interpretation of field data, and input of existing ArcGIS raster images and dip data. After completeing the construction of the 3D model, we built a new cross section representative of the fault-propagation folding clearly exhibited in many field sites. We then incorporated our interpreted subsurface fault geometries into the the new cross section and utilized 3D Move’s Unfolding and Move On Fault modules. Together, these modules gave us the ability to restore the area to predeformation geometries and test hypotheses of fold formation.

Fault-Propagation Fold TheoryA fault-propagation fold forms in front of the tip of a thrust fault, along with short forelimb (B-B’) and backlimb (A-A’) kink bands (Step I). As the fault tip propagates upward, the hanging wall advances toward the foreland. This movement expands both the forelimb and backlimb at constant angles, and reduces the length of the midlimb while propagating upward (Step II). The length and the angle of the backlimb is controlled by the location of the fault tip, and as propagation continues, band A is pinned to the footwall, band B’ is transported along the foreland, and the convergence of interior bands A’ and B move the hangingwall16 (Step III). Both A-A’ and B-B’ achieve their maximum length prior to the tip of the fault breaching the uppermost strata4.

The cross section displayed in Figure 4 is an example of the distinctive fault-propagation fold geometries that we have documented along the fold system (sub-surface fault not interpreted).

Fold GeometryThe Stillwell anticline is a 500 m wide, 8 km long, well-exposed basement cored fold system in the Big Bend region containing three NW-trending, NE-vergent, left-stepping en echelon segments12. The three segments likely grew to the NW or SE, toward each other, and eventually linked. Although no Laramide-age faults are exposed in the area, many locations display fold geometries accordant with our hypothesis of fault- propagation folding. At these locations, the geology is characterized by narrow, steeply-dipping forelimbs, sub-horizontal midlimbs, and gently-dipping backlimbs.

Stratigraphy Fluctuations in sea level within the study area led to the deposition of predominantly calcareous units. The units have significant variability in strength, which can have a fundamental effect on fault propagation and geometry, fold geometry, and the formation and propagation of fractures17. The topographic expression is best defined by the thick, relatively strong Santa Elena limestone underlain by the weaker Sue Peaks Formation and overlain by the very weak Del Rio claystone. The young and weak Boquillas Formation, Buda Limestone, and Del Rio claystone have been eroded except in the anticline’s central transition zone9,15,17 (see Section IV).

period of marine deposition, the subsidence ended in the late Cretaceous7,13. The Laramide Orogeny (ca. 80–55 Ma) is associated with the shallow subduction of the Pacific plate beneath western North America. This event initiated contractional deformation along the western and southern borders of Texas5. Structures in the area related to this event include high-angle reverse faults, strike slip faults, monoclines, anticlines, and few synclines4 (Fig. 2). The Stillwell anticline (SA in Figure 2), to the northwest of the Sierra del Carmen (SDC), is an asymmetric, NW-trending fold system.

The first significant rifting event took place in the middle Proterozoic, causing high angle NW-trending strike slip faults and establishing a zone of crustal weakness6,9,11. The set of faults was then reactivated by the Ouachita orogeny (ca. 330–285 Ma) and produced a set of high angle NW striking reverse faults11,13,14. The region experienced rifting again between 200 and 85 Ma when the Gulf of Mexico opened and the sea transgressed to cover the area11,12,13. After a long

The Laramide-age Stillwell anticline is located in the Big Bend region of west Texas, within the Texas lineament (Fig. 1). The Texas lineament is an 80 km wide, NW-trending zone of crustal weakness and deformation that extends from the Big Bend region to Arizona8. This area is still active, with fault and fold patterns related to repetitive cycles of collision and rifting throughout history13.

1) Can we accurately represent the Stillwell system with 3D modeling software?2) Are previous fold-formation hypotheses viable based on 3D computer modeling of the fold system?3) Are the results obtained from 3D modeling consistent with previous 2D computer model results?4) Can 3D modeling be used to develop new hypotheses of fold formation?

We performed 3D kinematic and mechanical modeling to best constrain the formation of the Stillwell anticline, located in west Texas. The area is characterized by bedded Cretaceous carbonate rocks, with the present-day surface approximately 600 m above the Paleozoic basement. At most locations, the anticline exhibits geometries characteristic of fault-propagation folding, including a gently dipping backlimb, a well-defined midlimb, and a steeply dipping forelimb. However, the 8-12° dip of the midlimb, along with the 50-100 m hinterland-foreland vertical offset present at a number of locations, are not consistent with a simple fault-propagation fold model. In addition, the linear and localized deformation associated with this en echelon fold suggests that folding may be related to reactivation of basement faults. Subsurface fault geometry is fundamental to the shape and amplitude of fault-propagation folds but is difficult to constrain without any exposure of the faults involved. Structural cross-section construction, 3D model building, and forward and reverse kinematic modeling can help us better constrain the coupled fault-fold system. We utilized 3D Move, by Midland Valley, to build a working 3D model of the anticline in order to test a 2-stage fold formation hypothesis that we developed based on field data and previous kinematic modeling.

Upper Kb Contact

Kb-Kbu Boundary

Kbu-Kdr Boundary

Kdr-Kse Boundary

Kse-Ksp Boundary

Ksp-Kdc Boundary

Legend

Figure 5. Sequential three step model (left to right) of fault-propagation fold evolution. Modified from 14Figure 5 Sequential three step model (left to right) of fault-propagation fold evolution Modified from 14

Hinterland HinterlandForeland Foreland Foreland

I II IIIBB

B

B’ B’ B’

A’

A’A’

AA A

Hinterland

Figure 4. Field photograph reveals an example of the similarity of many fold geometries in the system to the classic fault-propagation fold model (Fig. 5). Modified from 1

No V.E.

Photo reflected to match cross section

SW NE

50 m50 m

800

700

900

Kse

Kdr

Kbu

600Ksp

Topographic Profile

Figure 3. Stratigraphy of the Stillwell anticline area. Modified from 3, 9,15

PEN FORMATION

BOQUILLAS FORMATION [Kb]

BUDA LIMESTONE [Kbu]

SANTA ELENA LIMESTONE [Kse]

DEL RIO CLAYSTONE [Kdr]

SUE PEAKS FORMATION [Ksp]

DEL CARMEN LIMESTONE [Kdc]

DIABASE SILL

BLACK GAPBASALT FLOWS

ALLUVIALGRAVELS

Met

ers

100

200

300

400

500

600

GU

LFIA

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OM

AN

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Quaternary alluvium, colluvium, landslide deposits

TELEPHONE CANYON FM. [Ktc]MAXON SANDSTONE [Kms]

GLEN ROSE LIMESTONE [Kgr]

UNDIFFERENTIATED PALEOZOIC ROCKS

700

800

900

Figure 2. Shaded relief map with major Laramide-age faults and folds of the Big Bend region (in red), the Stillwell anticline (SA), and the outline of Big Bend National Park (BBNP, in blue). Also shown is Sierra Del Carmen (SDC) and Santiago Mountains (SM) in yellow. Modified from 10,12,17

BBNP

Mexico

USA

SA

SM

SDC

fold:

fault ormonocline:

anticline:

KEY:0 25km

Figure 1. Distribution and deformation associated with the Laramide orogeny, with the Texas lineament (TL) shown for reference. Modified from 17

TX

Mexico

PacificOcean

N

500km

Laramid

eO

rog

eny

TLTL

Fig. 1

References

This research was funded by NSF RUI # 1220235. Thanks to the Black Gap Wildlife Management Area for their hospitality and logistical support of our field research. We would also like to thank the Midland Valley IT Team for their support with 3D Move. Finally, we would like to thank the Trinity University Department of Geosciences for their continued logistical and financial support.

Acknowledgements

XI. Conclusions

V. 3D Structural ModelingIV. Geologic Map

III. The Stillwell Anticline

II. Geologic Background

Research Questions

I. Introduction

3D computer modeling of the Stillwell anticline fold system, west Texas: testing models of fold formationRebecca Schauer (rschauer@trinity.edu), Benjamin Surpless, Mark Mlella, and Nicola Hill; Trinity University, Department of Geosciences, San Antonio, Texas 78212

109

8I

II

III

7

65

43

211. We began modeling the area by importing an existing, georeferenced geologic map of the Stillwell anticline modified from 15 and imported a geo- referenced digital elevation model (DEM). We then overlaid the geologic map on the DEM.

2. We traced the geologic contacts from the imported geologic map image using the “Horizon” function in order to model our field-defined stratigraphy. The bound- aries between units were assigned a color and defined using the “Stratigraphy” function.

3. To ensure the precision of the contacts and our lines, we imported existing satellite images from ArcMap. We adjusted lines to more accurately represent geolog- ic contacts. This step was performed in 2D.

4. Using our existing cross sections, we drew section lines for the cross sections using the “Trace” function. Then, we inserted vertical images of each area into the section, gathered surface intersect- ions, and adjusted image positions to match topography.

5. We used the “Horizon” function and previously defined stratigraphy to trace boundary lines on each cross section (6-6’ shown, right). We assumed that the areas beyond the zone of deformation are subhorizontal (consistent with field data) and the area has uniform unit thicknesses (consistent with previous studies of the region).

6. We determined other areas where cross sections were needed to effec-tively build the model, and drew sec-tion lines using the “Trace” function. We added 7 more cross sections, bringing the total to 13.

7. To accurately construct these 7 new cross sections, we used existing field-based strike and dip data from ArcMap and from field notes and images using the “Dip” function.

8. We created cross sections by gathering surface and line intersections and projecting dip data to the section (I), drawing a template line (II), and projecting remaining boundary lines using the “Horizons from Template” function (III). We made the same assumptions as listed in 5.

9. We repeated the steps in 8 for the remaining section lines. For ease in creating the surface, we extended all boundary lines to the edges of the geologic map overlaid in 1.

10. We gathered all similar boundary lines into the “Surface” function. Within the function, we chose “Spline Curves” as the Method and set the Sample Density to 100.

VI. Workflow

With the use of 3D Move, we successfully constructed a valid, testable 3D model of the Stillwell anticline system. The success of this modeling confirms that our existing cross sections are structurally viable, our interpretations of what we see in the field area are valid, and our data taken from the field area are accurate. However, the boundary lines that we traced on the geologic map in Step 2 of the Workflow had to be modified once superimposed on the satellite images (Step 3 in Section IV). Our modeling results suggest:

1) The deformational shape of our surfaces is consistent with what is expected with a fault-propagation fold, so it is likely that thrust faults with ramp-flat geometries (Section III) are in part responsible for the deformation in the anticline.

2) A simple fault-propagation fold does not account for the three left-stepping segments or the hinterland-foreland vertical offsets documented throughout the fold system. We agree with Beasley et al. (2013) in their interpretation of pre-existing basement-cored, high-angle reverse faults that acted as nucleation points in subsequent flat-ramp fault propagation. 3) There are two areas of folding at high angles to the anticline fold axis. The first syncline occurs where the South segment dies out and the Central segment begins, and the second occurs where the Central segment dies out and the North segment begins. We expected this folding in the southern area based on field data, but we did not document the syncline in the northern area in the field, due to significant erosion of units overlying unit Kse. However, we were not surprised by the location of these previously unidentified fold, which is consistent with overlapping fold (and therefore fault) segments in an en echelon anticline system.

VII. Implications of the 3D Model

VIII. Two - Stage Fold Evolution

X. Reverse Trishear Kinematic Modeling With a successful, working 3D model of the Stillwell anticline, we moved to the second stage of testing. We first built a new cross section that incorporates our interpreted subsurface fault geometries. We tested this fault geometry using 3D Move’s Move On Fault module, which uses rules governed by trishear kinematics. With this tool, we were able to test both the location and geometry of our fault system, which we should be able to apply to the formation of the Stillwell anticline system. A successful reverse model should bring the entire area back to predeformation geometry.

In our proposed model, the fault propagated horizontally in the weak Sue Peaks Formation (Ksp) and ramped upward across beds in the Santa Elena limestone (Kse), creating the anticline geometries that we documented in the field. To test fault-fold models, we varied one parameter at a time, holding all other parameters constant, in order to observe how each parameter affected the cross section. We tested a wide range of parameters including propagation to slip ratio, trishear angle, displacement, and trishear angle offset. After testing all of the parameters, we discovered that the optimal values are: Propagation to slip ratio: 1.00 Trishear angle: 35.00° Displacement: -400 meters Trishear angle offset: 0.55

80 m

A’A

Backlimb Midlimb (8 - 12° dip)

Forelimb

Footwall

Hanging wallFault tip

2γ

θ = 0

θ = γ

u 1= s

v 1 = 0

un = 0

vn = 0

u 2 = s2

cos(θ)

v 2 = -s2

sin(θ)

f

e line

Fault-propagation folding explains most of the geometries observed along the Stillwell anticline. However, some locations contain geometries that require further explanation. For example, in the northern-most and southern-most segments of the anticline are characterized by a dip of 8-12° toward the foreland (Fig. 7) and a 50-100 meter hinterland -foreland vertical offset (see Fig. 6B), features that are consistent with high angle reverse faults17 . In earlier studies, it was determined that this high angle reverse fault and flat-ramp system were not synchronous or connected in the subsurface17. Previous reconstructions suggest that a high angle en echelon reverse fault system preceded the flat-ramp system. It is likely that a monocline was formed from the deeper, high angle fault which then created a nucleation point for the ramp.

Figure 6. We repeated the process in Workflow 10 to create the remaining surfaces. Note that each surface represents a boundary between two rock units. These two images are different views of the same completed model. In A., note the 2 synclines at high angles to the anticline axis. In B., note the hinterland-foreland vertical offset.

IX. Trishear Kinematics The trishear kinematic model allows for the incremental development of folds in a triangular zone of distributed shear that expands ahead of a propagating fault tip2,6. The model accounts for variations in stress and the resulting strain during deformation, with this, complex fold and fault geometries can be recreated. Figure 8 is a simplified velocity description of the trishear model. In the shear zone (yellow in Fig. 8), fault-parallel velocity is assumed to be s at the top of the zone and 0 (zero) at the bottom of this zone, along a fault-normal tie line6. To conserve area, there is a component of velocity toward the

footwall (green in Fig. 8) of the shear zone. v1 is the vertical velocity of the hanging wall and u1 is the horizontal velocity (pink in Fig. 8). v2 and u2 are the velocities based on position within the trishear zone and can be calculated: v2 = s2sin(θ) and u1 = s2cos(θ), where s2 is the calculated velocity of a given position in the trishear zone and θ is the direction of the net velocity vector at any point within the trishear zone. Therefore, a trishear model allows for the derivation of the complete velocity field within the trishear zone6.

Figure 8. Diagram showing the trishear fault propagation model. Velocity vectors within the hanging wall and shear zone and sectors of equal velocity are illustrated schematically. The symmetric shear zone has an apical angle of 2θ. Modified from 6.

4

2

3

5

1

Surface-Kb Boundary

Kb-Kbu Boundary

Kbu-Kdr Boundary

Kdr-Kse Boundary

Kse-Ksp Boundary

Ksp-Kdc Boundary

Legend

Figure 9. Reverse trishear kinematic modeling of the Stillwell anticline. (1) Our interpreted cross section. This image shows the position of the fault tip and the trishear zone, prior to any reverse modeling. (2) The model after 100 meters of displacement have been removed. (3) The model after 200 meters of displacement have been removed (4) The model after 300 meters of displacement have been removed. (5) The model restored to predeformation geometries, after 400 meters of displacement have been removed.

Figure 7. Cross-sectional exposure in the northern segment of the Stillwell anticline. Modified from 1

Field observations, cross section construction, model building, and reverse trishear modeling of the Stillwell anticline suggest that:

transitions between left-stepping fold segments (between north and central and between central and south) support lower amplitude folding where the segments overlap, resulting in synclines at a high angle to the anticline axis

a single-stage flat-ramp fault propagation fold model can explain most, but not all, features of the Stillwell anticline system

a pre-existing high-angle basement fault system remains the best explanation for the localization of deformation, the vertical offset between hinterland and foreland, and the left-stepping en echelon nature of the Stillwell anticline

These results, when combined with previous research, support an asynchronous, two-stage model of fold formation of the Stillwell anticline system. In this model, a reactivated, high-angle reverse fault created a monocline, which offset the hinterland and foreland. Subsurface geometries created by this en echelon fault system likely became the nucleation position for the ramping upward of later the flat-ramp fault propagation that we modeled. This work improves our understanding of the origin and evolution of Laramide-age deformation in the Big Bend area; these results imply that pre-existing structures play an important role in accommodating and localizing strain.

Trinity University

A

B

syncline

syncline

hinterland

foreland

verticaloffset

Note that the vertical offset between the hinterland (left) and foreland (right) is not affected by reverse modeling of a flat-ramp fault system, supporting previous hypotheses of fold formation.

Present-day fault geometry.

Retro-deformed cross-section (400 m of slip removed)

Retro-deformed cross-section (300 m of slip removed)

Retro-deformed cross-section (200 m of slip removed)

Retro-deformed cross-section (100 m of slip removed)