THE GEOMETRY AND MECHANICS OF A HANGING WALL ANTICLINE, GRAND CANYON, AZ. Phil Resor, Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305 e-mail: [email protected] Abstract anticipate this will provide the foundation for a new The western Grand Canyon provides a rare and more complete mechanical investigation into the opportunity to directly observe normal faults and formation of hanging wall structures associated with associated structures over large vertical cross continental normal faults. sections with nearly complete exposure. Detailed Geophysical observations of subsurface normal mapping and mechanical modeling of these faults suggest that deformation associated with these structures can improve our understanding of faults is localized in the hanging wall while the deformation associated with normal faults and footwall block remains relatively undeformed. This thereby improve our ability to infer hydrocarbon asymmetric distribution of deformation (Fig. 1) is migration pathways and to predict the occurrence of commonly interpreted from seismic reflection hydrocarbon traps in regions of continental profiles from extending sedimentary basins (e.g. the extension. GPS measurements of deformed Gulf of Mexico (Shelton, 1984)) and inferred from sandstones within the upper Esplanade fm. are used aftershock distributions associated with major normal to evaluate both kinematic and mechanical models. fault earthquakes (Ellsworth, personal Inclined shear, a widely used kinematic model, can communication). Most explanations for the reproduce the observed hanging wall fold shape with development of these structures, associated with fault geometries that are permitted by field normal faults, are purely kinematic and include the a observations. This model, however fails to predict priori assumption that only the hanging wall deforms. the observed footwall deformation. Simple elastic Thus, the mechanics of deformation associated with dislocation models can fit both footwall and hanging normal faults, and the asymmetry of resulting wall shapes and are consistent with field structures is still poorly understood. observations that suggest nearly planar high-angle faults to depths of ~0.5 km. 3D fold geometry and field studies of secondary deformation patterns (joints and small faults) may help to further evaluate these models by constraining the relationship between slip magnitude and fold shape and strain magnitudes and orientations, respectively. Finally, more complex mechanical models need to be evaluated to understand how elastic strains may relax, leading to an apparently “elastic” fold shape preserved over geologic time.

Introduction

Knowledge of the geometry of individual normal Figure 1. Examples of hanging wall faults, normal fault systems and secondary structures deformation. a) Cross section view of aftershocks is important for assessing migration pathways and (gray circles -scaled relative to magnitude) and structural trapping of hydrocarbons in areas of crustal fault interpretation from the 1995 Kozani-Grevena extension. The development of rollover (reverse- earthquake (M 6.5), Greece. Aftershocks are drag) anticlines is particularly important for generally concentrated in the hanging wall even development of large-scale traps. It is generally thought the fault appears to be relatively straight assumed that rollover is associated with concave over the depth range of the aftershocks upward (listric) faults. This relationship is well- (unpublished figure). b) Line drawing from documented in areas of “thin-skinned” extension seismic reflection profile, Gulf of Mexico. associated with prograding deltas (e.g. Gulf of Hanging wall deformation over a listric normal fault. Observed structures include antithetic and Mexico, Niger Delta), but is still controversial in synthetic faults and a hanging wall anticline. areas of continental extension. This paper describes (After Diegel et al., 1995) our effort in progress to quantify fault and rollover geometry associated with a single well-exposed fault system exposed in the western Grand Canyon. We

Stanford Rock Fracture Project Vol. 13, 2002 PJ-1 Hamblin (1965) used faults of the western Grand Canyon region to illustrate a phenomenon that he termed “reverse drag” – the development of a monoclinal fold in the hanging wall with beds dipping into the fault plane. Hamblin proposed a simple kinematic model for “reverse drag”, suggesting that the folding occurred in response to a decrease in fault dip with depth. Scattered exposures along the Hurricane fault from St. George Utah to the Grand Canyon suggest that the fault dip may decrease with depth, however the outcrops are spaced over a large horizontal distance (~200 km) and may reflect variation in fault dip along strike rather than with depth. This paper presents preliminary results of an effort to map the fault surface and both hanging wall and footwall structures associated with the Froggy Fault exposed in Lone Mountain and Whitmore Point using modern quantitative field and remote sensing methods. This area affords the opportunity to map a fault with ~200 m of offset over a vertical section of more than 1,000 m, exposed over a horizontal length of less than 10,000 m. The resulting 3D structural database provides a means for evaluating both kinematic and mechanical models of hanging wall deformation.

Geologic Background The Colorado River cuts through the transition between the Colorado Plateau and the Basin and Range tectonic provinces in the western Grand Canyon (Fig. 2). This transition is manifested in a series of sub-parallel normal faults of moderate offset that are well exposed in the canyon walls of the Colorado River drainage system. Fault scarps in quaternary basalts and alluvium as well as recent Figure 2. Location map and aerial photo of earthquakes (e.g. the 1992 St. George, Utah field area. The study area is highlighted by the earthquake, Mw 5.6) indicate that the area is rectangle. Through going faults in the western tectonically active (e.g. Stewart et al., 1997 and canyon are associated with the transition from the references therein). Both hanging wall and foot wall relatively undeformed Colorado Plateau to the rocks of these normal faults are well-exposed, and highly extended Basin and Range province. The the canyon contains relatively simple pre-existing study area is located along the Froggy fault, one of a series of generally north striking normal structure. The study area thus presents an opportunity faults that crosses the Colorado River in the to investigate processes of continental extension in western Grand Canyon. Oblique aerial photo of both the hanging and footwall without the large the field area shows the well-developed hanging rotations and cross-cutting fault patterns typical of wall (roll-over) anticline and a synthetic fault. The much of the Basin and Range province (e.g. Proffett, footwall is relatively undeformed with a slight 1977). Huntoon and Billingsley (1981) have mapped upwarp toward the fault and minor secondary the area at a scale of 1:48,000, but no detailed studies faulting. The well-exposed bedding surface is of the fault exposures in the western Grand Canyon comprised of the upper sands of the Permian exist. The canyon exposes more than 1,000-m of Esplanade fm. Photo from Hamblin (1965). vertical section through a variety of lithologies and therefore provides an excellent opportunity to study fault geometry and secondary structures in a setting where evidence of deformation mechanisms can be directly observed.

Stanford Rock Fracture Project Vol. 13, 2002 PJ-2 slickenside orientations have been measured wherever possible. The faults are consistently steep with an average dip of 74 degrees (Fig 5). Although fault architecture varies with lithology, the overall dip of fault planes does not appear to change significantly with rock type or depth.

Figure 4. Stratigraphy of the Upper Esplande fm. a) Simplified Stratigraphic column of the Figure 3. Simplified geologic map of the upper Esplanade fm. as measured in Camp study area. The Froggy fault is the largest normal Canyon. Arrows indicate surface mapped using fault with ~200-m of down to the southwest offset. differential GPS. b) Lone Mountain anticline The Lone mountain monocline is localized in the looking west from the intervening fault block. hanging wall of the Froggy fault. Parashant and Well-exposed pavement surfaces are sandstones the Grand Canyons provide 2D cross-sections from a. c) Example of a pavement surface in the through the regional structure. Modified from upper Esplanade being mapped with GPS. Note Huntoon and Billingsley (1981). hummocky erosion on exposed surface.

Structural Mapping Modern mapping and GIS methods allow us to create 3D geologic databases to describe the geometry of map-scale geologic structures with spatial resolution (data density) of less than 10-m and precisions on the order of 1-m, thus providing important constraints for understanding the development of these structures through numerical models (e.g. Maerten et al., 2001). By integrating detailed geologic mapping, GPS surveying, and a high-resolution DEM we are in the process of creating a 3D structural model of the Froggy Fault and its associated secondary structures. Ongoing geologic field work has focused on Figure 5. Fault dip data from the Froggy fault mapping the trace and geometry of the Froggy and system. There is no apparent systematic trend in other major faults in the area, mapping the extent of fault dip with depth. well-exposed bedding surfaces in the Permian Esplanade formation (Figs. 3 and 4), and mapping In order to document the 3D structure of the the distribution of secondary joints and faults. All study area, including fault offsets and fold geometry, major faults in the study area have been walked out we have mapped bedding surfaces of the Upper and mapped onto an air photo base and slip plane and Esplanade formation. The upper Esplanade

Stanford Rock Fracture Project Vol. 13, 2002 PJ-3 formation is comprised of ~50 m of interbedded sand permitting evaluation of the models using the field and siltstone that overlies the sand-rich, cliff forming, data. lower Esplanade. Individual sand packages are 1-10 m thick, continuous over several kilometers, and encased in siltstone so that the tops of beds may be traced continuously across much of the study area and easily correlated across major faults. Thin interbedded marine Limestones and the preponderance of siltstones suggest that these sediments were deposited in an environment with relatively low topography and near-horizontal bedding surfaces. Present day erosion of sandstone pavements, however, can create topography on the exposed surfaces of approximately 2m. We are in the process of quantifying the geometry of these bedding surfaces using 3 different methods. Individual well-exposed beds have been surveyed using differential GPS. This method allows for collection of high-density data over relatively limited areas with horizontal and vertical precisions of 1m and 3m respectively. To date over 14,000 GPS points have been collected on 4 beds in the central portion of the study area (Fig 6). Surface- fitting to these data provides a 3D picture of the Lone Mt. Rollover and footwall deformation. To expand the study area and collect more uniformly-spaced data we are in the process of constructing a high-resolution (2-3 m) digital elevation model (DEM) for the area. By combining this DEM with detailed geologic mapping of Esplanade bedding surfaces in a GIS database we plan to “extract” an extensive 3D description of structures associated with the Froggy Fault (Fig 7) with sub-meter precision. Finally, traditional strike and dip measurements have been collected across the structure as a cross-check for other surveying methods. The complete 3D structural database will form the basis for evaluating models of hanging wall and footwall deformation associated with normal faulting. Preliminary results using a 2D section of GPS data are presented in the following section. Figure 6. GPS data from the study area. a) GPS points overlain on USGS digital orthoquad aerial photograph. Points are color-coded to Modeling individual bedding surfaces within the upper Preliminary modeling of the Froggy fault and Esplande fm. Major faults shown in white. Black associated deformation has been limited to evaluation box is srea of data extracted for 2D profile of 2D models using a single profile through the data. modeling. b) and c) Continuous surfaces fit to the Individual beds within the upper Esplanade have hanging wall GPS data, looking WNW. The been shifted vertically to create a single ideal Froggy fault and synthetic fault would be deformed bedding surface. The profile has been immediately to right of the figures. B. Matlab evaluated using a general kinematic model, variably GRIDDATA surface, the surface honors all data points yielding a realtivley noisy surface. C. inclined shear (White, 1992) -- and a simple Third order polynomial fit to the same data set. mechanical model, a dislocation (fault with constant Note that in both cases bed dips increase rather offset) in a homogeneous elastic half-space. These smoothly toward the fault. Along strike models lead to different fault and bed geometries as undulations are still under analysis, but may be well as different strain distributions, therefore real structural variations, or simply due to errors in correlation or small cross faults.

Stanford Rock Fracture Project Vol. 13, 2002 PJ-4 (Fig. 9) have constant bed dip along lines that trend parallel to the shear direction. The models also lead to a constant orientation of maximum elongation (dependent on the shear angle) and strain gradients that trend parallel to the chosen shear direction.

Figure 7. Schematic showing DEM mapping technique. Individual bedding plane outcrops are mapped on high-resolution color aerial photos. The bedding polygons are then used in a GIS program to extract DEM data, effectively Figure 8. Fault geometry “predicted” by surveying the bedding surface. A 3D geologic inclined shear kinematic model. Depending on description of the entire study area is then created the assumed shear angle the predicted fault by integrating data from several surfaces in the flattens at depths from 1 to 8 km. Inset shows upper Esplanade fm. predicted dips in the depth range directly observable in the field. Table shows numerical values for the same depth range. Only the 30 Kinematic Model – Inclined Shear shear model can be ruled out by current field Kinematic models of hanging wall deformation observations (Fig. 4). assume a kinematic deformation mechanism that defines a unique relationship between the fault shape Elastic Models – Half Space Dislocations and the geometry of hanging wall strata. Given the Elastic models have been shown to be useful in geometry of the strata (e.g. from a seismic reflection modeling earthquake deformation. Their use in survey) the fault shape is “predictable” from this modeling larger geologic structures that develop over relationship (or vice versa). Many different models long time periods is somewhat more controversial, have been proposed including bedding parallel slip but many studies have found a remarkable similarity (e.g. Suppe, 1983) and distributed shear models (e.g. between predicted geometries from simple elastic Verrall, 1981). The most popular models include models and geologic structures (e.g., Willemse et al., some sort of variation on the distributed shear model. 1996; Gupta and Scholz, 1998). Although it is Here we adopt the model of White (1992), as it is one unlikely that the elastic stresses associated with the of the most general, allowing for shear at any total slip on a large fault are preserved over geologic arbitrary angle. time, it appears that these stresses may play an A series of geometric constructions have been important role in the development of large-scale and made using a polynomial fit to the measured fold associated smaller-scale structures. Mechanical geometry (Fig. 8). The various reconstructions models have an inherent advantage over kinematic assume shear angles from +30 degrees - antithetic to models because they include a complete mechanical the master fault, to -10 degrees - synthetic to the description of the deformation. master fault. Shear angles outside of this range are Deformation of bedding planes associated with either not permitted by the reconstruction (<-15) or the Froggy fault has been modeled (Fig 10) using a will clearly violate the observed fault dips (>30). simple edge dislocation in an elastic half space All of the modeled faults are listric at depth with the (Savage, 1980). The edge dislocation was used shear angle controlling the rate at which the fault rather than a more realistic crack model because of flattens. Antithetic shear cases “predict” flattening of the ease with which it can be incorporated in simple the fault at relatively shallow depths (1-3 km), while inversion schemes to find best fitting fault parameters the synthetic case “predicts” flattening of the fault at including the slip and depth to which slip occurs. At ~10 km depth. The folds generated by these models

Stanford Rock Fracture Project Vol. 13, 2002 PJ-5 distances greater than ~10% of the fault half-length from the fault tip the two models are relatively indistinguishable. Fold Shape Bedding Dip Strain

Figure 9. Comparison between kinematic and elastic model predictions for columns 1). fold shape, 2) bedding dip, and 3). strain patterns (orientation of maximum extension, and contours of maximum extension values). Each row presents the results of one model. The models in the first two rows are inclined shear kinematic models with shear at 0 and 15 degrees, respectively. Inclined shear models predict constant bed dips parallel to the shear angle, a constant orientation of maximum extension, and strain gradients parallel to the angle of shear. The model in the bottom row is a dislocation model in an elastic half-space. Bedding dips and strain patterns are rather complex due to the interaction between the fault and the earth’s surface. In addition to high dips and strains near the fault there is also a region of high strain near the fold “hinge” at the earth’s surface.

The fold shape predicted by the dislocation removing one degree of regional dip a much better models is quite similar to the observed fold; in fit is obtained (Fig 10b). Finally, by including the particular the model predicts not only the hanging synthetic fault parallel to the Froggy fault in the wall, but also the footwall shape. The dislocation mechanical model an even better fit can be model yields a relatively poor fit to the raw GPS obtained, although the model under predicts the observations because there is not enough vertical high dips observed in the intervening block. separation between the footwall and the crest of the In comparison to the kinematic models the rollover anticline (Fig 10a). This appears to be fold shape and strain patterns vary both with depth caused by a regional dip associated with the and distance from the fault. The steepest dips are Hurricane fault ~5 km to the east. Both hanging close to the fault with decreasing dips away from wall and footwall strata dip gently to the east even the fault. The fold is both broader and higher in at great distances from the Froggy fault. By amplitude near the surface and flattens and narrows

Stanford Rock Fracture Project Vol. 13, 2002 PJ-6 with depth. The maximum elongation in the Evaluation Using Field Data hanging wall is parallel to the surface in the near Field observations can provide valuable data surface region, dips toward the fault close to the for evaluating the permissibility of the various fault, and dips way from the fault far from the kinematic and mechanical models. Although both fault. High strains are localized both near the fault, kinematic and elastic models can adequately fit the especially in the tip region, and in the near surface shape of deformed hanging wall strata, only the region. mechanical model also fits the observed footwall deformation. As previously mentioned, fault dip with depth can be used to limit the angles of inclined shear in kinematic models. Inclined shear at 30, antithetic to the main fault, is one of the most commonly used kinematic models for normal fault deformation because the orientation of the shear planes is consistent with the predictions of Mohr-Coulomb faulting and Andersonian stress (failure on planes dipping 60). For our data, however, this model predicts fault dips of less than 65 degrees at the base of Parashant Canyon (-427 m), significantly lower than the 75-80 degree fault dips observed in the area. Inclined shear from ~15 to -15 is permissible based on the limited fault dip data set. Planar faults modeled in the elastic dislocation models are consistent with the current field observations that show no apparent decrease in fault dip with depth. Additional observations of fault dip throughout the study area, and especially in the Grand Canyon (-756 m) may help evaluate the remaining models. Indicators of strain orientation and magnitude can also be used to evaluate the models. Small- scale structures such as joints and small faults may help to accommodate the development of roll-over anticlines and the orientation, density and, offset (for faults) associated with these structures can provide insight into strain patterns and magnitudes. These data will be collected during a field session in autumn 2002. Finally, the 3D geometry of the fold shape, and changes in fold shape associated with varying offset may provide valuable additional data to help model the mechanics of rollover development. These data will be available once the full 3D structural model has been constructed and will be augmented with profiles from larger faults in the area.

Conclusions

Both kinematic and mechanical models can fit Figure 10. Dislocation models fit to a 2D the shape of deformed strata in the hanging wall profile through the GPS data. A. Single along a 2D profile through the Froggy fault while dislocation fit to raw GPS data. B. Single honoring the available fault dip data. The dislocation fit to data with one degree regional mechanical model, however, also predicts the dip removed. C. Two dislocation model fit to observed footwall deformation and includes a data with regional dip removed. complete mechanical description of the deformation. Further observations of the 3D structure and strain patterns may provide additional

Stanford Rock Fracture Project Vol. 13, 2002 PJ-7 data for evaluating the kinematic and mechanical Journal of Geophysical Research, B, Solid Earth models. and Planets, v. 103, no. 1, p. 823-834. We have chosen to model the observed Hamblin, W. K., 1965, Origin of 'reverse drag' on the structures using simple elastic models to determine downthrown side of normal faults: Geological how well these models can explain the data, and Society of America Bulletin, v. 76, no. 10, p. 1145- 1164. where more complicated models may be necessary. Huntoon, P. W., and Billingsley, G. H., Jr., 1981, Misfits between the simple dislocation model and Geologic map of the Hurricane fault zone and field observations may justify using more complex vicinity, western Grand Canyon, Arizona: Grand mechanical models. The current models involve Canyon Nat. Hist. Assoc., scale Scale 1:48,000. rather high amounts of slip over relatively short King, G. C. P., Stein, R. S., and Rundle, J. B., 1988, The fault intervals, leading to high strain gradients. Growth of Geological Structures by Repeated This consistent pattern may be indicative of a more Earthquakes .1. Conceptual-Framework: Journal of complex mechanical process involved in the fold Geophysical Research-Solid Earth and Planets, v. development. King and Stein (1988) proposed a 93, no. B11, p. 13307-13318. Maerten, L., Pollard, D. D., and Maerten, F., 2001, model for the development of dip-slip structures Digital mapping of three-dimensional structures of that incorporated an elastic plate with both the Chimney Rock fault system, central Utah: overlying and underlying viscoelastic layers. They Journal of Structural Geology, v. 23, no. 4, p. 585- reported that reasonable fits to 2D profiles through 592. large-scale geologic structures required relatively Proffett, J. M., Jr., 1977, Cenozoic geology of the thin or weak elastic layers. The relatively short Yerington District, Nevada, and implications for the wave length of the Lone Mt. structure suggests that nature and origin of Basin and Range faulting: the mechanical explanation is in the near surface, Geological Society of America Bulletin, v. 88, no. rather than at depth as predicted by the King and 2, p. 247-266. Savage, J. C., 1980, Dislocations in Seismology, in Stein model. More realistic models could also Nabarro, F. R. N., ed., Dislocations in Solids, North include the effect of unroofing during deformation. Holland Publishing Company. Recent work has shown that the Hurricane fault Shelton, J. W., 1984, Listric normal faults; an illustrated may have formed and accrued its entire offset over summary: AAPG Bulletin, v. 68, no. 7, p. 801-815. the last 3-5 Million year (Fenton, et al., 2001). Stewart, M. E., Taylor, W. J., Pearthree, P. A., Solomon, During this time the Grand Canyon may have B. J., and Hurlow, H. A., 1997, Neotectonics, fault downcut through Mesozoic and Paleozoic strata, segmentation, and seismic hazards along the leading to the present-day levels of exposure. Hurricane Fault in Utah and Arizona; an overview of environmental factors in an actively extending region [Monograph] Mesozoic to Recent geology of Acknowledgements Utah: Geology Studies, v. 42, Part 2, p. 235-254. Funding for this research has been provided by Suppe, J., 1983, Geometry and Kinematics of Fault- the Stanford McGee Award, Geological Society of Bend Folding: American Journal of Science, v. 283, America Research Grant, American Association of no. 7, p. 684-721. Petroleum Geologists Grant-in-Aid, and the Verrall, 1981, Structural interpretation with application Stanford Rock Fracture Project. The Stanford to North Sea problems, Course Notes, Joint ARCO Graduate Fellowship has funded my studies Association for Petroleum Exploration Courses at Stanford. (UK). White, N., 1992, A Method for Automatically Determining Normal-Fault Geometry at Depth: References Journal of Geophysical Research-Solid Earth, v. 97, Diegel, F. A., Karlo, J. F., Schuster, D. C., Shoup, R. C., no. B2, p. 1715-1733. Tauvers, P. R., Roberts, D. G., and Snelson, S., Willemse, E. J. M., Pollard, D. D., Aydin, A., Knipe, R. 1995, Cenozoic structural evolution and tectono- J. e., Main, I. G. e., and Wojtal, S. F., 1996, Three- stratigraphic framework of the northern Gulf Coast dimensional analyses of slip distributions on normal continental margin, in Jackson, M. P. A., Roberts, fault arrays with consequences for fault scaling: D. G., and Snelson, S., ed., Salt tectonics: a global Special issue; Scaling laws for fault and fracture prespective: AAPG Memoir: Tulsa, OK, American populations; analyses and applications, v. 18, no. 2- Association of Petroleum Geologists, p. 109-151. 3, p. 295-309. Fenton, C. R., Webb, R. H., Pearthree, P. A., Cerling, T. E., and Poreda, R. J., 2001, Displacement rates on the Toroweap and Hurricane faults: Implications for Quaternary downcutting in the Grand Canyon ; Arizona: Geology, v. 29, no. 11, p. 1035-1038. Gupta, A., and Scholz, C. H., 1998, Utility of elastic models in predicting fault displacement fields:

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