Fault displacement-distance AUTHORS Amanda N. Hughes Department of Earth relationships as indicators of and Planetary Sciences, Harvard University, 20 Oxford Street, Cambridge, Massachusetts contractional fault-related 02138; [email protected] Amanda N. Hughes is a structural geologist for folding style the Chevron Energy Technology Company in Houston, Texas. She received a Ph.D. in earth Amanda N. Hughes and John H. Shaw and planetary sciences from Harvard University (2012) and a B.S. degree in geology from Washington and Lee University (2006). Her research combines geological observations, ABSTRACT seismic reflection interpretation, and kinematic and mechanical modeling approaches in un- We present a method of using fault displacement-distance derstanding structural growth in the context of profiles to distinguish fault-bend, shear fault-bend, and fault- petroleum systems and seismic hazards studies. propagation folds, and use these insights to guide balanced John H. Shaw Department of Earth and and retrodeformable interpretations of these structures. We Planetary Sciences, Harvard University, 20 Ox- first describe the displacement profiles associated with different ford Street, Cambridge, Massachusetts 02138; end-member fault-related folding models, then provide exam- [email protected] ples of structures that are consistent with these model-based John H. Shaw is the Harry C. Dudley Professor of predictions. Natural examples are imaged in high-resolution Structural and Economic Geology and chair of two- and three dimensional seismic reflection data sets from the the Department of Earth and Planetary Sciences Niger Delta, Sichuan Basin, Sierras Pampeanas, and Cascadia at Harvard University. Shaw received his Ph.D. to record variations in displacement with distance updip along from Princeton University (advisor: John Suppe), and subsequently worked for Texaco’s Explora- faults (termed displacement-distance profiles). Fault-bend folds tion and Production Technology Department in exhibitconstantdisplacementalongfaultsegmentsandchanges Houston, Texas. Shaw’s research focuses on the in displacement associated with bends in faults, shear fault- nature of faulting and fault-related folding in the bend folds demonstrate an increase in displacement through crust, with applications to petroleum trap and the shearing interval, and fault-propagation folds exhibit de- reservoir characterization and regional earth- creasing displacement toward the fault tip. More complex quake hazards assessment. Shaw leads an AAPG field course in the Canadian Rockies, and offers structures are then investigated using this method, demonstrat- a short course on seismic interpretation ing that displacement-distance profiles can be used to provide methods based on an AAPG Seismic Atlas insight into structures that involve multiple fault-related fold- (AAPG Studies in Geology 53, coedited by ing processes or have changed kinematic behavior over time. C. Connors and J. Suppe). These interpretations are supported by comparison with the kinematics inferred from the geometry of growth strata overly- ACKNOWLEDGEMENTS ing these structures. Collectively, these analyses illustrate that the displacement-distance approach can provide valuable in- We thank CGGVeritas for their provision of data and support of the project, which was instru- sights into the styles of fault-related folding. mental. We also thank ExxonMobil and Chev- ron, which supported this research. We are grateful for the insightful comments and sugges- tions of our reviewers, M. Scott Wilkerson and Brent A. Couzens-Schultz, and editors Stephen E. Laubach and Rick Groshong. We are also in- Copyright ©2014. The American Association of Petroleum Geologists. All rights reserved. debted to Landmark Graphics Corporation, which Manuscript received January 9, 2012; provisional acceptance March 13, 2012; revised manuscript received provided software that was critical to this re- June 15, 2012; final acceptance May 31, 2013. search through their Strategic University Alliance DOI:10.1306/05311312006

AAPG Bulletin, v. 98, no. 2 (February 2014), pp. 227–251 227 Grant Program (Agreement 2007-CONT-005191). INTRODUCTION The AAPG Editor thanks Senior Associate Editor Richard H. Groshong and the following reviewers The ability to classify the structural style of a fault-related fold for their work on this paper: Brent A. Couzens- Schultz and M. Scott Wilkerson. is essential to many different applications. Understanding the kinematic history of fault-related folds can provide important constraints on the geometry and evolution of traps in petro- DATASHARE 51 leum geology. Similarly, various fault-related fold models make Uninterpreted seismic data are available in an different predictions about rock strains that may affect reser- electronic version on the AAPG Web site (www voir properties. Moreover, properly characterizing fault-related .aapg.org/datashare) as Datashare 51. folds can also be an important aspect of seismic hazard assess- ment. Various fault-related folding models predict character- istic relationships between uplift and displacement on the underlying fault, so the ability to identify the structural style of active fault-related folds is essential to properly defining the slip on an active fault based on an observed pattern of uplift. This is especially important in cases where faults do not reach the surface and only fold patterns are observable at the surface. Over the past two decades, kinematic models for several different types of contractional fault-related folds have been developed and successfully applied to describe a variety of natural structures (e.g., Suppe, 1983; Suppe and Medwedeff, 1990; Erslev, 1991; Allmendinger, 1998; Suppe, et al., 2004; Shaw et al., 2005). With this proliferation of fault-related fold models, it is sometimes challenging to properly identify which class of models most appropriately applies to a given structure. Additionally, many natural structures are sufficiently complex, or have exhibited different fault-related folding mechanisms over their history, that they are not well explained by a single model. Thus, it is desirable to have an independent means of discerning the style of fault-related folding present in the structure. One way of achieving this is by observing displace- ment as a function of distance along the fault (termed the displacement-distance profile) because each of the major types of contractional fault-related fold models—fault bend, shear fault bend, and fault propagation—has a distinctive pattern in its displacement-distance relationship (Figure 1). This study will first illustrate the displacement-distance profiles expected for end-member fault-related folding mod- els. These predictions will then be compared with a series of structures imaged with seismic reflection data to illustrate that the predicted displacement profile for each of these models is consistent with patterns of displacement observed in nat- ural structures. By establishing that the displacement profiles characteristic of each folding model are unique and appli- cable to natural examples, we are then able to interpret the displacement-distance profile for a complex, multistage natural structure. We restore parts of its deformation history that are

228 Displacement Variations and Folding Styles Figure 1. Illustration of how to construct a displacement-distance profile. (A) Example structure. Distance is measured from the inter- section of the lowest offset rock layer in the footwall and the fault (P) along the fault toward the tip (d), and displacement is measured (a, b, and c) for each layer. (B) The resulting displacement-distance plot, where distance along the fault from P to d is plotted along the x-axis, and the displacement of each layer that intersects the fault at that distance determines the y value of each point. consistent with the different fault-related-folding bends. Other researchers have sought to charac- mechanisms indicated by the observed displace- terize displacement profiles for natural structures. ment profile. Analysis of the geometry of overlying McConnell et al. (1997) made observations of growth strata further supports these interpreta- displacement-distance profiles in field outcrops tions, suggesting that analyzing displacement pro- in the Appalachians, whereas Briggs et al. (2006) files may be used as an important independent measured variations in displacement on structures means of identifying which fault-related-folding in the Niger Delta. Additionally, a significant body mechanisms may have been active throughout the of previous work on along-strike variations in dis- deformation history of a given structure. placement on thrust faults (for example, Wilkerson, 1992; Wilkerson et al., 2002; Bergen and Shaw, 2010) has provided insight into the lateral propa- PREVIOUS WORK ON gation, linkage, and termination of thrust faults. DISPLACEMENT-DISTANCE PROFILES The goal of our study is to develop a com- prehensive understanding of the patterns of dis- A displacement-distance profile is generated by placement along faults in the various classes of measuring the offset between the footwall and fault-relatedfolds,inamannerthatcaninformin- hanging-wall cutoffs in a cross section for several terpretations of natural structures. We will extend rock units in a fault-related fold (the displacement), the analysis of displacements of end-member fault- and plotting it as a function of distance along the propagation folds from previous studies (Hedlund, fault surface from some defined point along the 1997) to a broader range of structural styles and fault (Figure 1). Previous quantitative work on then compare these profiles to those of natural displacement profiles has primarily focused on structures in a variety of geologic settings. normal faults (e.g., Muraoka and Kamata, 1983; Kattenhorn and Pollard, 2001), although variation in displacement in contractional structures has DATA SETS also been measured in various studies. Williams and Chapman (1983) established the basic con- Structuresthatareusedasexamplesinthisarti- cept of a displacement-distance profile for a thrust cle come from a variety of geographic locations fault, which was extended by Hedlund (1997) to and contractional tectonic environments. The examining existing fault-propagation-folding mod- faults studied were mapped in two- and three- els. Rowan and Ratliff (1988) noted that displace- dimensional (2-D and 3-D) seismic reflection data ment along thrust and reverse faults varies as a sets from the Niger Delta, offshore Nigeria in the function of structural style and the presence of fault Gulf of Guinea (2-D and 3-D), the Sichuan Basin,

Hughes and Shaw 229 south-central China (2-D), the Cascadian accre- development of shear in many of the structures, tionary prism off the western shore of Vancouver which is manifest in the geometries of the struc- Island, Canada (2-D), and the Sierras Pampeanas, tures that develop (Suppe et al., 2004; Corredor in the foreland of the Andean mountains in north- et al., 2005b). ern Argentina (2-D). Structures analyzed in this Structures within the accretionary prism of study were chosen based on the following char- the subduction zone in Cascadia, off the western acteristics: outstanding seismic imaging of the sed- coast of Canada, were also analyzed in this study. imentary layers, minimal ambiguity regarding fault These data were acquired as part of a 2-D seismic geometry, and readily correlated stratigraphy on reflection campaign on the part of the accretionary either side of the fault. The lattermost condition was prism offshore Vancouver Island in Ocean Drilling ensured by either correlating stratigraphy across a Program (ODP) Leg 146 (Davis and Hyndman 2-D seismic grid survey or 3-D seismic survey, 1989; Hyndman et al., 1990, 1994). Subduction of where available. In cases where this was not possi- the Juan de Fuca oceanic plate (which is the remnant ble, examples were chosen in which the stratigra- of the much more extensive Farallon plate) under phy has a sufficiently distinctive seismic character continental North America at this location has per- that correlation across the fault was unambiguous. sisted since the Eocene (Riddihough, 1984; Atwater, The Sichuan Basin in south-central China is a 1989; Hyndman and Hamilton, 1993; and others). continental basin in a convergent tectonic setting. Current convergence rates are about 45 mm/yr The basin lies at the eastern margin of the Hima- (1.77 in./yr), orthogonal to the plate margin and layan uplift, and is bounded on all sides by fold- the coastline of British Columbia (Riddihough, and-thrust belts (Burchfiel et al., 1995; Royden 1984, DeMets et al., 1990). The structures inves- et al., 1997). The structure analyzed in this study tigated in this article are the westernmost frontal is in the interior of the basin, but associated with thrusts of the active accretionary prism overlying deformation propagating outward from the Long- the subduction zone. menshan fold-and-thrust belt, which defines the Finally, we include an example of a basement- northwestern margin of the basin. The lithology of involved structure from the western Sierras Pam- this part of the basin consists of Paleozoic and peanas region of northern Argentina. In this sec- Mesozoic carbonates interbedded with siliciclastics tion of the subduction zone, the Nazca plate (Meng et al., 2005). The fault in this study soles subducts at a nearly horizontal angle (Barazangi and into a detachment localized in a Triassic evaporite Isacks, 1976) at a rate of approximately 10 cm/yr layer (Hubbard et al., 2010). (3.94 in./yr) (Minster and Jordan, 1978; DeMets The Niger Delta is a linked extensional and et al., 1990; and others). Associated with this shallow- contractional passive-margin system that formed as angle subduction, contractional deformation ex- a result of sedimentary loading from the outflow of tends several hundred kilometers further into the the Niger River into the Gulf of Guinea. The sed- continent and is characterized by predominantly iments in this system are composed of Cenozoic basement-involved thrust faulting. Deformation marine shales and more coarsely-grained turbidites of upper Paleozoic and Cenozoic sediments over- that overlie the attenuated transition between Af- lying a basement consisting of Precambrian meta- rican continental crust and oceanic crust (Damuth, morphic and Paleozoic plutonic rocks has occured 1994; Bilotti and Shaw, 2005; Corredor et al., from about 10 m.y. to the present (Jordan and 2005a). Gravity-driven collapse of the sediments Allmendinger, 1986), primarily through what have deposited in the Niger River Delta results in ac- been characterized as basement-involved fault- tive extension onshore and on the continental shelf. propagation folds (Zapata and Allmendinger, 1996; This displacement is linked through a detachment Jordan et al., 2001). The particular structure analyzed in overpressured shale units to contractional de- for this study lies in the Bolsones embayment of the formation at the toe of the system in deep water. Bermejo basin, in the transitional region between the The lithologically weak marine shales promote the pre-Cordillera and the Sierras Pampeanas, north of

230 Displacement Variations and Folding Styles San Juan, Argentina. Studies of syntectonic deposi- is plotted in black on each displacement-distance tion of sediments suggest that thick-skinned thrust profile. The minimum and maximum fault dips systems in this region have been active for at least the that are permissible from the seismic reflection data past 5 m.y. (Zapata and Allmendinger, 1996). are then interpreted, and measurements of dis- placement of the stratigraphic layers across each of the end-member fault geometries are reported METHODS as the minimum and maximum fault dip on each of the displacement-distance profiles as a means of Displacement was measured as the distance along characterizing the uncertainty in the measurement. the fault between the mapped terminations of a Although uncertainty because of fault geom- given stratigraphic layer at the fault surface (such etry is the primary source for this measurement, as is done in Williams and Chapman, 1983, and additional sources of uncertainty exist that are others). This is contrasted with a simple mea- difficult to quantify but which may affect the re- surement of throw, the vertical component of liability of the measurement. Special care must be displacement, which has been used as a proxy taken to minimize contributions from these fac- for displacement in some previous studies (e.g., tors. For example, it is challenging to quantify how Mansfield and Cartwright, 1996). Although the much uncertainty results from tracing a reflector latter approach has the benefit of being measure- through a poorly imaged zone; these shadow zones able without relying on quality of imaging imme- are common in the footwall near a fault because diately adjacent to the fault surface, it is not ap- of perturbations to the velocity field in the hang- propriate for the structures in this study because ing wall and migration-related processing effects the dip and nonplanarity of the faults, as well as the (Kleyn, 1983). Additionally, changes in the thick- style of folding adjacent to the fault, have a signif- ness and internal structure of a stratigraphic unit icant influence on the relations between uplift and can lead to the bifurcation of a seismic reflector slip. We have ensured that the quality of the seis- (Sherriff, 1977), which can contribute to uncer- mic reflections is sufficiently high that the uncer- tainty in how to extend the interpretation of the tainty in the geometry of fault and horizon cutoffs stratigraphic layer through the bifurcated region. is minimal and does not significantly impact the Additionally, out-of-the-plane displacement on a overall interpretations. We choose as the origin for fault may lead to variations in measured displace- our measurements the intersection of the lowest ment along the fault in cross section. If the layers observable reflector in the footwall with the fault and fault are perfectly planar, the displacement- surface (P in Figure 1), with distance up the fault distance profile measured records the dip-slip com- as positive; the choice of a different origin would ponent of displacement. However, if the layers are serve to shift the plot along the x axis, but would folded or change thickness along strike, oblique dis- not alter the observed trend. placement could result in changes in the trends ob- Numerous factors contribute to uncertainty served in the displacement-distance relationship, so when interpreting reflections. Because the faults one should carefully consider the influence of this analyzed in this study have shallow dips, the angle factor in the case of a particular structure. Each of between the stratigraphic layers and the fault is these factors can contribute to local changes in small, so a small change in the fault dip can create observed displacement gradients. The structures in a significant change in the apparent displacement this study were chosen specifically to have minimal measured along the fault. As a result, uncertainty in contributions from each of these sources of error. the fault dip is one of the largest potential sources Other factors can contribute to uncertainty in of error in the measurement; this is the source of the absolute value of the measured displacement, error quantified and reported in this study follow- but have little effect on the overall trend of the ing the method described by Bergen and Shaw displacement gradients; as this study is interested in (2010). The favored, or most likely, fault geometry the latter, these sources of error are not explicitly

Hughes and Shaw 231 Figure 2. Kinematic models il- lustrating (A) fault-bend, (B) shear fault-bend, and (C) fault- propagation folding. (D) A plot of the displacement along the fault as a function of distance along the fault, termed the displacement- distance profile, for each struc- tural style, illustrates the trends in displacement that characterize each model. Portions of the fault for which displacement cannot be measured in the particular examples shown in A–C(caused by the choice of specific fold/fault cutoff geometries), are shown in dashed lines to illustrate the more general trend in displacement for each structural class.

addressed in this study. These factors can include MODEL PREDICTIONS AND EXAMPLES uncertainties in seismic velocity in the depth con- version process, or other artifacts of processing Fault-related folds develop as strata pass over bends the seismic data, including the challenge of ac- in faults, are deformed above propagating fault tips, counting for lateral variations in velocity and out- and/or are folded above detachment surfaces. These of-plane energy in 2-D surveys. Uncertainties in structures are common in orogenic and passive- the interval velocities used in converting the seis- margin fold-and-thrust belts throughout the world mic data from time to depth can range as much as (for example, Rich, 1934; Rodgers, 1950, 1990, ±5% (Sherriff, 1977) and could create variations in 1991; Suppe, 1983; Suppe and Medwedeff, 1990; the absolute values of displacement measurements Erslev, 1991; McConnell, 1994; Shaw and Suppe, of as much as 10%, although the relative smooth- 1994; Erslev and Mayborn, 1997; Corredor et al., ness of the velocities in these regions would ensure 2005a; Shaw et al., 2005; Yue et al., 2005; Hubert- that the trends in displacement gradient observed Ferrari et al., 2007). In this study, we examine the in the study would remain unaltered. Addition- displacement-distance profile characteristics of ally, the imaging resolution of the seismic data is three main types of fault-related folds: fault-bend a fundamental limit on the scale of measurement folds, shear fault-bend folds, and fault-propagation possible; given dominant wavelengths of seismic folds. Each of these structural styles is character- reflection data between 100 and 300 m (328 and ized by a distinct fold geometry and distribution of 984 ft) (for the depth range of interest to this study) displacement along the fault (Figure 2). and the ability to resolve features with minimum vertical separation of one-fourth wavelength, fea- turesbetween25and75m(82and246ft)in Fault-Bend Folding thickness represent the minimum resolvable fea- ture. This source of uncertainty associated with Fault-bend-folding theory was developed by Suppe the resolution limit of seismic data is sufficiently (1983) as a geometrically and kinematically consis- small compared to uncertainties in fault dips and tent way of predicting the geometry of parallel folds cutoff geometries that it is not explicitly consid- that develop as strata are displaced over a fault bend. ered in the calculation of error for this study. The theory indicates that displacement remains

232 Displacement Variations and Folding Styles Figure 3. (A) A kinematic model of a fault-bend fold dem- onstrates the decrease in dis- placement across an anticlinal fault bend, from S0 below the bend to S1 above the bend. Dis- tance is measured from point P. (B) The displacement-distance profile for this structure shows a linear gradient between these two displacement values, as ma- terial within the fold limb has only undergone folding for a part of its structural history. Note the lo- cations of the active (1) and pas- sive (2) axial surface locations in the cross section and displacement- distance profile. constant along planar fault segments and changes As fault-bend-folding theory prescribes a unique abruptly at fault bends. In the case of a simple relationship between the displacement observed thrust ramp extending to an upper detachment, along the fault on either side of a fault bend (the R the theory predicts constant displacement along value in Suppe, 1983) for a given fault geometry, the fault ramp. Similarly, displacement on the up- the manner in which displacement changes at a per detachment above the bend is also the same fault bend is also predicted. The displacement ob- everywhere, although it is generally less than dis- served for a given layer that is always above, or al- placement on the ramp. The magnitude of the ways below, the fault bend during the displace- change in displacement is dependent on the fault ment history is equal to the displacement on the geometry and stratigraphic cutoff angles and can underlying segment of the fault. The ratio of this be predicted by quantitative fault-bend-folding displacement fully above and below the fault bend theory. Based on this, it might be expected that a can be predicted by the R value, or the ratio of the displacement profile across a fault bend would be displacement above (S1) to the displacement be- characterized by two zones of constant slip sepa- low (S0) the fault bend, which is uniquely derived rated by an immediate change at the fault bend. for a given structural geometry using fault-bend- However, what one actually measures are two zones folding theory. The zone of displacement gradient of constant displacement, separated by a linear gra- can also be quantified. On a plot of displacement as dient of displacement in a finite zone beginning at a function of distance up the fault, the displace- the fault bend. This observation highlights the fact ment gradient region caused by the fault bend be- that displacement, and not slip, is what is actually gins at the location of the bend and extends for a measured along the fault when matching hanging- region equal in length to S0.Giventhatthechangein wall and footwall cutoffs. Although slip along the displacement across this region is S1-S0, the slope of fault changes instantaneously at the fault bend, this displacement gradient is (S1-S0)/S0,whichis displacement is the result of cumulative motion of equivalent to R-1 (Figure 3). The displacement at the hanging wall over the footwall. Material that is in any given point in the gradient is straightforward to the sloped region of the displacement profile began predict because the gradient is linear. beneath the fault bend, but after some increment of slip, passed over the fault bend; therefore, its dis- Examples of Fault-Bend-Folding Behavior placement reflects that it experienced deformation inbothslipregimesoverpartsofitsdeformational To test these predictions of fault-bend-fold theory, history. we first generate a displacement-distance profile of

Hughes and Shaw 233 Figure 4. (A) A discrete-element model (DEM) of a fault-bend fold. (B) The displacement-distance profile for the DEM model (black dots) agrees very well with the decrease in displacement pre- dicted by the R-1 value derived from fault-bend-folding kinemat- ics (Suppe, 1983) for this fault- bend geometry (−0.15 for this example, gray dashed line).

mechanical model of a fault-bend fold developed The value of examining displacement patterns using the discrete-element approach after Benesh in a mechanical model is that both the displace- et al. (2007) and Benesh (2010). This numerical ments along the fault segments and the fold ge- model was developed using the Particle Flow Code ometries are emergent model behaviors and can be in Two-Dimensions (PFC-2D) (Itasca, 1999), a com- measured very precisely. The model reproduces mercial discrete-element modeling code distributed the primary features of fault-bend-fold theory: a by the Itasca Consulting Group. Layers of rock are fold limb of relatively constant dip and constant modeled as aggregates of circular particles that in- layer thickness, with an anticlinal axial surface tied teract with friction and cohesion at their contacts to the fault bend and a passive synclinal axial surface based on the method described by Cundall and that has been translated along the upper detach- Strack (1979), with values assigned to emulate the ment (Figure 4A). Measurement of the offset of bulk mechanical properties of rocks in laboratory stratigraphic layers in the hanging wall and foot- settings (Itasca, 1999). The aggregate material is wall of the model display a constant displacement contained by walls that serve to define a ramp-to-flat along the fault ramp and detachment, and a linearly fault geometry necessary to produce an anticlinal decreasing displacement in the fold limb region. fault-bend fold, to drive deformation from the Fault-bend-folding theory predicts constant dis- hinterland, and to confine the particles to the re- placement along the ramp and detachment, with a gion of interest. As the hinterland wall is displaced gradient of −0.15 in the fold limb region (calcu- to the right, the rock material must deform and lated as R-1 for the prescribed fault geometry), pass over the fault bend, and the foreland wall which is in excellent agreement with the observed moves such as to relieve tectonic stresses while displacement distribution (Figure 4B). maintaining the confining stress on the rocks ad- In addition, we evaluated the displacement- jacent to it (see Benesh, 2010, for a more thorough distance relationship for several natural fault-bend description of the modeling approach). folds to assess how well they conformed to the

234 Displacement Variations and Folding Styles Figure 5. (A) Uninterpreted, migrated, depth-converted seis- mic reflection data from the SichuanBasin,China.(B)Inter- pretation of the seismic reflection data, with the faults (red), strati- graphic layers (a through k), and uncertainty of fault location (black dashed lines). (C) Displacement- distance profile of data (blue), with minimum (white) and max- imum (gray) measurements based on the range of possible fault dips, with light gray lines connecting minimum, preferred, and maximum displacement values for a given stratigraphic layer and a linear best fit to the preferred values (dark-gray dashed line). The range in which the possible fault geometries were chosen in the construction of the low and high estimates of uncertainty are indicated (black dashed lines) to illustrate the sensitivity of the measure- ment to uncertainties in fault geometry. Data courtesy of CNPC; modified from Shaw et al., 2005, chapter 1A-2.

kinematic theory. In the case of a simple thrust layers offset across this fault demonstrates that dis- ramp from the Sichuan Basin, China (Figure 5), we placement decreases across each of the two anti- observe, within the uncertainty of the measurement, clinal fault bends (Figure 6B). Based on geometric that the displacement along the thrust ramp is con- fault-bend-folding relationships, the angle between stant, as predicted by the fault-bend-folding model. bedding and the fault below the bend (q)andthe In contrast, when material in the hanging wall change in fault dip at the bend (f) define the ex- moves across a fault bend, the theory predicts that pected R-value for the change in displacement at a fault-bend fold is formed, and the amount of each fault bend. This yields predicted gradients in displacement along the fault varies as described displacement of −0.13 and −0.23 above the lower above. To examine this behavior, we analyzed an and upper fault bends, respectively. The measured anticlinal fault-bend fold overlying a fault with two displacements are consistent with these predic- distinct anticlinal bends from the southern Niger tions of displacement gradients, within the un- Delta (Figure 6A). Measurement of the stratigraphic certainty of the measurement, suggesting that this

Hughes and Shaw 235 Figure 6. (A) Seismic reflection profile of an anticlinal fault-bend fold from the offshore Niger Delta, Nigeria. Interpretation of fault surface (red), fault bends (1 and 2), and stratigraphic horizons (a through i). Distances are measured from the intersection of the lowest layer and the fault (P). (B) Measured displacement-distance relationship (blue), with minimum (white) and maximum (gray) estimates. Displacement gradient for the modeled fault-bend fold (C) is also plotted (black dashed), with the locations of fault bends (1) and (2) highlighted in the seismic cross section and displacement-distance profile. The R-1 values, which are the displacement gradients predicted by fault-bend-folding kinematics (Suppe, 1983), are reported for each segment. Data courtesy of Mabon Limited; modified from Shaw et al., 2005, chapter 1B-1; uninterpreted seismic data may be accessed through AAPG Datashare 51 site (http://www.aapg.org /datashare/). structure is consistent with fault-related folding exhibiting unique geometric relationships. Such theory. Furthermore, a fault-bend-fold model gen- structures form in regions where a weak lithology erated from the observed fault geometry and back- is involved in the deformation, such as salt (ex- limb dips that is consistent with these displacement amples include offshore Brazil, Angola, Gulf of gradients predicts the dips of the forelimb seg- Mexico, Zagros) or overpressured shale (southern ments to within ±1° (variation is caused by non- Caribbean, Niger Delta, Baram Delta, and others). linearity of the limbs), indicating that the structural Shearing in this stratigraphic interval generates a geometry is well represented by the fault-bend- geometrically-distinct class of structures that are folding model. characterized by a backlimb that dips more shal- lowly than a fault-bend-folding model for the same fault geometry (Suppe et al., 2004). Based on Shear Fault-Bend Folding shear fault-bend-folding theory, the amount of dis- placement measured in this interval increases with Structures that form in regions in which a strati- distance up the fault ramp throughout the shear- graphic zone of finite thickness undergoes distrib- ing interval. Above the shear interval, parallel fold- uted shear deformation have been recognized as ing results in constant displacement along the ramp

236 Displacement Variations and Folding Styles Figure 7. (A and B) Simple and pure shear fault-bend-folding models, with the following features labeled: shear angle (a), fault dip (q), backlimb dip (d), height of the shear interval (h), displacement at the top of the shear interval (S), displacement at the base of the shear interval, in the case of pure shear (S1), and sheared interval highlighted (hatched). (C) Displacement-distance profile for simple shear (SS) and pure sure (PS) models, with quantities used in the slope calculation for the layers in the shear interval highlighted. (D and E) Plots of the relationship between backlimb dip and displacement gradient in the sheared interval for lines of constant fault dip (q)for pure and simple shear, respectively. The locations of the fault and limb geometry for Figure 8 are plotted as white squares.

Hughes and Shaw 237 (Figure 1B). This produces a pattern of changing relationship between backlimb dip (d) and dis- slip and displacement along planar fault segments placement gradient for lines of constant fault dip is that strongly contrasts with standard fault-bend- shown in Figure 7D and E for pure and simple fold theory, which prescribes changes in slip and shear, respectively. Given an observed fault dip displacement only across fault bends. and backlimb dip for a natural example, these For a given fault dip (q), backlimb dip (d), and graphs can be used to determine the displacement height of the shearing layer above the detachment gradient for pure shear and simple shear models (h) (Figure 7A, B, sheared interval highlighted), that match the prescribed fault and backlimb ge- a displacement gradient and maximum displace- ometry. Thus, a comparison of the observed dis- ment can be calculated for a simple shear and placement gradient, in conjunction with other ob- pure shear fault-bend-fold model that is consis- servations, can help to determine whether the tent with the prescribed geometry. Based on these structure in question is better modeled as a pure geometric parameters, the shear angle can be shear or simple shear fault-bend fold. Note that the calculated: existing pure shear fault-bend-folding theory does    not explicitly define the geometry of the layers in d a ¼ −1 sin 1 2 the shear interval. As such, a balanced, permissible, cot d q þ − d  2C sin cot1 cos but nonunique solution is given here (Figure 7B). − 1 Because the displacement gradient is dependent on sind cotq þ 1− cosd the slip at the base of the ramp and the top of the shear interval, the displacement gradient is unlikely where C is 1 for pure shear and 1/2 for simple to change greatly for other, perhaps equally valid shear. Once the shear angle is known, the slip (s) solutions; however, one can envision a case where can be calculated as follows: deformation in the sheared interval is accommo- dated in such a way that the increase in displace- h tana ment in the shear interval is nonlinear. s ¼ cosq þ tanðÞd=2 sinq Example of Shear Fault-Bend-Folding Behavior as derived in the appendix of Suppe et al. (2004). This slip value represents the displacement for the To assess if the displacement pattern predicted by layer at the top of the shear interval and all layers shear fault-bend-fold theory is observed in natural above it, which undergo parallel folding in the structures, we assess a contractional fault-related model. fold from Cascadia, off the western coast of Van- The displacement at the top of the shear sec- couver Island (Figure 8A), that illustrates the com- tion can then be used to determine the displace- mon features of this structural style (Suppe et al., ment gradient in the displacement-distance profile 2004). Measured displacement along the fault in the sheared interval (Figure 7C). For the end- (Figure 8B, blue) demonstrates that displacement member simple shear model, as described by Suppe increases greatly through the lowest stratigraphic et al. (2004), displacement along the fault is zero layers (a through f), increases gradually in the over- at the base of the thrust ramp, and s (as calculated lying section (f through k), and that above that in- above) at a distance of h/(sin q) along the fault. terval (k through p), displacement along the fault Therefore, the change in displacement (s)overthe ramp is relatively constant. A line-length (palin- distance from the base of the ramp to a distance of spastic) method (Shaw et al., 2005) of measuring the h/(sin q) results in a displacement gradient of s ×sin shear profile of the structure (Figure 8B, red) re- q/h in the shear interval. For pure shear, the dis- veals a similar trend. Thus, we conclude that the placement along the ramp does not decrease to shear within this structure is responsible for the zero, but rather, to a value defined by the amount observed displacement gradient on the thrust of slip, s1, at the base of the ramp. A graph of the ramp.

238 Displacement Variations and Folding Styles Figure 8. (A) Seismic reflection profile of a shear fault-bend fold in the Cascadia accretionary prism, offshore Vancouver Island, west- ern Canada, with interpreted fault (red) and stratigraphic layers a through p. Axial surfaces (1) and (2) bound a fold limb with a dip of 14° and (2) and (3) another dip panel of 7°. The location of the top of the shear interval is defined by the place where the axial sur- face intersects the fault plane, so (2) corresponds to a shear interval that reaches the height of layer f, and is related to the development of the steeper dip panel, whereas (3) corresponds to a shear interval that extends up to layer k and is related to the shallower dip panel. A sim- ple shear fault-bend-fold model was constructed based on these geometric observations (inset). (B) Displacement-distance profile for data (blue), minimum (white) and maximum (gray) estimates, the model displacement (dark- blue dashed line). (C) Palinspastic estimate of shear (red) and model shear profile (dark-red dashed line). Locations of stratigraphic layers that mark transitions in the shear interval (k and f) are highlighted. Data modified from Hyndman et al. 1994 (line 89–04), from Shaw et al., 2005, chapter 1B-4; uninterpreted seismic data may be accessed through AAPG Datashare 51 (http://www .aapg.org/datashare/).

A shear fault-bend-fold model was constructed that in the seismic data, the synclinal axial trace using the kinematic theory (Suppe et al., 2004) (labeled 1 in Figure 8A) appears to be linear and based on the fault geometry and the identification intersects the ramp at the point where it also in- of the shear interval from the displacement gradi- tersects the detachment, which is consistent with ent measurements (Figure 8, inset). As the dis- the prediction for a simple shear fault-bend fold, placement-distance profile indicates that displace- but not a pure shear fault-bend fold (e.g., Corredor ment decreases to zero at the base of the fault, we et al., 2005b, see Figure 7A and B for a compari- conclude that a simple shear fault-bend-folding son). The model was constructed to match the solution is appropriate for this structure. The sim- observed fold limb dips of 14° (between the axial ple shear model is further supported by the fact surfaces labeled 1 and 2) and 7° (between 2 and 3)

Hughes and Shaw 239 in the backlimb, resulting in shear angles (a)of29° These folds develop as slip is consumed, and the and 12°, and displacement gradients of 0.44 and resulting folds commonly have steeply dipping or 0.17, respectively. The displacement-distance pro- overturned forelimbs that are pinned to the fault file for this model is broadly consistent with both tip. Most fault-propagation folds have many qual- the palinspastic approach and the displacement itative similarities (Shaw et al., 2005): gradient approach, although note that the addi- tional displacement measured in the lowest strati- 1. A highly asymmetric shape, with a relatively graphic interval of the displacement distance pro- steep and narrow forelimb and a longer, more file (a through f) is caused by deformation in the gently dipping backlimb; footwall, which is not considered in the model. 2. Slip that decreases along the fault toward the Combining these two approaches provides a use- fault tip; and ful means of highlighting such aspects of the de- 3. A syncline pinned to the upward projection of formation in natural structures that are not cap- the fault tip. tured in the kinematic model. Many studies of fault displacement consider Many theories have been developed that pro- the location of the maximum displacement as rep- vide a geometric and kinematic model of defor- resentative of the point at which the fault initiated mation for these structures, the most commonly (Ellis and Dunlap, 1988; Briggs et al., 2006; and applied of which include constant-thickness and others). This is based on the assumption that, as the fixed-axis fault-propagation folding (Suppe and fault grows and slip accumulates on the structure, Medwedeff, 1990), and trishear folding (Erslev, the place where the fault first initiated will accu- 1991; Allmendinger, 1998). These models make mulate the greatest amount of slip. As the point of specific predictions about the shape of the fold in maximum displacement on many natural faults is relationship to the amount of displacement and observed to be in the center of the structure, this the fault dip. In addition, a variety of other models has provided the motivation for the development have been developed to address a specific subset of bilateral, or double-edged, fault-propagation- of the natural structures or to attempt to explain folding models (Kattenhorn, 1994; Tavani et al., a specific observation (for example, basement- 2006). We propose that in some cases, pure or sim- involved models by McConnell, 1994; Narr and ple shear of a layer of finite thickness in the hanging Suppe, 1994; Spang and McConnell, 1997; vari- wall can produce a displacement maximum in the able forelimb thickness by Jamison, 1987; exter- center of a fault, irrespective of where the fault nally applied shear in Mitra, 1990; forelimb dip nucleated. In the previous example (Figure 8A), steepening with increasing slip in McConnell, 1994; the fold and fault geometry suggests that the struc- complex geometries in Chester and Chester, 1990; ture is a shear fault-bend fold, and the displace- mixed-mode structures in Erslev and Mayborn, ment gradient observed is also consistent with that 1997; and double-tipped fault propagation in model. In a shear fault-bend-folding model, the Kattenhorn, 1994, and Tavani et al., 2006). fault propagates to its full extent before significant Fault-propagation folds are generally charac- displacement has accrued. This suggests that shear terized by regions of constant slip at the base of should be considered and tested before inferring the thrust ramp, and decreasing displacement along that the location of maximum displacement is in- the upper part of the fault (Figure 1). Each of the dicative of the location of fault nucleation. existing kinematic models for fault-propagation folding generates distinct predictions for fold ge- Fault-Propagation Folding ometry, uplift, and displacement (Figure 9A–C). However, for any model with a constant propagation- Fault-propagation folds are an important class of to-slip ratio (which is required by constant-thickness structures that form at the tips of faults as they and fixed-axis models and may be specified in propagate upward through sedimentary layers. trishear models), the gradient in displacement is

240 Displacement Variations and Folding Styles Figure 9. (A–C) Kinematic models of the most commonly applied fault-propagation-folding models. (D) Displacement-distance profile for constant-thickness (circles) and fixed-axis (squares) models of varying fault dip, illustrating that the models are the same at 29°; at higher fault dips, constant-thickness models have shallower gradients, and at steeper dips, constant-thickness models have steeper gradients. (E) Displacement gradient as a function of fault dip shows that fixed-axis models have a constant displacement gradient (gray), whereas displacement gradient decreases as fault dip increases for constant-thickness models (black). Trishear models with P/S (propagation/slip) ratios and fault geometries identical with the previous models show the same trends in displacement gradient, in- dicating that displacement gradient is a function of P/S ratio for trishear models.

linear (Figure 9D). In detail, the slope of this lin- fault dip, as prescribed by the models. As fault dip ear trend depends on model type, propagation-to- increases, the first factor decreases the displace- slip (P/S) ratio, and fault dip. We examine these ment gradient. However, the fold tightness also relationships in more detail for the constant thick- decreases, so the second factor increases the dis- ness, fixed axis, and trishear models. placement gradient. These factors do not entirely For models of constant-thickness fault-propaga- offset, so overall, displacement gradient decreases tion folds developing from a fault stepping up from with increasing fault dip. Additionally, P/S ratio a detachment, displacement gradient changes as a increases with increasing fault dip for constant- function of fault dip because (1) for a given amount thickness models. In fixed-axis models, both of of shortening, the distance between bed cutoffs these factors are at play, but layer thickness changes that have been displaced along the fault varies as a in the forelimb of the fault-propagation fold is an function of the dip of the fault on which slip is additional factor. The effect of this additional fac- being accommodated, and (2) fault-propagation- tor is such that displacement gradients and P/S folding-related strain in the hanging wall, reflected ratios for fixed-axis fault-propagation folds are in- by the tightness of the fold, varies as a function of sensitive to fault dip (Figure 9E).

Hughes and Shaw 241 Figure 10. (A) Seismic reflection profile of a fault-propagation fold in the Niger Delta, offshore Nigeria, with fault (red) and stratigraphic layers (a through f) interpreted. (B) Higher resolution image of the fault tip area, with the predicted fault tip location labeled (T). (C) Displacement-distance profile displays a linearly decreasing displacement for layers a–f (blue) with minimum (white) and maximum (gray) displacement estimates. The fault tip location is predicted by the point where the line intersects the x-axis (where displacement = 0), T. Data are owned and provided courtesy of CGGVeritas, Crawley, United Kingdom; uninterpreted seismic data may be accessed through AAPG Datashare 51 (http://www.aapg.org/datashare/).

For fixed-axis and constant-thickness mod- fold models, as is true of other fault-propagation- els, a given initial layer and fault geometry leads to folding models. the development of a unique fault-propagation- fold limb geometry, P/S ratio, and displacement Examples of Fault-Propagation Folding gradient. However, because the trishear model inherently has more variable parameters, a given To assess if natural structures exhibit displacement fault and layer geometry does not determine a gradients predicted by fault-propagation-fold mod- unique fold geometry without specifying addi- els, we examine a structure from the northern Niger tional model attributes. Therefore, to compare this Delta (Figure 10A) that is imaged in high-quality approach to the previous ones, trishear models seismic reflection data. Qualitative observations, with the same fault geometry, layer geometry, such as folding unassociated with a fault bend and and P/S ratios were generated. The displacement an active synclinal axial surface tied to the upward gradients for these models match those for the extension of the fault, serve to identify this struc- corresponding fixed-axis and constant-thickness ture as a fault-propagation fold. The displacement models (Figure 9E), indicating that fault geometry profile for this structure exhibits a distinctive linear and P/S ratio are the factors that determine the dis- negative gradient along the fault (Figure 10B), placement gradients for trishear fault-propagation- with displacement values that approach zero. This

242 Displacement Variations and Folding Styles Figure 11. Kinematic model of a fault-propagation fold just before (A) and after breakthough along the same fault trajectory (B) and a steepened fault tra- jectory (C). (D) Displacement distance profiles corresponding to each case (labeled A–C): The profile for A (black), where D1 indicates the maximum offset on the fault prior to break- through; B (dark gray), where D2 indicates the amount of dis- placement accrued after fault breakthrough; C (light gray), which demostrates the slight modification of the slope caused by fault-bend folding (R-1 = 0.08 for this fault-bend geometry).

pattern is generally consistent with fault-propagation- In some cases, the faults may propagate through folding models and, thus, helps confirm our inter- the folded forelimb to the Earth’s surface, form- pretation of this structure. ing what is typically called a breakthrough fault- The location of the fault tip may be predicted propagation fold (Suppe and Medwedeff, 1990; by the observed displacement gradient based on Shaw et al., 2005). These structures still display the where the displacement-distance curve projects to folding associated with their fault-propagation- a zero displacement value. The predicted fault tip folding history (Figure 11A), but the hanging wall location is seemingly consistent with the seismic is translated up the fault ramp because of additional image because there are truncated reflectors be- displacement (Figure 11B, C). This results in ob- low the fault along this point but continuously served displacements that reflect the contribu- folded horizons above. The ability to predict this tions from both parts of the structure’shistory;the location may be useful in cases where the delinea- expected negatively-sloping displacement-distance tion of a petroleum trap relies on the position of relationship caused by fault-propagation folding, the fault tip. This approach may prove particu- which is offset by the amount of displacement ac- larly useful in structures in which seismic reflection crued after the fault broke through to the surface. data quality near the fault tip is poor; because fault- Thus, on a displacement-distance profile, a break- propagation-fold forelimbs are commonly steeply through fault-propagation fold has a negatively dipping (and difficult to image in seismic reflec- sloping region that transitions at greater distance up tion), this situation is common for this class of the fault to a roughly horizontal line reflecting the structures. Special care must be taken to consider slip that occurred after breakthrough (Figure 11D). faults that propagate through growth stratigraphy The amount of slip that occurred after the break- or unconformities because they will display more through is defined by the height of this horizontal complex displacement patterns; specifically, fault segment of the displacement-distance profile (D2 propagation through the pregrowth to growth tran- in Figure 11C), and the maximum amount of slip sition will be manifest as a decrease in displace- that occurred during fault-propagation folding (D1) ment and displacement gradient, the details of can be estimated by the total slip (D1 + D2)minus which are dependent on sedimentation and fault- the breakthrough slip (D2), after considering any propagation rates. fault-bend-related changes in displacement (the

Hughes and Shaw 243 Figure 12. (A) Seismic reflec- tion profile of a breakthrough fault-propagation fold from the Sierras Pampeanas, Argentina, with fault (red) and stratigraphic layers (a through i) interpreted, and predicted fault tip location, T. (B) Measured displacement- distance relationship (blue), with minimum (white) and maximum (gray) estimates for layers a through i. Linear fit projects to the predicted fault tip location (red point, T). Data courtesy of BHP; modified from Shaw et al., 2005, Chapter 1B-2; uninter- preted seismic data may be ac- cessed through AAPG Datashare 51 (http://www.aapg.org /datashare/).

influence of displacement across a fault bend on displacement variation with distance indicates a the solution may be observed by comparing the negative linear trend, which is consistent with the displacement-distance relationships for the struc- interpretation of this structure as a fault-propagation tures in Figures 11B, C). Notably, in these break- fold (Figure 12B). Although the data quality is through structures, the place where the negatively insufficient to define displacements above hori- sloping part of the displacement-distance curve zon i, the projection of the negatively sloping would intersect with the x-axis corresponds to a trend indicates that the location where displace- fault tip position that is above the land surface or ment would reach zero is substantially above the sea floor at the time of deformation, which would land surface (Figure 12A, B). Thus, this structure result in a fault that would be observable at the sur- can be reasonably interpreted as a breakthrough face. Thus, even in cases where the displacement- fault-propagation fold, with as much as 800 m distance profile is incomplete because of poor data, (2600 ft) of slip occurring after the fault had bro- one can commonly distinguish fault-propagation ken through using the method of estimating slip folds that have and have not broken through to the shown in Figure 11. surface. We illustrate the patterns of displacement in a Applications to More Complex Structures breakthrough fault-propagation fold using an exam- ple from the Sierras Pampeanas region of Argentina. Previous sections have outlined the predicted dis- The seismic image defines this structure as a tight, placements for different contractional fault-related asymmetric fold with a steep forelimb fold that is folding styles and illustrated that these displace- not associated with a fault bend (i.e., not a fault- ment-distance relationships are observed in natural bend fold) (Figure 12A). Measurement of the structures from a variety of tectonic settings. Here,

244 Displacement Variations and Folding Styles Figure 13. (A) Uninterpreted and (B) interpreted seismic reflection profile of two contractional fault-related folds offshore Niger Delta, Nigeria. Pregrowth layers (a through g), growth layers (h, j), drape layers (i), and faults (red) are denoted. Arrows point to features discussed in the text: (I) intersection of axial surface and fault, indicating the top of the shear interval, (II) anticlinal fault bend, (III) drape sedimentation, (IV) fold limb, (V) projected fault tip location, (VI) synclinal fault bend, (VII) growth triangle, and (VIII) minor backthrust. Data are owned and provided courtesy of CGGVeritas, Crawley, United Kingdom.

Hughes and Shaw 245 Figure 14. (A and B) Displacement-distance profiles for the structures analyzed in Figure 13. (C–F) Sequential kinematic model of the development of these structures, with structural styles determined from observations from the displacement-distance plots. we illustrate the application of this method to struc- ramp. The increasing displacement gradient occurs tures with more complex deformation histories from horizons a to b, consistent with the region of to highlight the utility of displacement-distance shear defined by shear fault-bend-folding theory. measurements in defining the structural style and Based on the theory, the top of this shear interval is tectonic history of structures that combine differ- identified by the stratigraphic horizon that intersects ent fault-related folding processes. the fault at the location where the anticlinal axial Our example consists of two thrust sheets and surface also meets the fault (layer b intersects the associated fault-related folds from the deep-water fault at location I in Figure 13B). Above this sheared fold and thrust belt of the Niger Delta (uninter- interval, the displacement-distance profile indicates preted and interpreted seismic profiles, Figures 13A, a constant displacement between layers b and d, B). The hinterland structure (hereafter referred to which suggests that parallel folding occurs in this as A) has a displacement-distance profile charac- region. The region above this, from d to g, is char- terized by a region at the base of the fault with acterized by a linearly decreasing displacement gra- increasing displacement, a constant-displacement dient. The location of this decrease in displacement region in the middle of the fault, and decreasing is coincident with an anticlinal bend in the under- displacement along the uppermost fault that is as- lying fault, which suggests that fault-bend folding sociated with a fault bend (Figure 14A). This pat- may account for at least part of this decrease in dis- tern suggests that this structure involves compo- placement. A fault dip change from 38° to 20°, as nents of fault-bend folding and shear fault-bend observed from the seismic reflection data (Figure 13, folding. The upward-increasing displacements at location II), predicts a gradient in displacement of thebaseoftherampareconsistentwithshearfault- 0.33, or 19°. The rest of the decrease in displace- bend folding in the backlimb of the structure asso- ment may be caused by distributed shear in the ciated with movement of hanging-wall strata above forelimb; there are two compelling reasons that this the fault bend defined by the base of the thrust may occur in this structure. This fault geometry is

246 Displacement Variations and Folding Styles slightly beyond the boundary of the solution space appear similar between the structures, the com- for fault-bend folding, which is to say that the bination of fault geometry and displacement al- folding caused by this fault geometry cannot be lows for the differentiation of fault-bend and fault- modeled by preserving layer thickness and area, propagation folding in these two examples. Based and thus, distributed layer thinning and thicken- on the interpretation of the forelimb of the struc- ing processes are required. Additionally, because ture as a fault-propagation fold, the fault tip (the these layers consist of weakly lithified, near-sea- location where displacement along the fault de- floor sediments (confirmed by the observation that creases to zero) would be located just below hori- the upper detachment of the fault was the paleo- zon f (Figure 13, V). This is broadly consistent seafloor, which is indicated by the sediments that with the observation of offset layers below this onlap onto the forelimb and exhibit geometries char- point, and continuous, folded layers above it. Based acteristic of drape sedimentation (Figure 13, III), it on the curved nature of the forelimb fold limb, is not surprising that they would not deform strictly changes in layer thickness, and the upward de- in accordance with fault-bend-folding theory, as the crease in bed dips, this structure is interpreted as a assumptions of the preservation of layer thick- trishear fold (Erslev, 1991; Allmendinger, 1998; ness and accommodation of folding by flexural slip and others). mechanisms may not be preferred in weakly lithified The growth strata and folding patterns indicate sediments. Despite these modest differences, the that these two faults are part of a break-forward predicted decrease in displacement from fault- sequence. Thus, displacement along the foreland bend-folding theory clearly captures the first-order structure (B) imbricates and refolds the hinterland displacement patterns in this structure. structure (A) (fold limbs IV and VII in Figure 13). By the same method of analysis, the foreland Despite this complexity, the displacement-distance structure (Figure 13, structure B) exhibits constant profiles maintain recognizable signatures of the ba- displacement at depth and decreasing displacement sic fault-related folding components that generated along the uppermost part of the fault that is not these structures. associated with a fault bend. This pattern of dis- Based on the insights from the displacement- placement is consistent with components of both distance profiles and growth strata, we generated standard fault-bend folding and fault-propagation a balanced kinematic model of both structures folding. The region of constant slip on the lower (Figure 14C–F). Based on the detailed observations part of this thrust ramp is consistent with the back- from structure A, it was modeled as a shear fault- limb of the structure forming by standard fault- bend fold, with the shear interval and fault ge- bend folding. Notably, the beds in the backlimb of ometry defined by observations from the seismic the structure are parallel to the underlying fault reflection data and displacement-distance profile (fold limb IV in Figure 13), consistent with stan- (Figure 14A). After displacement was complete dard fault-bend folding and distinct from struc- on the structure A, displacement was modeled on ture A, which involved a component of shear fault- the foreland structure as a fault-bend-fold back- bend folding. On the upper part of the thrust ramp limb with a trishear fault-propagation-fold fore- for structure B, the displacement-distance profile limb, based on the observations made from the shows a negative slope reaching zero displacement displacement-distance profile (Figure 14B). at a distance of about 6 km (3.7 mi) (Figure 14B). Many of the parameters necessary to model the Unlike in structure A, the decrease in displacement forelimb of structure B as a trishear fault-propagation is not associated with an anticlinal fault bend (in fold may be constrained from the displacement- contrast, a minor synclinal bend is present, indi- distance profile. The base of the propagating sec- cated by VI in Figure 13), suggesting that the de- tion is inferred to be the location of the transition crease in displacement observed in structure B is between constant displacement and decreasing caused by fault-propagation folding. Thus, al- displacement. The location of the fault tip is also though the decreases in displacement may at first evident because it is the location where displacement

Hughes and Shaw 247 reaches zero. The distance between those two points also geometrically dissimilar in some ways from represents the distance that the fault propagated the model; this is likely because these sediments during this phase of its history. Additionally, the were not deeply buried and, therefore, preferen- amount of displacement at the base of this seg- tially deformed with more distributed shearing ment can be easily measured. These two obser- instead of flexural slip. Additionally, the thickness vations combine to give a propagation-to-slip ra- of the drape sedimentary package, i, is thinner in tio (P/S) of 3.96 for structure B; knowledge of the natural example; this is due to a combination of this value provides an important input constraint factors, including the lower structural relief ob- for modeling this structure as a trishear fault- served than modeled for structure A, and an propagationfold.Basedontheseobservations oversimplification of the depositional environ- and the observed dip of the fault, a trishear fault- ment (it has been commonly observed in off- propagation-fold forelimb model was generated shore settings that sediments tend to pond be- to model this structure’s geometry, concurrent with hind bathymetric highs [such as structure A], fault-bend folding in the backlimb (Figure 14E–F). resulting in sediment-starved basinward regions This model invokes the following series of events [e.g., Shaw et al., 2004]). As a result, it is per- for this structure: missible that some of the deformation on struc- tures A and B may have been concurrent. For 1. The fault propagated as a fracture from the lower structure B, the deep fold panel (Figure 13, IV) detachment to the base of the fault-propagation and forelimb trishear geometries are well rep- interval; resented in the model geometry. Additionally, the 2. As displacement on the fault commenced, the modeled growth strata deposited over this fold backlimb deformed as a fault-bend fold while thickens over the backlimb and forelimb, which is the tip of the fault propagated upward through consistent with the stratigraphic thickening and the stratigraphic section; and fold geometries observed in the seismic reflection 3. The fault tip propagated to its currently ob- data. The modeled folding caused by the minor served location when the lower part of the fault synclinal bend in fault B (Figure 13, VI) is not ob- had accumulated the observed, maximum amount served in the data, which is perhaps caused by the of displacement. presence of a minor backthrust (Figure 13, VIII), which accommodated the uplift in lieu of fault- Because the only observations that went into bend folding. the construction of the kinematic models were In summary, we suggest that the modeled displacement-distance relationships, fault geome- structural geometries based on parameters defined tries, and stratigraphic thicknesses, comparison of by the displacement profiles are generally consistent the resulting fold geometries with the fold shapes with the patterns of folding and faulting expressed observable in the seismic reflection data provides in this natural example. Specifically, the observed an objective test of the utility of this approach. The displacement profiles help characterize these struc- pregrowth backlimb fold geometry of structure A tures as complex fault-related folds involving com- is consistent with the fold observed in the seismic ponents of fault-bend, shear fault-bend, and fault- reflection data, because the limb dips and widths propagation folding. Moreover, in cases where the of the original fold and imbricated panels are both modeled geometries are locally inconsistent with well represented in the model. The geometry of the the natural folds, this helps identify regions of the growth strata over this backlimb is also consis- natural structures where deformation may be ac- tent with the observed growth geometries of lay- commodated by deformation mechanisms (e.g., ershandj.ThemodeledforelimbofstructureA nonparallel folding) or secondary structures that is consistent with the location, size, and dip di- are not represented in the models. rection of the forelimb in the natural example. Fault-related folds with different structural styles However, the forelimb of the natural structure is are commonly observed in close spatial association

248 Displacement Variations and Folding Styles in many fold and thrust belts (Woodward et al., present in a given contractional structure. The 1988; Woodward and Rutherford, 1989; Spratt method can also serve as a somewhat indepen- et al., 2004; Shaw et al., 2005; Hughes, 2012; and dent way of interpreting structural style, which, others). The factors that favor the formation of when combined with geometric observations, will one structural style over another may include sedi- lead to the development of detailed and accurate mentation rate, boundary conditions, fault fric- structural models of contractional fault-related tion, and the mechanical properties of the stratig- folds. raphy (Wiltschko, 1979a, b; Berger and Johnson, 1980; Chester et al., 1991; Erickson, 1996; Strayer et al., 2004; Hughes, 2012; and others). The fact REFERENCES CITED that these properties may vary locally within a fold and thrust belt allows for the development of lo- Allmendinger, R., 1998, Inverse and forward numerical mod- eling of trishear fault propagation folds: Tectonics, v. 17, cally variable structural styles. Thus, because fault- no. 4, p. 640–656, doi:10.1029/98TC01907. related folds with different structural styles have Atwater, T., 1989, Plate tectonic history of the northeast Pa- been documented in close spatial association in other cific and western North America, in E. L. Winterer, regions, and because the factors that contribute to D. M. Hussong, and R. W. Decker eds., The eastern Pa- cific Ocean and Hawaii: Geological Society of America, structural style vary locally, we can be confident in Geology of North America Series, N, p. 21–72. the permissibility of our interpretation of differ- Barazangi, M., and B. L. Isacks, 1976, Spatial distribution of ences in structural style in this example. earthquakes and subduction of the Nazca plate beneath South America: Geology, v. 4, p. 686–692, doi:10.1130 /0091-7613(1976)4<686:SDOEAS>2.0.CO;2. Benesh, N. P., 2010, The mechanics of fault-bend folding and CONCLUSIONS tear-fault systems in the Niger Delta: Ph.D. thesis, Har- vard University, Cambridge, 121 p. Benesh, N. P., A. Plesch, J. H. Shaw, and E. K. Frost, 2007, We present a quantitative method for relating the Investigation of growth fault bend folding using discrete displacement measured along a contractional fault element modeling: Implications for signatures of active to the style of folding deformation present in a folding above blind thrust faults: Journal of Geophysical given structure. We include results from various Research, v. 112, B03S04, doi:10.1029/2006JB004466. Bergen, K., and J. H. Shaw, 2010, Displacement profiles and styles of fault-related folds by comparing the ex- displacement-length scaling relationships of thrust faults pected displacement-distance relationships to ob- constrained by seismic reflection data: Geological Socie- servations from seismic reflection datasets in a vari- ty of America Bulletin, v. 122, no. 7–8, p. 1209–1219, doi:10.1130/B26373.1. ety of tectonic settings. We then apply this method Berger, P., and A. Johnson, 1980, First-order analysis of de- to a complex structure, illustrating that this ap- formation of a thrust sheet moving over a ramp: Tectono- proach can be successfully used to gain insight into physics, v. 70, p. T9–T24, doi:10.1016/0040-1951(80) the mixed structural styles that may be present in 90276-0. Bilotti, F., and J. H. Shaw, 2005, Deep-water Niger Delta natural structures. By this approach, we are able to fold and thrust belt modeled as a critical-taper wedge: The identify shearing intervals, parallel folding inter- influence of elevated basal fluid pressure on structural vals, and fault-propagation-folding intervals, and to styles: AAPG Bulletin, v. 89, p. 1475–1491. observe the impact of fault bends on displacement Briggs, S. E., R. J. Davies, J. A. Cartwright, and R. Morgan, 2006, Multiple detachment levels and their control on fold distributions. Additionally, by generating a bal- styles in the compressional domain of the deepwater west anced structural model based on our interpreta- Niger Delta: Basin Research, v. 18, no. 4, p. 435–450, tion, we are able to compare the fold and growth doi:10.1111/j.1365-2117.2006.00300.x. Burchfiel, B. C., C. Zhiliang, L. Yuping, and L. H. Royden, geometry of the model with observations in the 1995, Tectonics of the Longmen Shan and adjacent re- seismic reflection data, confirming the validity of gions, central China: International Geology Review, our interpretation. We suggest that this approach v. 37, p. 661–735, doi:10.1080/00206819509465424. has value for the structural interpretation of seis- Chester, J. S., and F. M. Chester, 1990, Fault-propagation folds above thrusts with constant dip: Journal of Struc- mic reflection data because it can help to eluci- tural Geology, v. 12, no. 7, p. 903–910, doi:10.1016/0191 date the styles of fault-related folding deformation -8141(90)90063-5.

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