Fault displacement-distance AUTHORS relationships …projects.iq.harvard.edu/files/harvardshell/files/hughes_shaw_aapg...Fault displacement-distance relationships as indicators of

AUTHORS

Amanda N. Hughes � Department of Earthand Planetary Sciences, Harvard University, 20Oxford Street, Cambridge, Massachusetts02138; [email protected]

Amanda N. Hughes is a structural geologist forthe Chevron Energy Technology Company inHouston, Texas. She received a Ph.D. in earthand planetary sciences from Harvard University

Fault displacement-distancerelationships as indicators ofcontractional fault-relatedfolding styleAmanda N. Hughes and John H. Shaw

(2012) and a B.S. degree in geology fromWashington and Lee University (2006). Herresearch combines geological observations,seismic reflection interpretation, and kinematicand mechanical modeling approaches in un-derstanding structural growth in the context ofpetroleum systems and seismic hazards studies.

John H. Shaw � Department of Earth andPlanetary Sciences, Harvard University, 20 Ox-ford Street, Cambridge, Massachusetts 02138;[email protected]

John H. Shaw is the Harry C. Dudley Professor ofStructural and Economic Geology and chair ofthe Department of Earth and Planetary Sciencesat Harvard University. Shaw received his Ph.D.from Princeton University (advisor: John Suppe),and subsequently worked for Texaco’s Explora-tion and Production Technology Department inHouston, Texas. Shaw’s research focuses on thenature of faulting and fault-related folding in thecrust, with applications to petroleum trap andreservoir characterization and regional earth-quake hazards assessment. Shaw leads an AAPGfield course in the Canadian Rockies, and offersa short course on seismic interpretationmethods based on an AAPG Seismic Atlas(AAPG Studies in Geology 53, coedited byC. Connors and J. Suppe).

ACKNOWLEDGEMENTS

We thank CGGVeritas for their provision of dataand support of the project, which was instru-

ABSTRACT

We present a method of using fault displacement-distanceprofiles to distinguish fault-bend, shear fault-bend, and fault-propagation folds, and use these insights to guide balancedand retrodeformable interpretations of these structures. Wefirst describe the displacement profiles associated with differentend-member fault-related folding models, then provide exam-ples of structures that are consistent with these model-basedpredictions. Natural examples are imaged in high-resolutiontwo- and three dimensional seismic reflection data sets from theNiger Delta, Sichuan Basin, Sierras Pampeanas, and Cascadiato record variations in displacement with distance updip alongfaults (termed displacement-distance profiles). Fault-bend foldsexhibit constant displacement along fault segments and changesin displacement associated with bends in faults, shear fault-bend folds demonstrate an increase in displacement throughthe shearing interval, and fault-propagation folds exhibit de-creasing displacement toward the fault tip. More complexstructures are then investigated using this method, demonstrat-ing that displacement-distance profiles can be used to provideinsight into structures that involve multiple fault-related fold-ing processes or have changed kinematic behavior over time.These interpretations are supported by comparison with thekinematics inferred from the geometry of growth strata overly-ing these structures. Collectively, these analyses illustrate thatthe displacement-distance approach can provide valuable in-sights into the styles of fault-related folding.

mental. We also thank ExxonMobil and Chev-ron, which supported this research. We aregrateful for the insightful comments and sugges-tions of our reviewers, M. Scott Wilkerson andBrent A. Couzens-Schultz, and editors StephenE. Laubach and Rick Groshong. We are also in-debted to Landmark Graphics Corporation, whichprovided software that was critical to this re-search through their Strategic University Alliance

Copyright ©2014. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received January 9, 2012; provisional acceptance March 13, 2012; revised manuscript receivedJune 15, 2012; final acceptance May 31, 2013.DOI:10.1306/05311312006

AAPG Bulletin, v. 98, no. 2 (February 2014), pp. 227–251 227

Grant Program (Agreement 2007-CONT-005191).The AAPG Editor thanks Senior Associate EditorRichard H. Groshong and the following reviewersfor their work on this paper: Brent A. Couzens-Schultz and M. Scott Wilkerson.

DATASHARE 51

Uninterpreted seismic data are available in anelectronic version on the AAPG Web site (www.aapg.org/datashare) as Datashare 51.

228 Displacement Variations and Folding Styles

INTRODUCTION

The ability to classify the structural style of a fault-related foldis essential to many different applications. Understanding thekinematic history of fault-related folds can provide importantconstraints on the geometry and evolution of traps in petro-leum geology. Similarly, various fault-related fold models makedifferent predictions about rock strains that may affect reser-voir properties. Moreover, properly characterizing fault-relatedfolds 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 theunderlying fault, so the ability to identify the structural styleof active fault-related folds is essential to properly defining theslip on an active fault based on an observed pattern of uplift.This is especially important in cases where faults do not reachthe surface and only fold patterns are observable at the surface.

Over the past two decades, kinematic models for severaldifferent types of contractional fault-related folds have beendeveloped and successfully applied to describe a variety ofnatural 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 foldmodels, it is sometimes challenging to properly identify whichclass of models most appropriately applies to a given structure.Additionally, many natural structures are sufficiently complex,or have exhibited different fault-related folding mechanismsover their history, that they are not well explained by a singlemodel. Thus, it is desirable to have an independent meansof discerning the style of fault-related folding present in thestructure. One way of achieving this is by observing displace-ment as a function of distance along the fault (termed thedisplacement-distance profile) because each of themajor typesof contractional fault-related fold models—fault bend, shearfault bend, and fault propagation—has a distinctive pattern inits displacement-distance relationship (Figure 1).

This study will first illustrate the displacement-distanceprofiles expected for end-member fault-related folding mod-els. These predictions will then be compared with a series ofstructures imaged with seismic reflection data to illustratethat the predicted displacement profile for each of these modelsis consistent with patterns of displacement observed in nat-ural structures. By establishing that the displacement profilescharacteristic of each folding model are unique and appli-cable to natural examples, we are then able to interpret thedisplacement-distance profile for a complex, multistage naturalstructure. We restore parts of its deformation history that are

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-foldingmechanisms indicated by the observed displace-ment profile. Analysis of the geometry of overlyinggrowth strata further supports these interpreta-tions, suggesting that analyzing displacement pro-files may be used as an important independentmeans of identifying which fault-related-foldingmechanisms may have been active throughout thedeformation history of a given structure.

PREVIOUS WORK ONDISPLACEMENT-DISTANCE PROFILES

A displacement-distance profile is generated bymeasuring the offset between the footwall andhanging-wall cutoffs in a cross section for severalrock units in a fault-related fold (the displacement),and plotting it as a function of distance along thefault surface from some defined point along thefault (Figure 1). Previous quantitative work ondisplacement profiles has primarily focused onnormal faults (e.g., Muraoka and Kamata, 1983;Kattenhorn and Pollard, 2001), although variationin displacement in contractional structures hasalso been measured in various studies. Williamsand Chapman (1983) established the basic con-cept of a displacement-distance profile for a thrustfault, which was extended by Hedlund (1997) toexamining existing fault-propagation-folding mod-els. Rowan and Ratliff (1988) noted that displace-ment along thrust and reverse faults varies as afunction of structural style and the presence of fault

bends. Other researchers have sought to charac-terize displacement profiles for natural structures.McConnell et al. (1997) made observations ofdisplacement-distance profiles in field outcropsin the Appalachians, whereas Briggs et al. (2006)measured variations in displacement on structuresin the Niger Delta. Additionally, a significant bodyof previous work on along-strike variations in dis-placement on thrust faults (for example,Wilkerson,1992; Wilkerson et al., 2002; Bergen and Shaw,2010) has provided insight into the lateral propa-gation, linkage, and termination of thrust faults.

The goal of our study is to develop a com-prehensive understanding of the patterns of dis-placement along faults in the various classes offault-related folds, in a manner that can inform in-terpretations of natural structures. We will extendthe analysis of displacements of end-member fault-propagation folds from previous studies (Hedlund,1997) to a broader range of structural styles andthen compare these profiles to those of naturalstructures in a variety of geologic settings.

DATA SETS

Structures that are used as examples in this arti-cle come from a variety of geographic locationsand contractional tectonic environments. Thefaults studied were mapped in two- and three-dimensional (2-D and 3-D) seismic reflection datasets from the Niger Delta, offshore Nigeria in theGulf of Guinea (2-D and 3-D), the Sichuan Basin,

Hughes and Shaw 229

south-central China (2-D), the Cascadian accre-tionary prism off the western shore of VancouverIsland, Canada (2-D), and the Sierras Pampeanas,in the foreland of the Andean mountains in north-ern Argentina (2-D). Structures analyzed in thisstudy were chosen based on the following char-acteristics: outstanding seismic imaging of the sed-imentary layers, minimal ambiguity regarding faultgeometry, and readily correlated stratigraphy oneither side of the fault. The lattermost conditionwasensured by either correlating stratigraphy across a2-D seismic grid survey or 3-D seismic survey,where available. In cases where this was not possi-ble, examples were chosen in which the stratigra-phy has a sufficiently distinctive seismic characterthat correlation across the fault was unambiguous.

The Sichuan Basin in south-central China is acontinental basin in a convergent tectonic setting.The basin lies at the eastern margin of the Hima-layan uplift, and is bounded on all sides by fold-and-thrust belts (Burchfiel et al., 1995; Roydenet al., 1997). The structure analyzed in this studyis in the interior of the basin, but associated withdeformation propagating outward from the Long-menshan fold-and-thrust belt, which defines thenorthwestern margin of the basin. The lithology ofthis part of the basin consists of Paleozoic andMesozoic carbonates interbeddedwith siliciclastics(Meng et al., 2005). The fault in this study solesinto a detachment localized in a Triassic evaporitelayer (Hubbard et al., 2010).

The Niger Delta is a linked extensional andcontractional passive-margin system that formed asa result of sedimentary loading from the outflow ofthe Niger River into the Gulf of Guinea. The sed-iments in this system are composed of Cenozoicmarine shales and more coarsely-grained turbiditesthat overlie the attenuated transition between Af-rican continental crust and oceanic crust (Damuth,1994; Bilotti and Shaw, 2005; Corredor et al.,2005a). Gravity-driven collapse of the sedimentsdeposited in the Niger River Delta results in ac-tive extension onshore and on the continental shelf.This displacement is linked through a detachmentin overpressured shale units to contractional de-formation at the toe of the system in deep water.The lithologically weak marine shales promote the

230 Displacement Variations and Folding Styles

development of shear in many of the structures,which is manifest in the geometries of the struc-tures that develop (Suppe et al., 2004; Corredoret al., 2005b).

Structures within the accretionary prism ofthe subduction zone in Cascadia, off the westerncoast of Canada, were also analyzed in this study.These data were acquired as part of a 2-D seismicreflection campaign on the part of the accretionaryprism offshore Vancouver Island in Ocean DrillingProgram (ODP) Leg 146 (Davis and Hyndman1989; Hyndman et al., 1990, 1994). Subduction ofthe Juande Fuca oceanic plate (which is the remnantof the much more extensive Farallon plate) undercontinental North America at this location has per-sisted since the Eocene (Riddihough, 1984; Atwater,1989; Hyndman and Hamilton, 1993; and others).Current convergence rates are about 45 mm/yr(1.77 in./yr), orthogonal to the plate margin andthe coastline of British Columbia (Riddihough,1984, DeMets et al., 1990). The structures inves-tigated in this article are the westernmost frontalthrusts of the active accretionary prism overlyingthe subduction zone.

Finally, we include an example of a basement-involved structure from the western Sierras Pam-peanas region of northern Argentina. In this sec-tion of the subduction zone, the Nazca platesubducts at a nearly horizontal angle (Barazangi andIsacks, 1976) at a rate of approximately 10 cm/yr(3.94 in./yr) (Minster and Jordan, 1978; DeMetset al., 1990; andothers).Associatedwith this shallow-angle subduction, contractional deformation ex-tends several hundred kilometers further into thecontinent and is characterized by predominantlybasement-involved thrust faulting. Deformationof upper Paleozoic and Cenozoic sediments over-lying a basement consisting of Precambrian meta-morphic and Paleozoic plutonic rocks has occuredfrom about 10 m.y. to the present (Jordan andAllmendinger, 1986), primarily throughwhat havebeen characterized as basement-involved fault-propagation folds (Zapata and Allmendinger, 1996;Jordan et al., 2001).Theparticular structure analyzedfor this study lies in the Bolsones embayment of theBermejo basin, in the transitional region between thepre-Cordillera and the Sierras Pampeanas, north of

San Juan, Argentina. Studies of syntectonic deposi-tion of sediments suggest that thick-skinned thrustsystems in this region have been active for at least thepast 5 m.y. (Zapata and Allmendinger, 1996).

METHODS

Displacement was measured as the distance alongthe fault between the mapped terminations of agiven stratigraphic layer at the fault surface (suchas is done in Williams and Chapman, 1983, andothers). This is contrasted with a simple mea-surement of throw, the vertical component ofdisplacement, which has been used as a proxyfor displacement in some previous studies (e.g.,Mansfield and Cartwright, 1996). Although thelatter approach has the benefit of being measure-able without relying on quality of imaging imme-diately adjacent to the fault surface, it is not ap-propriate for the structures in this study becausethe dip and nonplanarity of the faults, as well as thestyle of folding adjacent to the fault, have a signif-icant influence on the relations between uplift andslip. We have ensured that the quality of the seis-mic reflections is sufficiently high that the uncer-tainty in the geometry of fault and horizon cutoffsis minimal and does not significantly impact theoverall interpretations. We choose as the origin forour measurements the intersection of the lowestobservable reflector in the footwall with the faultsurface (P in Figure 1), with distance up the faultas positive; the choice of a different origin wouldserve to shift the plot along the x axis, but wouldnot alter the observed trend.

Numerous factors contribute to uncertaintywhen interpreting reflections. Because the faultsanalyzed in this study have shallow dips, the anglebetween the stratigraphic layers and the fault issmall, so a small change in the fault dip can createa significant change in the apparent displacementmeasured along the fault. As a result, uncertainty inthe fault dip is one of the largest potential sourcesof error in the measurement; this is the source oferror quantified and reported in this study follow-ing the method described by Bergen and Shaw(2010). The favored, ormost likely, fault geometry

is plotted in black on each displacement-distanceprofile. The minimum and maximum fault dipsthat are permissible from the seismic reflection dataare then interpreted, and measurements of dis-placement of the stratigraphic layers across eachof the end-member fault geometries are reportedas the minimum and maximum fault dip on eachof the displacement-distance profiles as a means ofcharacterizing the uncertainty in the measurement.

Although uncertainty because of fault geom-etry is the primary source for this measurement,additional sources of uncertainty exist that aredifficult to quantify but which may affect the re-liability of the measurement. Special care must betaken to minimize contributions from these fac-tors. For example, it is challenging to quantify howmuch uncertainty results from tracing a reflectorthrough a poorly imaged zone; these shadow zonesare common in the footwall near a fault becauseof perturbations to the velocity field in the hang-ing wall and migration-related processing effects(Kleyn, 1983). Additionally, changes in the thick-ness and internal structure of a stratigraphic unitcan lead to the bifurcation of a seismic reflector(Sherriff, 1977), which can contribute to uncer-tainty in how to extend the interpretation of thestratigraphic layer through the bifurcated region.Additionally, out-of-the-plane displacement on afault may lead to variations in measured displace-ment along the fault in cross section. If the layersand fault are perfectly planar, the displacement-distance profile measured records the dip-slip com-ponent of displacement. However, if the layers arefolded or change thickness along strike, oblique dis-placement could result in changes in the trends ob-served in the displacement-distance relationship, soone should carefully consider the influence of thisfactor in the case of a particular structure. Each ofthese factors can contribute to local changes inobserved displacement gradients. The structures inthis studywere chosen specifically to haveminimalcontributions from each of these sources of error.

Other factors can contribute to uncertainty inthe absolute value of the measured displacement,but have little effect on the overall trend of thedisplacement gradients; as this study is interested inthe 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 ofthe displacement along the faultas a function of distance along thefault, termed the displacement-distance profile, for each struc-tural style, illustrates the trends indisplacement that characterizeeach model. Portions of the faultfor which displacement cannotbe measured in the particularexamples shown in A–C (causedby the choice of specific fold/faultcutoff geometries), are shown indashed lines to illustrate the moregeneral trend in displacementfor each structural class.

addressed in this study. These factors can includeuncertainties in seismic velocity in the depth con-version process, or other artifacts of processingthe seismic data, including the challenge of ac-counting for lateral variations in velocity and out-of-plane energy in 2-D surveys. Uncertainties inthe interval velocities used in converting the seis-mic data from time to depth can range as much as±5% (Sherriff, 1977) and could create variations inthe absolute values of displacement measurementsof as much as 10%, although the relative smooth-ness of the velocities in these regions would ensurethat the trends in displacement gradient observedin the study would remain unaltered. Addition-ally, the imaging resolution of the seismic data isa fundamental limit on the scale of measurementpossible; given dominant wavelengths of seismicreflection data between 100 and 300 m (328 and984 ft) (for the depth range of interest to this study)and the ability to resolve features with minimumvertical separation of one-fourth wavelength, fea-tures between 25 and 75 m (82 and 246 ft) inthickness represent the minimum resolvable fea-ture. This source of uncertainty associated withthe resolution limit of seismic data is sufficientlysmall compared to uncertainties in fault dips andcutoff geometries that it is not explicitly consid-ered in the calculation of error for this study.

232 Displacement Variations and Folding Styles

MODEL PREDICTIONS AND EXAMPLES

Fault-related folds develop as strata pass over bendsin faults, are deformed above propagating fault tips,and/or are folded above detachment surfaces. Thesestructures are common in orogenic and passive-margin fold-and-thrust belts throughout the world(for example, Rich, 1934; Rodgers, 1950, 1990,1991; Suppe, 1983; Suppe and Medwedeff, 1990;Erslev, 1991; McConnell, 1994; Shaw and Suppe,1994; Erslev and Mayborn, 1997; Corredor et al.,2005a; Shaw et al., 2005; Yue et al., 2005; Hubert-Ferrari et al., 2007). In this study, we examine thedisplacement-distance profile characteristics ofthree main types of fault-related folds: fault-bendfolds, shear fault-bend folds, and fault-propagationfolds. Each of these structural styles is character-ized by a distinct fold geometry and distribution ofdisplacement along the fault (Figure 2).

Fault-Bend Folding

Fault-bend-folding theory was developed by Suppe(1983) as a geometrically and kinematically consis-tent way of predicting the geometry of parallel foldsthat develop as strata are displaced over a fault bend.The theory indicates that displacement remains

Figure 3. (A) A kinematicmodel of a fault-bend fold dem-onstrates the decrease in dis-placement across an anticlinalfault bend, from S0 below thebend to S1 above the bend. Dis-tance is measured from point P.(B) The displacement-distanceprofile for this structure shows alinear gradient between thesetwo displacement values, as ma-terial within the fold limb has onlyundergone folding for a part ofits structural history. Note the lo-cations of the active (1) and pas-sive (2) axial surface locations inthe cross section and displacement-distance profile.

constant along planar fault segments and changesabruptly at fault bends. In the case of a simplethrust ramp extending to an upper detachment,the theory predicts constant displacement alongthe fault ramp. Similarly, displacement on the up-per detachment above the bend is also the sameeverywhere, although it is generally less than dis-placement on the ramp. The magnitude of thechange in displacement is dependent on the faultgeometry and stratigraphic cutoff angles and canbe predicted by quantitative fault-bend-foldingtheory. Based on this, it might be expected that adisplacement profile across a fault bend would becharacterized by two zones of constant slip sepa-rated by an immediate change at the fault bend.However, what one actuallymeasures are two zonesof constant displacement, separated by a linear gra-dient of displacement in a finite zone beginning atthe fault bend. This observation highlights the factthat displacement, and not slip, is what is actuallymeasured along the fault when matching hanging-wall and footwall cutoffs. Although slip along thefault changes instantaneously at the fault bend,displacement is the result of cumulative motion ofthehangingwall over the footwall.Material that is inthe sloped region of the displacement profile beganbeneath the fault bend, but after some increment ofslip, passed over the fault bend; therefore, its dis-placement reflects that it experienced deformationin both slip regimes over parts of its deformationalhistory.

As fault-bend-folding theory prescribes a uniquerelationship between the displacement observedalong the fault on either side of a fault bend (the Rvalue in Suppe, 1983) for a given fault geometry,the manner in which displacement changes at afault bend is also predicted. The displacement ob-served for a given layer that is always above, or al-ways below, the fault bend during the displace-ment history is equal to the displacement on theunderlying segment of the fault. The ratio of thisdisplacement fully above and below the fault bendcan be predicted by the R value, or the ratio of thedisplacement above (S1) to the displacement be-low (S0) the fault bend, which is uniquely derivedfor a given structural geometry using fault-bend-folding theory. The zone of displacement gradientcan also be quantified.On a plot of displacement asa function of distance up the fault, the displace-ment gradient region caused by the fault bend be-gins at the location of the bend and extends for aregion equal in length to S0.Given that the change indisplacement across this region is S1-S0, the slope ofthis displacement gradient is (S1-S0)/S0, which isequivalent to R-1 (Figure 3). The displacement atany given point in the gradient is straightforward topredict because the gradient is linear.

Examples of Fault-Bend-Folding Behavior

To test these predictions of fault-bend-fold theory,we first generate a displacement-distance profile of

Hughes and Shaw 233

Figure 4. (A) A discrete-elementmodel (DEM) of a fault-bend fold.(B) The displacement-distanceprofile for the DEM model (blackdots) agrees very well with thedecrease in displacement pre-dicted by the R-1 value derivedfrom fault-bend-folding kinemat-ics (Suppe, 1983) for this fault-bend geometry (−0.15 for thisexample, gray dashed line).

mechanical model of a fault-bend fold developedusing the discrete-element approach after Beneshet al. (2007) and Benesh (2010). This numericalmodel was developed using the Particle FlowCodein Two-Dimensions (PFC-2D) (Itasca, 1999), a com-mercial discrete-element modeling code distributedby the Itasca Consulting Group. Layers of rock aremodeled as aggregates of circular particles that in-teract with friction and cohesion at their contactsbased on the method described by Cundall andStrack (1979), with values assigned to emulate thebulk mechanical properties of rocks in laboratorysettings (Itasca, 1999). The aggregate material iscontained bywalls that serve to define a ramp-to-flatfault geometry necessary to produce an anticlinalfault-bend fold, to drive deformation from thehinterland, and to confine the particles to the re-gion of interest. As the hinterland wall is displacedto the right, the rock material must deform andpass over the fault bend, and the foreland wallmoves such as to relieve tectonic stresses whilemaintaining the confining stress on the rocks ad-jacent to it (see Benesh, 2010, for a more thoroughdescription of the modeling approach).

234 Displacement Variations and Folding Styles

The value of examining displacement patternsin a mechanical model is that both the displace-ments along the fault segments and the fold ge-ometries are emergent model behaviors and can bemeasured very precisely. The model reproducesthe primary features of fault-bend-fold theory: afold limb of relatively constant dip and constantlayer thickness, with an anticlinal axial surface tiedto the fault bend and a passive synclinal axial surfacethat has been translated along the upper detach-ment (Figure 4A). Measurement of the offset ofstratigraphic layers in the hanging wall and foot-wall of the model display a constant displacementalong the fault ramp and detachment, and a linearlydecreasing displacement in the fold limb region.Fault-bend-folding theory predicts constant dis-placement along the ramp and detachment, with agradient of −0.15 in the fold limb region (calcu-lated as R-1 for the prescribed fault geometry),which is in excellent agreement with the observeddisplacement distribution (Figure 4B).

In addition, we evaluated the displacement-distance relationship for several natural fault-bendfolds to assess how well they conformed to the

Figure 5. (A) Uninterpreted,migrated, depth-converted seis-mic reflection data from theSichuan Basin, China. (B) Inter-pretation of the seismic reflectiondata, with the faults (red), strati-graphic layers (a through k), anduncertainty of fault location (blackdashed lines). (C) Displacement-distance profile of data (blue),with minimum (white) and max-imum (gray) measurementsbased on the range of possiblefault dips, with light gray linesconnecting minimum, preferred,and maximum displacementvalues for a given stratigraphiclayer and a linear best fit to thepreferred values (dark-graydashed line). The range in whichthe possible fault geometrieswere chosen in the constructionof the low and high estimatesof uncertainty are indicated(black dashed lines) to illustratethe sensitivity of the measure-ment to uncertainties in faultgeometry. Data courtesy of CNPC;modified from Shaw et al., 2005,chapter 1A-2.

kinematic theory. In the case of a simple thrustramp from the Sichuan Basin, China (Figure 5), weobserve,within the uncertainty of themeasurement,that the displacement along the thrust ramp is con-stant, as predicted by the fault-bend-folding model.

In contrast, when material in the hanging wallmoves across a fault bend, the theory predicts thata fault-bend fold is formed, and the amount ofdisplacement along the fault varies as describedabove. To examine this behavior, we analyzed ananticlinal fault-bend fold overlying a fault with twodistinct anticlinal bends from the southern NigerDelta (Figure 6A). Measurement of the stratigraphic

layers offset across this fault demonstrates that dis-placement decreases across each of the two anti-clinal fault bends (Figure 6B). Based on geometricfault-bend-folding relationships, the angle betweenbedding and the fault below the bend (q) and thechange in fault dip at the bend (f) define the ex-pected R-value for the change in displacement ateach fault bend. This yields predicted gradients indisplacement of −0.13 and −0.23 above the lowerand upper fault bends, respectively. The measureddisplacements are consistent with these predic-tions of displacement gradients, within the un-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 faultsurface (red), fault bends (1 and 2), and stratigraphic horizons (a through i). Distances are measured from the intersection of the lowestlayer 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 gradientspredicted by fault-bend-folding kinematics (Suppe, 1983), are reported for each segment. Data courtesy of Mabon Limited; modifiedfrom 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 foldingtheory. Furthermore, a fault-bend-fold model gen-erated from the observed fault geometry and back-limb dips that is consistent with these displacementgradients predicts the dips of the forelimb seg-ments to within ±1° (variation is caused by non-linearity of the limbs), indicating that the structuralgeometry is well represented by the fault-bend-folding model.

Shear Fault-Bend Folding

Structures that form in regions in which a strati-graphic zone of finite thickness undergoes distrib-uted shear deformation have been recognized as

236 Displacement Variations and Folding Styles

exhibiting unique geometric relationships. Suchstructures form in regions where a weak lithologyis involved in the deformation, such as salt (ex-amples include offshore Brazil, Angola, Gulf ofMexico, Zagros) or overpressured shale (southernCaribbean, Niger Delta, BaramDelta, and others).Shearing in this stratigraphic interval generates ageometrically-distinct class of structures that arecharacterized by a backlimb that dips more shal-lowly than a fault-bend-folding model for the samefault geometry (Suppe et al., 2004). Based onshear fault-bend-folding theory, the amount of dis-placement measured in this interval increases withdistance up the fault ramp throughout the shear-ing interval. Above the shear interval, parallel fold-ing results in constant displacement along the ramp

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 shearinterval, 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) forpure 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 changingslip and displacement along planar fault segmentsthat strongly contrasts with standard fault-bend-fold theory, which prescribes changes in slip anddisplacement only across fault bends.

For a given fault dip (q), backlimb dip (d), andheight of the shearing layer above the detachment(h) (Figure 7A, B, sheared interval highlighted),a displacement gradient and maximum displace-ment can be calculated for a simple shear andpure shear fault-bend-fold model that is consis-tent with the prescribed geometry. Based on thesegeometric parameters, the shear angle can becalculated:

a ¼ cot−1�

sind2C

��1

sind cotqþ 1− cosd

�2

−1

sind cotqþ 1− cosd

����

where C is 1 for pure shear and 1/2 for simpleshear. Once the shear angle is known, the slip (s)can be calculated as follows:

s ¼ h tanacosqþ tan d=2ð Þ sinq

as derived in the appendix of Suppe et al. (2004).This slip value represents the displacement for thelayer at the top of the shear interval and all layersabove it, which undergo parallel folding in themodel.

The displacement at the top of the shear sec-tion can then be used to determine the displace-ment gradient in the displacement-distance profilein the sheared interval (Figure 7C). For the end-member simple shear model, as described by Suppeet al. (2004), displacement along the fault is zeroat the base of the thrust ramp, and s (as calculatedabove) at a distance of h/(sin q) along the fault.Therefore, the change in displacement (s) over thedistance from the base of the ramp to a distance ofh/(sin q) results in a displacement gradient of s × sinq/h in the shear interval. For pure shear, the dis-placement along the ramp does not decrease tozero, but rather, to a value defined by the amountof slip, s1, at the base of the ramp. A graph of the

238 Displacement Variations and Folding Styles

relationship between backlimb dip (d) and dis-placement gradient for lines of constant fault dip isshown in Figure 7D and E for pure and simpleshear, respectively. Given an observed fault dipand backlimb dip for a natural example, thesegraphs can be used to determine the displacementgradient for pure shear and simple shear modelsthat match the prescribed fault and backlimb ge-ometry. Thus, a comparison of the observed dis-placement gradient, in conjunction with other ob-servations, can help to determine whether thestructure in question is better modeled as a pureshear or simple shear fault-bend fold. Note that theexisting pure shear fault-bend-folding theory doesnot explicitly define the geometry of the layers inthe shear interval. As such, a balanced, permissible,but nonunique solution is given here (Figure 7B).Because the displacement gradient is dependent onthe slip at the base of the ramp and the top of theshear interval, the displacement gradient is unlikelyto change greatly for other, perhaps equally validsolutions; however, one can envision a case wheredeformation in the sheared interval is accommo-dated in such a way that the increase in displace-ment in the shear interval is nonlinear.

Example of Shear Fault-Bend-Folding Behavior

To assess if the displacement pattern predicted byshear fault-bend-fold theory is observed in naturalstructures, we assess a contractional fault-relatedfold from Cascadia, off the western coast of Van-couver Island (Figure 8A), that illustrates the com-mon features of this structural style (Suppe et al.,2004). Measured displacement along the fault(Figure 8B, blue) demonstrates that displacementincreases greatly through the lowest stratigraphiclayers (a through f), increases gradually in the over-lying section (f through k), and that above that in-terval (k through p), displacement along the faultramp is relatively constant. A line-length (palin-spastic)method (Shawet al., 2005) ofmeasuring theshear profile of the structure (Figure 8B, red) re-veals a similar trend. Thus, we conclude that theshear within this structure is responsible for theobserved displacement gradient on the thrustramp.

Figure 8. (A) Seismic reflectionprofile of a shear fault-bend foldin the Cascadia accretionary prism,offshore Vancouver Island, west-ern Canada, with interpreted fault(red) and stratigraphic layers athrough p. Axial surfaces (1) and(2) bound a fold limb with a dipof 14° and (2) and (3) anotherdip panel of 7°. The location of thetop of the shear interval is definedby the place where the axial sur-face intersects the fault plane,so (2) corresponds to a shearinterval that reaches the heightof layer f, and is related to thedevelopment of the steeper dippanel, whereas (3) correspondsto a shear interval that extendsup to layer k and is related tothe shallower dip panel. A sim-ple shear fault-bend-fold modelwas constructed based on thesegeometric observations (inset).(B) Displacement-distance profilefor data (blue), minimum (white)and maximum (gray) estimates,the model displacement (dark-blue dashed line). (C) Palinspasticestimate of shear (red) and modelshear profile (dark-red dashedline). Locations of stratigraphiclayers that mark transitions inthe shear interval (k and f) arehighlighted. Data modified fromHyndman et al. 1994 (line 89–04),from Shaw et al., 2005, chapter1B-4; uninterpreted seismic datamay be accessed through AAPGDatashare 51 (http://www.aapg.org/datashare/).

A shear fault-bend-foldmodel was constructedusing the kinematic theory (Suppe et al., 2004)based on the fault geometry and the identificationof the shear interval from the displacement gradi-ent measurements (Figure 8, inset). As the dis-placement-distance profile indicates that displace-ment decreases to zero at the base of the fault, weconclude that a simple shear fault-bend-foldingsolution is appropriate for this structure. The sim-ple shear model is further supported by the fact

that in the seismic data, the synclinal axial trace(labeled 1 in Figure 8A) appears to be linear andintersects the ramp at the point where it also in-tersects the detachment, which is consistent withthe prediction for a simple shear fault-bend fold,but not a pure shear fault-bend fold (e.g., Corredoret al., 2005b, see Figure 7A and B for a compari-son). The model was constructed to match theobserved fold limb dips of 14° (between the axialsurfaces labeled 1 and 2) and 7° (between 2 and 3)

Hughes and Shaw 239

in the backlimb, resulting in shear angles (a) of 29°and 12°, and displacement gradients of 0.44 and0.17, respectively. The displacement-distance pro-file for this model is broadly consistent with boththe palinspastic approach and the displacementgradient approach, although note that the addi-tional displacement measured in the lowest strati-graphic interval of the displacement distance pro-file (a through f) is caused by deformation in thefootwall, which is not considered in the model.Combining these two approaches provides a use-ful means of highlighting such aspects of the de-formation in natural structures that are not cap-tured in the kinematic model.

Many studies of fault displacement considerthe location of the maximum displacement as rep-resentative of the point at which the fault initiated(Ellis and Dunlap, 1988; Briggs et al., 2006; andothers). This is based on the assumption that, as thefault grows and slip accumulates on the structure,the place where the fault first initiated will accu-mulate the greatest amount of slip. As the point ofmaximum displacement on many natural faults isobserved to be in the center of the structure, thishas provided the motivation for the developmentof bilateral, or double-edged, fault-propagation-folding models (Kattenhorn, 1994; Tavani et al.,2006). We propose that in some cases, pure or sim-ple shear of a layer of finite thickness in the hangingwall can produce a displacement maximum in thecenter of a fault, irrespective of where the faultnucleated. In the previous example (Figure 8A),the fold and fault geometry suggests that the struc-ture is a shear fault-bend fold, and the displace-ment gradient observed is also consistent with thatmodel. In a shear fault-bend-folding model, thefault propagates to its full extent before significantdisplacement has accrued. This suggests that shearshould be considered and tested before inferringthat the location of maximum displacement is in-dicative of the location of fault nucleation.

Fault-Propagation Folding

Fault-propagation folds are an important class ofstructures that form at the tips of faults as theypropagate upward through sedimentary layers.

240 Displacement Variations and Folding Styles

These folds develop as slip is consumed, and theresulting folds commonly have steeply dipping oroverturned forelimbs that are pinned to the faulttip. Most fault-propagation folds have many qual-itative similarities (Shaw et al., 2005):

1. A highly asymmetric shape, with a relativelysteep and narrow forelimb and a longer, moregently dipping backlimb;

2. Slip that decreases along the fault toward thefault tip; and

3. A syncline pinned to the upward projection ofthe fault tip.

Many theories have been developed that pro-vide a geometric and kinematic model of defor-mation for these structures, the most commonlyapplied of which include constant-thickness andfixed-axis fault-propagation folding (Suppe andMedwedeff, 1990), and trishear folding (Erslev,1991; Allmendinger, 1998). These models makespecific predictions about the shape of the fold inrelationship to the amount of displacement andthe fault dip. In addition, a variety of othermodelshave been developed to address a specific subsetof the natural structures or to attempt to explaina specific observation (for example, basement-involved models by McConnell, 1994; Narr andSuppe, 1994; Spang and McConnell, 1997; vari-able forelimb thickness by Jamison, 1987; exter-nally applied shear in Mitra, 1990; forelimb dipsteepening with increasing slip in McConnell, 1994;complex geometries in Chester and Chester, 1990;mixed-mode structures in Erslev and Mayborn,1997; and double-tipped fault propagation inKattenhorn, 1994, and Tavani et al., 2006).

Fault-propagation folds are generally charac-terized by regions of constant slip at the base ofthe thrust ramp, and decreasing displacement alongthe upper part of the fault (Figure 1). Each of theexisting kinematic models for fault-propagationfolding generates distinct predictions for fold ge-ometry, uplift, and displacement (Figure 9A–C).However, for anymodelwith a constant propagation-to-slip ratio (which is required by constant-thicknessand fixed-axis models and may be specified intrishear models), the gradient in displacement is

Figure 9. (A–C) Kinematic models of the most commonly applied fault-propagation-folding models. (D) Displacement-distance profilefor constant-thickness (circles) and fixed-axis (squares) models of varying fault dip, illustrating that the models are the same at 29°; athigher fault dips, constant-thickness models have shallower gradients, and at steeper dips, constant-thickness models have steepergradients. (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-ear trend depends on model type, propagation-to-slip (P/S) ratio, and fault dip. We examine theserelationships in more detail for the constant thick-ness, fixed axis, and trishear models.

For models of constant-thickness fault-propaga-tion folds developing from a fault stepping up froma detachment, displacement gradient changes as afunction of fault dip because (1) for a given amountof shortening, the distance between bed cutoffsthat have been displaced along the fault varies as afunction of the dip of the fault on which slip isbeing accommodated, and (2) fault-propagation-folding-related strain in the hanging wall, reflectedby the tightness of the fold, varies as a function of

fault dip, as prescribed by the models. As fault dipincreases, the first factor decreases the displace-ment gradient. However, the fold tightness alsodecreases, so the second factor increases the dis-placement gradient. These factors do not entirelyoffset, so overall, displacement gradient decreaseswith increasing fault dip. Additionally, P/S ratioincreases with increasing fault dip for constant-thickness models. In fixed-axis models, both ofthese factors are at play, but layer thickness changesin the forelimb of the fault-propagation fold is anadditional factor. The effect of this additional fac-tor is such that displacement gradients and P/Sratios for fixed-axis fault-propagation folds are in-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 stratigraphiclayers (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 accessedthrough AAPG Datashare 51 (http://www.aapg.org/datashare/).

For fixed-axis and constant-thickness mod-els, a given initial layer and fault geometry leads tothe development of a unique fault-propagation-fold limb geometry, P/S ratio, and displacementgradient. However, because the trishear modelinherently has more variable parameters, a givenfault and layer geometry does not determine aunique fold geometry without specifying addi-tional model attributes. Therefore, to compare thisapproach to the previous ones, trishear modelswith the same fault geometry, layer geometry,and P/S ratios were generated. The displacementgradients for these models match those for thecorresponding fixed-axis and constant-thicknessmodels (Figure 9E), indicating that fault geometryand P/S ratio are the factors that determine the dis-placement gradients for trishear fault-propagation-

242 Displacement Variations and Folding Styles

fold models, as is true of other fault-propagation-folding models.

Examples of Fault-Propagation Folding

To assess if natural structures exhibit displacementgradients predicted by fault-propagation-fold mod-els, we examine a structure from the northernNigerDelta (Figure 10A) that is imaged in high-qualityseismic reflection data. Qualitative observations,such as folding unassociatedwith a fault bend andan active synclinal axial surface tied to the upwardextension of the fault, serve to identify this struc-ture as a fault-propagation fold. The displacementprofile for this structure exhibits a distinctive linearnegative gradient along the fault (Figure 10B),with displacement values that approach zero. This

Figure 11. Kinematic modelof a fault-propagation fold justbefore (A) and after breakthoughalong the same fault trajectory(B) and a steepened fault tra-jectory (C). (D) Displacementdistance profiles correspondingto each case (labeled A–C):The profile for A (black), whereD1 indicates the maximum offseton the fault prior to break-through; B (dark gray), where D2indicates the amount of dis-placement accrued after faultbreakthrough; C (light gray),which demostrates the slightmodification of the slopecaused by fault-bend folding(R-1 = 0.08 for this fault-bendgeometry).

pattern is generally consistent with fault-propagation-folding models and, thus, helps confirm our inter-pretation of this structure.

The location of the fault tip may be predictedby the observed displacement gradient based onwhere the displacement-distance curve projects toa zero displacement value. The predicted fault tiplocation is seemingly consistent with the seismicimage because there are truncated reflectors be-low the fault along this point but continuouslyfolded horizons above. The ability to predict thislocation may be useful in cases where the delinea-tion of a petroleum trap relies on the position ofthe fault tip. This approach may prove particu-larly useful in structures in which seismic reflectiondata quality near the fault tip is poor; because fault-propagation-fold forelimbs are commonly steeplydipping (and difficult to image in seismic reflec-tion), this situation is common for this class ofstructures. Special care must be taken to considerfaults that propagate through growth stratigraphyor unconformities because they will display morecomplex displacement patterns; specifically, faultpropagation through the pregrowth to growth tran-sition will be manifest as a decrease in displace-ment and displacement gradient, the details ofwhich are dependent on sedimentation and fault-propagation rates.

In some cases, the faults may propagate throughthe folded forelimb to the Earth’s surface, form-ing what is typically called a breakthrough fault-propagation fold (Suppe and Medwedeff, 1990;Shaw et al., 2005). These structures still display thefolding associated with their fault-propagation-folding history (Figure 11A), but the hanging wallis translated up the fault ramp because of additionaldisplacement (Figure 11B, C). This results in ob-served displacements that reflect the contribu-tions from both parts of the structure’s history; theexpected negatively-sloping displacement-distancerelationship caused by fault-propagation folding,which is offset by the amount of displacement ac-crued after the fault broke through to the surface.Thus, on a displacement-distance profile, a break-through fault-propagation fold has a negativelysloping region that transitions at greater distance upthe fault to a roughly horizontal line reflecting theslip that occurred after breakthrough (Figure 11D).The amount of slip that occurred after the break-through is defined by the height of this horizontalsegment of the displacement-distance profile (D2

in Figure 11C), and themaximum amount of slipthat occurred during fault-propagation folding (D1)can be estimated by the total slip (D1 + D2) minusthe breakthrough slip (D2), after considering anyfault-bend-related changes in displacement (the

Hughes and Shaw 243

Figure 12. (A) Seismic reflec-tion profile of a breakthroughfault-propagation fold from theSierras Pampeanas, Argentina,with fault (red) and stratigraphiclayers (a through i) interpreted,and predicted fault tip location,T. (B) Measured displacement-distance relationship (blue), withminimum (white) and maximum(gray) estimates for layers athrough i. Linear fit projects tothe predicted fault tip location(red point, T). Data courtesy ofBHP; modified from Shaw et al.,2005, Chapter 1B-2; uninter-preted seismic data may be ac-cessed through AAPG Datashare51 (http://www.aapg.org/datashare/).

influence of displacement across a fault bend onthe solution may be observed by comparing thedisplacement-distance relationships for the struc-tures in Figures 11B, C). Notably, in these break-through structures, the place where the negativelysloping part of the displacement-distance curvewould intersect with the x-axis corresponds to afault tip position that is above the land surface orsea floor at the time of deformation, which wouldresult in a fault that would be observable at the sur-face. Thus, even in cases where the displacement-distance profile is incomplete because of poor data,one can commonly distinguish fault-propagationfolds that have and have not broken through to thesurface.

We illustrate the patterns of displacement in abreakthrough fault-propagation fold using an exam-ple from the Sierras Pampeanas region of Argentina.The seismic image defines this structure as a tight,asymmetric fold with a steep forelimb fold that isnot associated with a fault bend (i.e., not a fault-bend fold) (Figure 12A). Measurement of the

244 Displacement Variations and Folding Styles

displacement variation with distance indicates anegative linear trend, which is consistent with theinterpretation of this structure as a fault-propagationfold (Figure 12B). Although the data quality isinsufficient to define displacements above hori-zon i, the projection of the negatively slopingtrend indicates that the location where displace-ment would reach zero is substantially above theland surface (Figure 12A, B). Thus, this structurecan be reasonably interpreted as a breakthroughfault-propagation fold, with as much as 800 m(2600 ft) of slip occurring after the fault had bro-ken through using the method of estimating slipshown in Figure 11.

Applications to More Complex Structures

Previous sections have outlined the predicted dis-placements for different contractional fault-relatedfolding styles and illustrated that these displace-ment-distance relationships are observed in naturalstructures from a variety of tectonic settings. Here,

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 featuresdiscussed in the text: (I) intersection of axial surface and fault, indicating the top of the shear interval, (II) anticlinal fault bend, (III) drapesedimentation, (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 thedevelopment of these structures, with structural styles determined from observations from the displacement-distance plots.

we illustrate the application of this method to struc-tures with more complex deformation historiesto highlight the utility of displacement-distancemeasurements in defining the structural style andtectonic history of structures that combine differ-ent fault-related folding processes.

Our example consists of two thrust sheets andassociated fault-related folds from the deep-waterfold and thrust belt of the Niger Delta (uninter-preted and interpreted seismic profiles, Figures 13A,B). The hinterland structure (hereafter referred toas A) has a displacement-distance profile charac-terized by a region at the base of the fault withincreasing displacement, a constant-displacementregion in the middle of the fault, and decreasingdisplacement along the uppermost fault that is as-sociated with a fault bend (Figure 14A). This pat-tern suggests that this structure involves compo-nents of fault-bend folding and shear fault-bendfolding. The upward-increasing displacements atthe base of the ramp are consistent with shear fault-bend folding in the backlimb of the structure asso-ciated with movement of hanging-wall strata abovethe fault bend defined by the base of the thrust

246 Displacement Variations and Folding Styles

ramp. The increasing displacement gradient occursfrom horizons a to b, consistent with the region ofshear defined by shear fault-bend-folding theory.Based on the theory, the top of this shear interval isidentified by the stratigraphic horizon that intersectsthe fault at the location where the anticlinal axialsurface also meets the fault (layer b intersects thefault at location I in Figure 13B). Above this shearedinterval, the displacement-distance profile indicatesa constant displacement between layers b and d,which suggests that parallel folding occurs in thisregion. The region above this, from d to g, is char-acterized by a linearly decreasing displacement gra-dient. The location of this decrease in displacementis coincident with an anticlinal bend in the under-lying fault, which suggests that fault-bend foldingmay account for at least part of this decrease in dis-placement. A fault dip change from 38° to 20°, asobserved from the seismic reflection data (Figure 13,location II), predicts a gradient in displacement of0.33, or 19°. The rest of the decrease in displace-ment may be caused by distributed shear in theforelimb; there are two compelling reasons that thismay occur in this structure. This fault geometry is

slightly beyond the boundary of the solution spacefor fault-bend folding, which is to say that thefolding caused by this fault geometry cannot bemodeled by preserving layer thickness and area,and thus, distributed layer thinning and thicken-ing processes are required. Additionally, becausethese layers consist of weakly lithified, near-sea-floor sediments (confirmed by the observation thatthe upper detachment of the fault was the paleo-seafloor, which is indicated by the sediments thatonlap onto the forelimb and exhibit geometries char-acteristic of drape sedimentation (Figure 13, III), itis not surprising that they would not deform strictlyin accordance with fault-bend-folding theory, as theassumptions of the preservation of layer thick-ness and accommodation of folding by flexural slipmechanisms may not be preferred in weakly lithifiedsediments. Despite these modest differences, thepredicted decrease in displacement from fault-bend-folding theory clearly captures the first-orderdisplacement patterns in this structure.

By the same method of analysis, the forelandstructure (Figure 13, structure B) exhibits constantdisplacement at depth and decreasing displacementalong the uppermost part of the fault that is notassociated with a fault bend. This pattern of dis-placement is consistent with components of bothstandard fault-bend folding and fault-propagationfolding. The region of constant slip on the lowerpart of this thrust ramp is consistent with the back-limb of the structure forming by standard fault-bend folding. Notably, the beds in the backlimb ofthe structure are parallel to the underlying fault(fold limb IV in Figure 13), consistent with stan-dard fault-bend folding and distinct from struc-ture A, which involved a component of shear fault-bend folding. On the upper part of the thrust rampfor structure B, the displacement-distance profileshows a negative slope reaching zero displacementat a distance of about 6 km (3.7 mi) (Figure 14B).Unlike in structure A, the decrease in displacementis not associated with an anticlinal fault bend (incontrast, a minor synclinal bend is present, indi-cated by VI in Figure 13), suggesting that the de-crease in displacement observed in structure B iscaused by fault-propagation folding. Thus, al-though the decreases in displacement may at first

appear similar between the structures, the com-bination of fault geometry and displacement al-lows for the differentiation of fault-bend and fault-propagation folding in these two examples. Basedon the interpretation of the forelimb of the struc-ture as a fault-propagation fold, the fault tip (thelocation where displacement along the fault de-creases to zero) would be located just below hori-zon f (Figure 13, V). This is broadly consistentwith the observation of offset layers below thispoint, and continuous, folded layers above it. Basedon the curved nature of the forelimb fold limb,changes in layer thickness, and the upward de-crease in bed dips, this structure is interpreted as atrishear fold (Erslev, 1991; Allmendinger, 1998;and others).

The growth strata and folding patterns indicatethat these two faults are part of a break-forwardsequence. Thus, displacement along the forelandstructure (B) imbricates and refolds the hinterlandstructure (A) (fold limbs IV and VII in Figure 13).Despite this complexity, the displacement-distanceprofiles maintain recognizable signatures of the ba-sic fault-related folding components that generatedthese structures.

Based on the insights from the displacement-distance profiles and growth strata, we generateda balanced kinematic model of both structures(Figure 14C–F). Based on the detailed observationsfrom structure A, it was modeled as a shear fault-bend fold, with the shear interval and fault ge-ometry defined by observations from the seismicreflection data and displacement-distance profile(Figure 14A). After displacement was completeon the structure A, displacement wasmodeled onthe foreland structure as a fault-bend-fold back-limb with a trishear fault-propagation-fold fore-limb, based on the observations made from thedisplacement-distance profile (Figure 14B).

Many of the parameters necessary to model theforelimb of structure B as a trishear fault-propagationfold may be constrained from the displacement-distance profile. The base of the propagating sec-tion is inferred to be the location of the transitionbetween constant displacement and decreasingdisplacement. The location of the fault tip is alsoevident because it is the location where displacement

Hughes and Shaw 247

reaches zero. The distance between those twopointsrepresents the distance that the fault propagatedduring this phase of its history. Additionally, theamount of displacement at the base of this seg-ment can be easily measured. These two obser-vations combine to give a propagation-to-slip ra-tio (P/S) of 3.96 for structure B; knowledge ofthis value provides an important input constraintfor modeling this structure as a trishear fault-propagation fold. Based on these observationsand the observed dip of the fault, a trishear fault-propagation-fold forelimb model was generatedto model this structure’s geometry, concurrent withfault-bend folding in the backlimb (Figure 14E–F).This model invokes the following series of eventsfor this structure:

1. The fault propagated as a fracture from the lowerdetachment to the base of the fault-propagationinterval;

2. As displacement on the fault commenced, thebacklimb deformed as a fault-bend fold whilethe tip of the fault propagated upward throughthe stratigraphic section; and

3. The fault tip propagated to its currently ob-served location when the lower part of the faulthad accumulated the observed,maximumamountof displacement.

Because the only observations that went intothe construction of the kinematic models weredisplacement-distance relationships, fault geome-tries, and stratigraphic thicknesses, comparison ofthe resulting fold geometries with the fold shapesobservable in the seismic reflection data providesan objective test of the utility of this approach. Thepregrowth backlimb fold geometry of structure Ais consistent with the fold observed in the seismicreflection data, because the limb dips and widthsof the original fold and imbricated panels are bothwell represented in themodel. The geometry of thegrowth strata over this backlimb is also consis-tent with the observed growth geometries of lay-ers h and j. The modeled forelimb of structure Ais consistent with the location, size, and dip di-rection of the forelimb in the natural example.However, the forelimb of the natural structure is

248 Displacement Variations and Folding Styles

also geometrically dissimilar in some ways fromthe model; this is likely because these sedimentswere not deeply buried and, therefore, preferen-tially deformed with more distributed shearinginstead of flexural slip. Additionally, the thicknessof the drape sedimentary package, i, is thinner inthe natural example; this is due to a combination offactors, including the lower structural relief ob-served than modeled for structure A, and anoversimplification of the depositional environ-ment (it has been commonly observed in off-shore settings that sediments tend to pond be-hind bathymetric highs [such as structure A],resulting in sediment-starved basinward regions[e.g., Shaw et al., 2004]). As a result, it is per-missible that some of the deformation on struc-tures A and B may have been concurrent. Forstructure B, the deep fold panel (Figure 13, IV)and forelimb trishear geometries are well rep-resented in the model geometry. Additionally, themodeled growth strata deposited over this foldthickens over the backlimb and forelimb, which isconsistent with the stratigraphic thickening andfold geometries observed in the seismic reflectiondata. The modeled folding caused by the minorsynclinal bend in fault B (Figure 13, VI) is not ob-served in the data, which is perhaps caused by thepresence of a minor backthrust (Figure 13, VIII),which accommodated the uplift in lieu of fault-bend folding.

In summary, we suggest that the modeledstructural geometries based on parameters definedby the displacement profiles are generally consistentwith the patterns of folding and faulting expressedin this natural example. Specifically, the observeddisplacement profiles help characterize these struc-tures as complex fault-related folds involving com-ponents of fault-bend, shear fault-bend, and fault-propagation folding. Moreover, in cases where themodeled geometries are locally inconsistent withthe natural folds, this helps identify regions of thenatural structures where deformation may be ac-commodated by deformation mechanisms (e.g.,nonparallel folding) or secondary structures thatare not represented in the models.

Fault-related foldswith different structural stylesare commonly observed in close spatial association

in many fold and thrust belts (Woodward et al.,1988; Woodward and Rutherford, 1989; Sprattet al., 2004; Shaw et al., 2005; Hughes, 2012; andothers). The factors that favor the formation ofone structural style over another may include sedi-mentation rate, boundary conditions, fault fric-tion, and the mechanical properties of the stratig-raphy (Wiltschko, 1979a, b; Berger and Johnson,1980; Chester et al., 1991; Erickson, 1996; Strayeret al., 2004; Hughes, 2012; and others). The factthat these properties may vary locally within a foldand thrust belt allows for the development of lo-cally variable structural styles. Thus, because fault-related folds with different structural styles havebeen documented in close spatial association in otherregions, and because the factors that contribute tostructural style vary locally, we can be confident inthe permissibility of our interpretation of differ-ences in structural style in this example.

CONCLUSIONS

We present a quantitative method for relating thedisplacement measured along a contractional faultto the style of folding deformation present in agiven structure. We include results from variousstyles of fault-related folds by comparing the ex-pected displacement-distance relationships to ob-servations from seismic reflection datasets in a vari-ety of tectonic settings. We then apply this methodto a complex structure, illustrating that this ap-proach can be successfully used to gain insight intothe mixed structural styles that may be present innatural structures. By this approach, we are able toidentify shearing intervals, parallel folding inter-vals, and fault-propagation-folding intervals, and toobserve the impact of fault bends on displacementdistributions. Additionally, by generating a bal-anced structural model based on our interpreta-tion, we are able to compare the fold and growthgeometry of the model with observations in theseismic reflection data, confirming the validity ofour interpretation. We suggest that this approachhas value for the structural interpretation of seis-mic reflection data because it can help to eluci-date the styles of fault-related folding deformation

present in a given contractional structure. Themethod can also serve as a somewhat indepen-dent way of interpreting structural style, which,when combined with geometric observations, willlead to the development of detailed and accuratestructural models of contractional fault-relatedfolds.

REFERENCES CITED

Allmendinger, R., 1998, Inverse and forward numerical mod-eling of trishear fault propagation folds: Tectonics, v. 17,no. 4, p. 640–656, doi:10.1029/98TC01907.

Atwater, T., 1989, Plate tectonic history of the northeast Pa-cific and western North America, in E. L. Winterer,D. M. Hussong, and R. W. Decker eds., The eastern Pa-cific Ocean and Hawaii: Geological Society of America,Geology of North America Series, N, p. 21–72.

Barazangi, M., and B. L. Isacks, 1976, Spatial distribution ofearthquakes and subduction of the Nazca plate beneathSouth America: Geology, v. 4, p. 686–692, doi:10.1130/0091-7613(1976)4<686:SDOEAS>2.0.CO;2.

Benesh, N. P., 2010, Themechanics of fault-bend folding andtear-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,Investigation of growth fault bend folding using discreteelement modeling: Implications for signatures of activefolding above blind thrust faults: Journal of GeophysicalResearch, v. 112, B03S04, doi:10.1029/2006JB004466.

Bergen, K., and J. H. Shaw, 2010, Displacement profiles anddisplacement-length scaling relationships of thrust faultsconstrained by seismic reflection data: Geological Socie-ty of America Bulletin, v. 122, no. 7–8, p. 1209–1219,doi:10.1130/B26373.1.

Berger, P., and A. Johnson, 1980, First-order analysis of de-formation of a thrust sheetmoving over a ramp: Tectono-physics, v. 70, p. T9–T24, doi:10.1016/0040-1951(80)90276-0.

Bilotti, F., and J. H. Shaw, 2005, Deep-water Niger Deltafold and thrust belt modeled as a critical-taper wedge: Theinfluence of elevated basal fluid pressure on structuralstyles: AAPG Bulletin, v. 89, p. 1475–1491.

Briggs, S. E., R. J. Davies, J. A. Cartwright, and R. Morgan,2006, Multiple detachment levels and their control on foldstyles in the compressional domain of the deepwater westNiger Delta: Basin Research, v. 18, no. 4, p. 435–450,doi:10.1111/j.1365-2117.2006.00300.x.

Burchfiel, B. C., C. Zhiliang, L. Yuping, and L. H. Royden,1995, Tectonics of the Longmen Shan and adjacent re-gions, central China: International Geology Review,v. 37, p. 661–735, doi:10.1080/00206819509465424.

Chester, J. S., and F. M. Chester, 1990, Fault-propagationfolds above thrusts with constant dip: Journal of Struc-tural Geology, v. 12, no. 7, p. 903–910, doi:10.1016/0191-8141(90)90063-5.

Hughes and Shaw 249

Chester, J., J. Logan, and J. Spang, 1991, Influence of layer-ing and boundary conditions on fault-bend and fault-propagation folding: Geological Society of America Bul-letin, v. 103, p. 1059–1072.

Corredor, F., J. H. Shaw, and F. Bilotti, 2005a, Structuralstyles in the deep-water fold and thrust belts of the NigerDelta: AAPG Bulletin, v. 89, p. 753–780, doi:10.1306/02170504074.

Corredor, F., J. H. Shaw, and J. Suppe, 2005b, Shear fault-bend fold, deep-water Niger Delta, in J. H. Shaw, C. D.Connors, and J. Suppe, eds., Seismic interpretation ofcontractional fault-related folds: AAPG Studies in Geol-ogy 53, p. 87–92.

Cundall, P. A., and O. D. L. Strack, 1979, A discrete numer-ical model for granular assemblies: Geotechnique, v. 29,p. 47–65, doi:10.1680/geot.1979.29.1.47.

Damuth, J. E., 1994, Neogene gravity tectonics and deposi-tional processes on the deep Niger-Delta continentalmargin: Marine and Petroleum Geology, v. 11, p. 320–346, doi:10:1016/0264-8172(94)90053-1.

Davis, E. E., and R. D. Hyndman, 1989, Accretion and recentdeformation of sediments along the northern Cascadiasubduction zone: Geological Society of America Bulle-tin, v. 101, p. 1465–1480, doi:10.1130/0016-7606(1989)101<1465:AARDOS>2.3.CO;2.

Demets, C., R.G.Gordon,D. F. Argus, and S. Stein, 1990,Cur-rent plate motions: Geophysical Journal International,v. 101, p. 425–478, doi:10.1111/j.1365-246X.1990.tb06579.x.

Ellis, M. A., and W. J. Dunlap, 1988, Displacement variationalong thrust faults: Implications for the development oflarge faults: Journal of Structural Geology, v. 10, no. 2,p. 188–192.

Erickson, S., 1996, Influence of mechanical stratigraphy onfolding vs. faulting, Journal of Structural Geology,v. 18, no. 4, p. 443–450.

Erslev, E., 1991, Trishear fault-propagation folding: Geology,v. 19, p. 617–620, doi:10.1130/0091-7613(1991)019<0617:TFPF>2.3.CO;2.

Erslev, E., and K. Mayborn, 1997, Multiple geometries andmodes of fault-propagation folding in the CanadianRockies: Journal of Structural Geology, v. 19, no. 3–4,p. 321–335.

Hedlund, C. A., 1997, Fault-propagation, ductile strain, anddisplacement-distance relationships: Journal of Structur-al Geology, v. 19, no. 3–4, p. 249–256.

Hubbard, J., J. H. Shaw, and Y. Klinger, 2010, Structural set-ting of the 2008 Mw 7.9 Wenchuan, China, earthquake:Bulletin of the Seismological Society of America, v. 100,no. 5B, p. 2713–2735, doi:10.1785/0120090341.

Hubert-Ferrari, A., J. Suppe, R. Gonzales-Mieres, and X.Wang, 2007, Mechanisms of active folding of the land-scape: Journal of Geophysical Research, v. 112, B03S09,doi:10.1029/2006JB004362.

Hughes, A., 2012, Insights into contractional fault-related fold-ing processes based on mechanical, kinematic, and empiri-cal studies: Ph.D. thesis, Harvard University, Cambridge,191 p.

Hyndman, R. D., and T. S. Hamilton, 1993, Queen Charlottearea Cenozoic tectonics and volcanism and their

250 Displacement Variations and Folding Styles

association with relative plate motions along the north-eastern Pacific Margin: Journal of Geophysical Research,v. 98, p. 14257–14277.

Hyndman, R. D., C. J. Yorath, R. M. Clowes, and E. E. Davis,1990, The northern Cascadia subduction zone at Van-couver Island: Seismic structure and tectonic history:Canadian Journal of Earth Science, v. 27, p. 313–329,doi:10.1139/e90-030.

Hyndman, R. D., G. D. Spence, T. Yuan, and E. E. Davis,1994, Regional geophysics and structural framework ofthe Vancouver Island margin accretionary prism, inG. K. Westbrook et al., eds., Proceedings of the OceanDrilling Program, Initial Reports: College Station, Texas,Ocean Drilling Program, v. 146, no. 1, 609 p.

Itasca, 1999, PFC2D: Theory and background, User’s Guide,Command Reference, FISH in PFC2D: Minneapolis,Minnesota, Itasca Consulting Group.

Jamison, W. R., 1987, Geometric analysis of fold developmentin overthrust terranes: Journal of Structural Geology, v. 9,no. 2, p. 207–219, doi:10.1016/0191-8141(87)90026-5.

Jordan, T. E., and R. W. Allmendinger, 1986, The SierrasPampeanas of Argentina: A modern analog of RockyMountain foreland deformation: American Journal of Sci-ence, v. 286, p. 737–764, doi:10.2475/ajs.286.10.737.

Jordan, T. E., F. Schlunegger, and N. Cardozo, 2001, Un-steady and spatially variable evolution of the NeogeneAndean Bermejo foreland basin, Argentina: Journal ofSouth American Earth Sciences, v. 14, p. 775–798,doi:10.1016/S0895-9811(01)00072-4.

Kattenhorn, S. A., 1994, Outcrop-scale fault-related folds,Valley and Ridge Province, Appalachians: Comparisonto kinematic model predictions: M.S. thesis, Universityof Akron, Akron, Ohio, 124 p.

Kattenhorn, S. A., and D. D. Pollard, 2001, Integrating 3-Dseismic data, field analogs, and mechanical models in theanalysis of segmented normal faults in the Wytch Farmoil field, southern England, United Kingdom: AAPGBulletin, v. 85, no. 7, p. 1183–1210.

Kleyn, A. H., 1983, Seismic reflection interpretation: Lon-don, England, Applied Science Publishers, 269 p.

Mansfield, C., and J. Cartwright, 1996, High resolution faultdisplacement mapping from three-dimensional seismicdata: Evidence for dip linkage during fault growth: Jour-nal of Structural Geology, v. 18, no. 2–3, p. 249–263.

McConnell, D. A., 1994, Fixed hinge, basement-involvedfault-propagation folds, Wyoming: Geological Society ofAmerica Bulletin, v. 106, p. 1583–1593, doi:10.1130/0016-7606(1994)106<1583:FHBIFP>2.3.CO;2.

McConnell, D., S. Kattenhorn, and L. Benner, 1997, Distri-bution of fault slip in outcrop-scale fault-related folds,Appalachian Mountains: Journal of Structural Geology,v. 19, no. 3–4, p. 257–267.

Meng, Q. R., E. Wang, and J. M. Hu, 2005, Mesozoic sedi-mentary evolution of the northwest Sichuan Basin: Im-plication for continued clockwise rotation of the SouthChina block: Geological Society of America Bulletin,v. 117, p. 396–410, doi:10.1130/B25407.1.

Minster, J. B., and T. H. Jordan, 1978, Present day plate mo-tion: Journal of Geophysical Research, v. 83, p. 5331–5354, doi:10.1029/JB083iB11p05331.

Mitra, S., 1990, Fault-propagation folds: Geometry, kinemat-ic evolution and hydrocarbon traps: AAPG Bulletin,v. 74, p. 921–945.

Muraoka, H., and H. Kamata, 1983, Displacement distribu-tion along minor fault traces: Journal of Structural Geol-ogy, v. 5, no. 5, p. 483–495, doi:10.1016/0191-8141(83)90054-8.

Narr, W., and J. Suppe, 1994, Kinematics of basement-involved compressive structures: American Journal ofScience, v. 294, p. 802–860, doi:10.2475/ajs.294.7.802.

Rich, J. L., 1934, Mechanics of low-angle overthrust faultingas illustrated by Cumberland thrust block, Virginia,Kentucky, and Tennessee: AAPG Bulletin, v. 18,p. 1584–1596.

Riddihough, R. P., 1984, Recent movements of the Juan deFuca plate system: Journal of Geophysical Research,v. 89, p. 6980-6994.

Rodgers, J., 1950, Mechanics of Appalachian folding as illus-trated by Sequatchie anticline, Tennessee and Alabama:AAPG Bulletin, v. 34, p. 672–681.

Rodgers, J., 1990, Fold-and-thrust belts in sedimentary rocks.Part 1: Typical examples: American Journal of Science,v. 290, p. 321–359.

Rodgers, J., 1991, Fold-and-thrust belts in sedimentary rocks.Part 2: Other examples, especially variants: AmericanJournal of Science, v. 291, p. 825–886.

Rowan, M. G., and R. A. Ratliff, 1988, Use of fault cut-offsand bed travel distance in balanced cross-sections: Dis-cussion 1: Journal of Structural Geology, v. 10, no. 3,p. 311–316, doi:10.1016/0191-8141(88)90065-X.

Royden, L. H., B. C. Burchfiel, R. W. King, E. Wang, Z. L.Chen, F. Shen, and Y. P. Liu, 1997, Surface deformationand lower crustal flow in eastern Tibet: Science, v. 276,p. 788–790, doi:10:1126/science.276.5313.788.

Shaw, J. H., and J. Suppe, 1994, Active faulting and growth fold-ing in the easternSantaBarbaraChannel,California:Geolog-ical Society of America Bulletin, v. 106, p. 607–626, doi:10.1130/0016-7606(1994)106<0607:AFAGFI>2.3.CO;2.

Shaw, J. H., E. Novoa, and C. D. Connors, 2004, Structuralcontrols on growth stratigraphy in contractional fault-related folds, in K. R. McClay, ed., Thrust tectonics andhydrocarbon systems: AAPG Memoir 82, p. 400–412.

Shaw, J. H., C. D. Connors, and J. Suppe, 2005, Seismic in-terpretation of contractional fault-related folds: AAPGStudies in Geology 53, 156 p.

Sherriff, R., 1977, Limitations on resolution of seismic reflec-tions and geologic detail derivable from them, in C. E.Payton, ed., Seismic stratigraphy—Applications to hy-drocarbon exploration: AAPG Memoir 26, p. 3–14.

Spang, J. H, andD. A.McConnell, 1997, Effect of initial faultgeometry on the development of fixed-hinge, fault propa-gation folds: Journal of Structural Geology, v. 19, no. 12,p. 1537–1541, doi:10.1016/S0191-8141(97)00065-5.

Spratt, D., J. Dixon, and E. Beattie, 2004, Changes in struc-tural style controlled by lithofacies contrast across trans-verse carbonate bank margins–Canadian Rocky Moun-tains and scaled physical models, in K. R. McClay, ed.,

Thrust tectonics and hydrocarbon systems: AAPGMemoir 82, p. 259–273.

Strayer, L., S. Erickson, and J. Suppe, 2004, Influence ofgrowth strata on the evolution of fault-related folds–Distinct-element models, in K. R. McClay, ed., Thrusttectonics and hydrocarbon systems: AAPG Memoir 82,p. 413–437.

Suppe, J., 1983, Geometry and kinematics of fault-bend fold-ing: American Journal of Science, v. 283, p. 684–721,doi:10.2475/ajs.283.7.684.

Suppe, J., and D. A. Medwedeff, 1990, Geometry and kine-matics of fault-propagation folding: Eclogae GeologicaeHelvetiae, v. 83, p. 409–454.

Suppe, J., G. T. Chou, and S. C. Hook, 1992, Rates of foldingand faulting determined from growth strata, in K. R.McClay, ed., Thrust tectonics: London, England, Chap-man and Hall, p. 105–121.

Suppe, J., C. D. Connors, and Y. Zhang, 2004, Shear fault-bend folding, in K. R. McClay, ed., Thrust tectonics andhydrocarbon systems: AAPG Memoir 82, p. 303–323.

Tavani, S., F. Storti, and F. Salvini, 2006, Double-edge fault-propagation folding: Geometry and kinematics: Journalof Structural Geology, v. 28, p. 19–35.

Wilkerson, M. S., 1992, Differential transport and continuityof thrust sheets: Journal of Structural Geology, v. 14,no. 6, p. 749–751, doi:10.1016/0191-8141(92)90132-G.

Wilkerson, M. S., T. Apotria, and T. Farid, 2002, Interpret-ing the geologic map expression of contractional fault-related fold terminations: Lateral/oblique ramps versusdisplacement gradients: Journal of Structural Geology,v. 24, p. 593–607, doi:10.1016/S0191-8141(01)00111-0.

Williams, G., and T. Chapman, 1983, Strains developed in thehangingwalls of thrusts due to their slip/propagation rate:A dislocation model: Journal of Structural Geology, v. 5,no. 6, p. 563–571, doi:10.1016/0191-8141(83)90068-8.

Wiltschko, D., 1979a, A mechanical model for thrust sheetdeformation at a ramp: Journal of Geophysical Research,v. 84, p. 1091–1104.

Wiltschko, D., 1979b, Partitioning of energy in a thrust sheetand implications concerning driving force: Journal ofGeophysical Research, v. 84, p. 6050–6058.

Woodward, N., and E. Rutherford Jr., 1989, Structural lithicunits in external orogenic zones, Tectonophysics, 158,p. 247–267, doi:10.1016/0040-1951(89)90327-2.

Woodward, N., K. Walker, and C. Lutz, 1988, Relationshipsbetween early Paleozoic facies patterns and structuraltrends in the Saltville thrust family, Tennessee Valleyand Ridge, southern Appalachians: Geological Societyof America Bulletin, v. 100, p. 1758–1769.

Yue, L.-F., J. Suppe, and J.-H. Hung, 2005, Structural geol-ogy of a classic thrust belt earthquake: The 1999 Chi-Chi earthquake Taiwan (Mw = 7.6): Journal of StructuralGeology, v. 27, p. 2058–2083.

Zapata, T. R., and R. W. Allmendinger, 1996, Growth stratalrecords of instantaneous and progressive limb rotation in thePrecordillera thrust belt and Bermejo basin, Argentina: Tec-tonics, v. 15, no. 5, p. 1065–1083, doi:10.1029/96TC00431.

Hughes and Shaw 251