AUTHORS

Nathan P. Benesh � Department of Earth andPlanetary Sciences, Harvard University, 20 OxfordStreet, Cambridge, Massachusetts 02138; presentaddress: ExxonMobil Upstream Research Compa-ny, Houston, Texas; benesh@post.harvard.edu

Nathan P. Benesh is a research geologist in the Struc-ture and Geomechanics Group at the ExxonMobilUpstream Research Company. He previously re-ceived his Ph.D. in earth and planetary sciences at

Geometry, kinematics, anddisplacement characteristics oftear-fault systems: An examplefrom the deep-water Niger DeltaNathan P. Benesh, Andreas Plesch, and John H. Shaw

Harvard University. His research interests focuson geomechanical modeling and the quantitativeevaluation of structures at the trap to regional scale.

Andreas Plesch � Department of Earth andPlanetary Sciences, Harvard University, 20 OxfordStreet, Cambridge, Massachusetts;plesch@fas.harvard.edu

Andreas Plesch is a senior research associate in theStructural Geology and Earth Resources Group inthe Earth and Planetary Science Department,Harvard University. He received his Ph.D. fromFree University, Berlin, Germany. His research in-terests revolve around three-dimensional model-ing and the analysis of structures on the reservoirto mountain belt scale with a focus on quantitativeaspects.

John H. Shaw � Department of Earth andPlanetary Sciences, Harvard University, 20 OxfordStreet, Cambridge, Massachusetts;shaw@eps.harvard.edu

John H. Shaw is the Harry C. Dudley professor ofstructural and economic geology and chair of theDepartment of Earth and Planetary Sciences,Harvard University. Prior to joining the Harvardfaculty, Shaw worked as an exploration and pro-duction geologist. His research interests includethe structural characterization of complex trapsand reservoirs in both conventional and uncon-ventional petroleum systems.

ACKNOWLEDGEMENTS

We thank CGGVeritas for providing the seismic

ABSTRACT

We use three-dimensional seismic reflection data and newmap-based structural restoration methods to define the displacementhistory and characteristics of a series of tear faults in the deep-waterNigerDelta. Deformation in the deep-waterNigerDeltais focused mostly within two fold-and-thrust belts that accom-modate downdip shortening produced by updip extension onthe continental shelf. This shortening is accommodated by aseries of thrust sheets that are locally cut by strike-slip faults.Through seismic mapping and interpretation, we resolve thesestrike-slip faults to be tear faults that share a common detach-ment level with the thrust faults. Acting in conjunction, thesestructures have accommodated a north–south gradient inwestward-directed shortening. We apply a map-based resto-ration technique implemented in Gocad to restore an upperstratigraphic horizon of the lateOligocene and use this analysisto calculate slip profiles along the strike-slip faults. The slipmagnitudes and directions change abruptly along the lengthsof the tear faults as they interact with numerous thrust sheets.The discontinuous nature of these slip profiles reflects the man-ner in which they have accommodated differential movementbetween the footwall and hanging-wall blocks of the thrustsheets. In cases for which the relationship between a strike-slip fault andmultiple thrust faults is unclear, the recognitionof this type of slip profile may distinguish thin-skinned tearfaults from more conventional deep-seated, throughgoingstrike-slip faults.

data used in this study and Landmark GraphicsCorporation for donating the software through itsUniversity Grant Program. We also thank Exxon-Mobil for its support of this work and ChevronCorporation for providing additional data sets.The AAPG Editor thanks the following reviewers fortheir work on this paper: Christopher F. Elders,Stephen J. Naruk, and Sandro Serra.

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

Manuscript received January 25, 2011; provisional acceptance March 30, 2011; revised manuscriptreceived May 5, 2013; final acceptance June 25, 2013.DOI:10.1306/06251311013

AAPG Bulletin, v. 98, no. 3 (March 2014), pp. 465–482 465

INTRODUCTION

The Niger Delta, situated in the Gulf of Guinea atthe southern end of the Cretaceous Benue troughrift basin, represents one of the largest moderndeltas and most productive regions for petroleumexploration in the world (Doust and Omatsola,1990; Figure 1). The delta serves as a prime ex-ample of gravity-driven tectonic deformation, acharacteristic of many deep-water passive margins(Evamy et al., 1978; Doust and Omatsola, 1990).The delta began to form as sediments that shedfrom the Niger River gradually filled the Benuetrough during the opening of the equatorial At-lantic, and, by the late Eocene, the delta had be-gun to prograde on top of the continental margin.Two distinct fold-and-thrust belts within the deltaaccommodate the shortening and downdip de-formation produced by gravity-driven extensionon the continental shelf. This gravity-driven ex-tension is caused by rapid sediment depositionthat leads to differential loading and the subse-quent formation of large normal faults within the

Figure 1. A generalized map of the main structural provinces of the Nof interest. Also shown are the locations of the three-dimensional (3seismic survey used in this study. Qua. = Quaternary; Plio. = Pliocene

466 Geometry, Kinematics, and Displacement Characteristics of

deltaic deposits on the continental shelf (Wu andBally, 2000). This updip extension is fed at depthonto several detachment surfaces within thick over-pressured shales of the early to middle Paleogenethat underlie the postrift deltaic deposits (Bilottiet al., 2005; Corredor et al., 2005). Shortening inthe deep water began in the late Miocene to theearly Pliocene to accommodate the slip that ex-tends downdip along these detachments. Thethrust faults produced by this shortening occur intwo distinct provinces, termed the “inner fold-and-thrust belt” and the “outer fold-and-thrust belt”(Connors et al., 1998; Corredor et al., 2005).

With the advent of petroleumexploration in thedeep-water Niger Delta in the 1990s, high-qualitytwo-dimensional (2-D) and three-dimensional (3-D)seismic reflection data have been acquired, whichhave allowed for the investigation of the nature ofthese gravity-driven contractional structures. Thesestudies have mainly focused on the analysis of thedeep-water thrust faults and fault-related folds, in-cluding their structural geometries and kinematics(e.g., Connors et al., 1998; Shaw et al., 2004; Suppe

iger Delta and a schematic diagram of the stratigraphy in the area-D) seismic reflection data volume and two-dimensional (2-D); Oligo. = Oligocene; Paleo. = Paleocene; Cret. = Cretaceous.

a Tear-Fault System

et al., 2004;Corredor et al., 2005), and the effects ofhigh basal fluid pressures (e.g., Bilotti et al., 2005)and multiple detachment surfaces (e.g., Corredoret al., 2005; Briggs et al., 2006) on their structuralstyles. It is generally accepted that these thrust-related structures provide the dominant means bywhich shortening is accommodated in the com-pressional toe of the delta; however, in this study,we show that transport-parallel strike-slip faultsare also an important factor. We use both high-resolution 2-D and 3-D seismic data (Figure 1) toanalyze a system of tear faults in the outer fold-and-thrust belt that partition distal contractionaldeformation.

The term “tear fault” has long been applied tostrike-slip faults that abruptly terminate thrustsheets alongstrike (e.g., Twiss and Moores, 1992).The Jacksboro and Russell Fork faults, which bracketthe Pine Mountain thrust sheet in the southern Ap-palachian Valley and Ridge Province in the easternUnited States, provide a well-known classic exam-ple of a tear-fault system (Mitra, 1988). Beyondthe Appalachians, thin-skinned tear faults that onlyinvolve the shallow sedimentary section have alsobeen noted in the Canadian Rocky Mountains(Benvenuto and Price, 1979), theWestern Foothillsof Taiwan (Mouthereau et al., 1999), the SantaBarbara Channel (Shaw and Suppe, 1994), and theMaracaibo Basin inVenezuela (Escalona andMann,2006), among other localities. These tear faults arecommonly recognized based on surface exposureor interpretations of 2-D seismic lines. The inher-ently 3-D nature of these faults, however, has madeit difficult to fully constrain their geometries, ki-nematics, and displacement characteristics. Leducet al. (2012) used 3-D seismic data to evaluate astrike-slip system that accommodates motion onprimarily extensional faults on the northern mar-gin of the Niger Delta, inboard of the outer fold-and-thrust belt; however, we know of no otherstudy in which 3-D seismic data have been appliedto carefully examine the full spatial relationshipand displacement profiles for multiple tear faultsand the thrust faults that they more commonlyterminate. The aimof this article, based on theworkof Benesh (2010), is to more fully characterize thenature of tear faults and their relationships with

thrust-fault systems using 3-D seismic reflectiondata that image such structures in the outer fold-and-thrust belt of the Niger Delta. The system weanalyze contains multiple strike-slip faults thatwork in tandem with the thrust structures to parti-tion strain and accommodate a gradient in shorten-ing across the fold-and-thrust belt. In addition toanalyzing the geometric and genetic relationshipsamong the faults, we quantify shortening across theregion, and, by means of a map-view surface resto-ration, we determine diagnostic slip profiles for thestrike-slip tear faults.

GEOLOGIC SETTING

The focus of this study is a series of tear faults thatoccur near the northern termination of the outerfold-and-thrust belt of the Niger Delta. The outerfold-and-thrust belt represents the more distal ofthe two fold-and-thrust belts that accommodateoutboard shortening driven by gravitational col-lapse and extension of the deltaic sequence on thecontinental shelf. For most of the outer fold-and-thrust belt, the primary detachment lies within theAkata Formation (Corredor et al., 2005), a time-transgressive, thick marine shale that generally sitsatop an Upper Cretaceous sedimentary sequence,which itself overlies an Early Cretaceous oceaniccrust (Avbovbo, 1978; Knox and Omatsola, 1989;Wu and Bally, 2000; Figure 1). This shale is be-lieved to be one of the major source rocks for hy-drocarbons in the delta and also contains somelocally developed turbidite sands. Additionally,the formation generally exhibits a low seismicvelocity that reflects fluid overpressures that lo-cally reach 90% of the lithostatic stress (Bilottiet al., 2005). Above the Akata Formation lies theAgbada Formation. This formation is Eocene toPleistocene in age and is believed to be the dom-inant petroleum-bearing unit in the delta. In ourstudy area, the lowest part of the Agbada consistsof channel complexes and basin-floor fans com-posed of sediments that are believed to be sourcedfrom the Dahomey trough of the onshore GuineaBasin. This unit tapers out southward and istermed the “Dahomey wedge” (Morgan, 2004;

Benesh et al. 467

Figure 2. A representative thrust faultfrom the outer fold-and-thrust belt in thenorthwestern part of the Niger Delta. Thisstructure displays the classic characteristicsof a shear fault-bend fold as reflected inthe long and shallowly dipping backlimb.The interpreted detachment level for thisstructure (red dashed line) is above theAkata Formation, within the Dahomeywedge. All seismic data presented here aremigrated and depth converted. Data areowned and provided courtesy of CGGVeritas,Crawley, UK.

Briggs et al., 2006; Figure 1). The overlying BeninFormation, found in some coastal regions, is notencountered in the deep-water region of our studyarea.

STRUCTURE

Most of the shortening is accommodated in theouter fold-and-thrust belt by thrust sheets, com-monly referred to as “toe thrusts,” that exhibit avariety of structural styles including detachment,fault-propagation, fault-bend, and shear fault-bendfolding (Shaw et al., 2004; Suppe et al., 2004;Corredor et al., 2005;Higgins et al., 2007; Kostenkoet al., 2008).Many of these folds that develop abovethe thrust faults involve a significant componentof pure and/or simple shear, reflected in long back-limbs that typically dip less than the fault ramp(Serra, 1977; Suppe et al., 2004; Shaw et al., 2005).

468 Geometry, Kinematics, and Displacement Characteristics of

This type of fold geometry is commonly producedwhen a weak hanging-wall stratigraphic intervalundergoes bed-parallel simple shear, or pure shearlocalized above the base of the thrust ramp, duringfold growth. Corredor et al. (2005) showed that thisshearwas generally localized in theAkata Formationand the lowermost part of theAgbada Formation formuch of the southern lobe of the outer fold-and-thrust belt.We find, however, that, in our northernstudy area, shear is limited to the lowermost part ofthe Agbada Formation, within the weak Dahomeywedge, as the basal detachment for the fold-and-thrust belt has generally risen to the top of theAkataFormation (Figure 2). As has been modeled and in-ferred in the southern Niger Delta (Cobbold et al.,2001, 2009; Mourgues and Cobbold, 2006), shearlocalized within the Dahomey wedge and the loca-tion of the basal detachment may arise from localoverpressure near the top and the bottom of theAkata Formation and the Agbada Formation,

a Tear-Fault System

Figure 3. A horizontalslice of seismic data at adepth of 4461 m (14,640 ft,left) and an illustratedstructural map (right). Thelocation of the seismicdata volume is shown inFigure 1. The dashed linesindicate the positions ofvarious figures and re-gional cross sections dis-cussed in the text. Dataare owned and providedcourtesy of CGGVeritas,Crawley, UK.

respectively (Bilotti et al., 2005; Briggs et al.,2006; Guzofski, 2007).

A migrated and depth-converted seismic profilefrom a 3-D seismic volume is presented in Figure 2.These seismic data show a typical toe-thrust struc-ture, or shear fault-bend fold, from the study area.The interpreted version of the profile also displaysthe four primary stratigraphic horizons that wemapped across the region and used for our structuralcharacterization. Starting with the deepest level, thehorizons represent the top of the Akata Formation,the topof theDahomeywedge, a prominentAgbadaFormation reflection of the late Oligocene, and an-other prominent Agbada Formation reflection ofthe late Miocene. Aided by these mapped horizons,which we will refer to as the “AF,” “DW,” “LO,”and “LM” horizons, we can see that the inter-preted structure displays the classic character-istics of a shear fault-bend fold; it possesses abacklimb that dips less than the fault ramp and hasa width much greater than the forelimb of the foldand greater than the amount of slip on the thrustramp (Suppe et al., 2004; Shaw et al., 2005).

A very low bathymetric slope is observed inthe distal part of the outer fold-and-thrust belt; thus,no significant propensity exists for regional fore-thrusts (east-dipping faults) to develop in preference

to backthrusts (west-dipping faults; Bilotti et al.,2005). We find, in fact, a much higher percentageof backthrusts compared to forethrusts in the studyarea. In addition to the thrust faults, we havemapped a small set of normal faults in the northernpart of our area and three primary strike-slip faultsthat crosscut the region striking northeast–south-west (Figure 3). Notably, most of the thrusts in thearea terminate into one or more of these strike-slipfaults. As noted previously, this truncation ofshortening structures is a defining characteristic oftear faults (Twiss and Moores, 1992).

With the availability of 3-D seismic reflectiondata, we were able to directly constrain the 3-D ge-ometry of the tear-fault systems using a combina-tion of vertical sections (inlines and crosslines) andtime and depth slices. As with thrust or normalfaults, we used abrupt fold limb (kink-band) ter-minations and horizon-fault cutoffs to precisely de-fine the position of the strike-slip fault traces in theseseismic sections (Figures 4, 5).

Vertical seismic sections provide the best meansof constraining the downdip extent of the tear-faultsystems. The section displayed in Figure 6 representsa typical image for any of the three primary strike-slip tear faults that crosscut the study area. We ob-serve significant vertical offsets across the strike-slip

Benesh et al. 469

Figure 4. Seismic dataillustrating the commonindicators (kink-band andhorizon terminations) thatare commonly used toidentify strike-slip faults inmap view. These dataare from a horizontal sliceat a depth of 4461 m(14,640 ft). Data are ownedand provided courtesyof CGGVeritas, Crawley,UK.

Figure 5. A second ex-ample of the interpreta-tion of strike-slip faults inmap view when usingthree-dimensional (3-D)seismic reflection data.These data are from ahorizontal slice at a depthof 4461m (14,640 ft). Dataare owned and providedcourtesy of CGGVeritas,Crawley, UK.

470 Geometry, Kinematics, and Displacement Characteristics of a Tear-Fault System

Figure 6. A representative cross sectionof the strike-slip faults in the study area.Note the vertical offset apparent for theLM, LO, and DW horizons that does notcontinue past the AF reflection. The reddashed line represents the likely detach-ment level. Data are owned and providedcourtesy of CGGVeritas, Crawley, UK.

faults for the Dahomey wedge, late Oligocene, andlateMiocene horizons; however, these offsets do notextend to the top Akata Formation horizon. InFigure 6, a vertical offset of approximately 0.25 km(0.16 mi) observed at the level of the DW hori-zon decreases to no discernable offset at the AFhorizon, which lies 0.5 km (0.3 mi) deeper. Thisabrupt downward decrease in separation suggeststhat the tear faults do not extend below the topAkata Formation. This interpreted fault termina-tion corresponds directly with the basal detach-ment horizon interpreted from the downward

termination of the thrust sheets (Figures 2, 7). Thisobservation supports the interpretation of the fold-and-thrust belt as a thin-skinned system and sug-gests that the tear-fault systems serve a function inaccommodating displacement gradients on the basaldetachment that are perpendicular to the generaleast–west transport direction.

Perhaps the best constraints on the 3-D geom-etry of the tear faults are provided by the time anddepth slices, where the strike-slip faults are typicallyimaged as discrete linear zones of low coherency.Structural and stratigraphic features, such as folds,

Benesh et al. 471

Figure 7. Seismic crosssection of a thrust faultin proximity to the south-ern strike-slip fault re-straining bend. The dark-blue dashed line showsthe division between stratadeposited before andduring growth. Data areowned and providedcourtesy of CGGVeritas,Crawley, UK.

thrust faults, and channel systems, are abruptly ter-minated across these strike-slip fault traces. Wedeveloped a 3-D representation of the tear faultsby mapping their traces in a series of closely spacedtime and depth slices, ranging from the sea floor tothe travel times and depths corresponding withthe basal detachment level. The faults have nearlyvertical dips along most of their extents, with sig-nificant changes in fault dip occurring in regions offault stepovers (Harding, 1985; Sylvester, 1988).Both extensional releasing and contractional re-straining bends are common along these tear-faultsystems. The timing of the deformation of thesestrike-slip faults is constrained by syntectonic growthstrata deposited across these restraining and re-leasing bend systems (Figure 8). In general, anupper Miocene horizon that sits approximately0.5 km (0.3 mi) stratigraphically higher than ourmapped late Miocene reflection marks the tran-sition from strata deposited pretectonically to syn-tectonically. The pretectonically deposited deltaicsection is characterized by laterally continuousstratigraphic horizons with stratigraphic thick-nesses that vary gradually. In contrast, the section

472 Geometry, Kinematics, and Displacement Characteristics of

deposited syntectonically thins abruptly onto struc-tural highs and includes stratigraphic onlaps andother features that indicate that the units weredeposited in the presence of bathymetry gener-ated by the growth of the underlying folds andfaults. Notably, the sections deposited during thegrowth of the toe thrusts and tear faults are co-incident (Figures 7, 8), further supporting ourinterpretation that the tear-fault systems are animportant factor in accommodating displacementgradients in the toe-thrust systems.

REGIONAL SHORTENING

To discern how the patterns of shortening in theouter fold-and-thrust belt are influenced by thestrike-slip faults, we estimated the total shorten-ing using three cross-sectional transects across theregion (see Figure 3 for map locations). The north-ern transect (AA′) is located north of the primarystrike-slip faults and encounters only two thrustfaults: one backthrust and one forethrust (Figure 9).Relative to the Akata Formation reflection, which

a Tear-Fault System

Figure 8. A seismiccross section through arestraining bend of thesouthern strike-slip faultexamined in Figure 5. Thedivision between pre-tectonically and syntecto-nically deposited strata ismarked by the dark-bluedashed line. This horizonmarks the beginning ofthe section deposited dur-ing the growth of boththe restraining bend andadjacent thrust faults(Figure 7). Data are ownedand provided courtesy ofCGGVeritas, Crawley, UK.

lies below the basal detachment, the overlying hori-zons are all shortened, with a maximum of 0.5 km(0.3 mi) of shortening reached at the level of thelate Oligocene reflection. Based on the palinspasticrestoration of these sections and shear fault-bendfolding theory, we assess that most of this short-ening results from displacement on the detach-ment and ductile deformation or shear within theDahomey wedge, with lesser amounts of shearbetween the Dahomey wedge and late Oligocenehorizons.

The central transect (BB′, Figure 10) is locatedbetween the northern and central strike-slip faultsand crosses the greatest number of thrust faults.Like the AA′ line, most of the faults in this sectionsole into the Dahomey wedge; however, severalsmaller faults terminate either between the lateOligocene and Dahomey wedge horizons or at theDahomey wedge horizon. This transect has under-gone considerably more shortening than the AA′line. Along the lateOligocene horizon,wemeasure3.0 km (1.9 mi) of shortening. As with AA′, most

Figure 9. Uninterpretedand interpreted regionalseismic profile along tran-sect AA’. The coloredhorizons represent theAF reflection (blue), thelikely detachment level(red, dashed), the DWreflection (green), the LOreflection (orange), andthe LM reflection (darkred). Amaximumof 0.5 km(1600 ft) of shorteningis measured along the LOhorizon for this transect.Data are owned andprovided courtesy ofCGGVeritas, Crawley, UK.

Benesh et al. 473

Figure 10. Uninterpreted and interpreted cross section along transect BB′. A maximum of 3.0 km (1.9 mi) of shortening is measuredalong the LO reflection (orange) for this transect. Data are owned and provided courtesy of CGGVeritas, Crawley, UK.

of this shortening is produced by shear within theDahomey wedge and is reflected in the consid-erable visible thinning and thickening within thatinterval. The shear above the Dahomey wedgehorizon also contributes some amount to the mea-sured maximum shortening.

The southernmost transect (CC′C″) containsfewer faults than section BB′ but more total short-ening (Figure 11). Because the toe-thrust systemsextend westward of the 3-D seismic coverage in thisregion,weextended the sectionusing constraints from2-D seismic reflection data. Measured along the late

Figure 11. Seismic profile for transect CC′C″. The left part of the pgeometries from two-dimensional (2-D) seismic lines. For this transectthe LO horizon (orange). Data are owned and provided courtesy of C

474 Geometry, Kinematics, and Displacement Characteristics of

Oligocene horizon, CC′C″ exhibits a maximum of3.8 km (2.4 mi) of shortening that is primarily pro-duced by ductile shear within the Dahomey wedge.

As illustrated by these transects, the contrac-tional structures in this region accommodate a gra-dient in westward-vergent shortening that increasesfrom north to south. This gradient is segmentedby the two northern strike-slip faults to produce anorthern low-shortening block, a central transitionblock, and a southern high-shortening block. Relativeto the northern low-shortening block, deformationextends farther to the west in the transition block

rofile between C′ and C″ represents an extrapolation of surface, we measure a maximum of 3.8 km (2.4 mi) of shortening alongGGVeritas, Crawley, UK.

a Tear-Fault System

Figure 12. An offsetchannel of the middle tolate Miocene (top), re-stored (left) and inter-preted (right). Restorationof the offset indicatesthat the fault has experi-enced 752 (±140) m (2470[±460] ft) of right-lateraldisplacement at this loca-tion. Data are owned andprovided courtesy ofCGGVeritas, Crawley, UK.

and farther still in the southern high-shorteningblock. This westward extension of the deformationfront, coupled with the north–south gradient inshortening, produces net right-lateralmotion alongthe strike-slip faults.

RESTORATION OF CHANNEL OFFSETS

In an effort to validate our interpretation of the senseof slip on the strike-slip faults and to define the fault-slip magnitude, we sought to determine piercingpoints that directly constrain the accumulated slip at

locations along the strike-slip faults. To this end, wehave identified in the 3-D seismic data two chan-nel systems that formed in the middle Miocene tolate Miocene that cross and are offset by the twonorthern primary strike-slip faults. These channelsoccur in the oldest part of the syntectonically de-posited section. Thus, we recognize that their pathsmay have been influenced by the initial formationof the fault system. As a result, apparent channeloffsets might overestimate true fault slip if thechannels traveled along the traces of the faults. Toavoid this pitfall, we selected sections of channelswith bends and meanders that are not aligned along

Benesh et al. 475

Figure 13. A channel ofthe middle to late Mio-cene that is offset by thecentral strike-slip fault(top), restored to a con-formable geometry (left)and interpreted (right). Therestored offset for thischannel indicates 1710(+100 or −600) m (5610[+330 or −1970] ft) ofright-lateral fault slip. Dataare owned and providedcourtesy of CGGVeritas,Crawley, UK.

the traces of the faults and thus provide more dis-tinct piercing-point offsets. The first of these chan-nels crosses themost northern strike-slip fault and iscomposed of two truncated arms of a 180° chan-nel bend (Figure 12).We find that a translation of752 (±140) m (2470 [±460] ft) along the strike-slip fault trace restores the bend and channel armsto a conformable position. The sense of translationagrees with right-lateral fault slip as inferred fromthe gradient in shortening across the fold-and-thrustbelt. The estimate of uncertainty that is included in

476 Geometry, Kinematics, and Displacement Characteristics of

our restoration measurement is derived from twosources. First, the inherent limitation in the reso-lution of seismic reflection data at depth (~50 m[160 ft]) produces some uncertainty in identifyingand tracing the specific amplitude or wavelet thatcorresponds to the impedance contrast producedby the presence of the channel. Second, given theamount of fault-related deformation that has oc-curred since the formation of the channel, we rec-ognize that not all parts of the channel trace arepreserved as they cross the fault. Thus, the restoration

a Tear-Fault System

measurement reflects our best attempt to alignwavelet signatures that we believewere contiguousor nearly contiguous in a pretectonic setting,withinthe limits of the data resolution.

The second channel crosses the central strike-slip fault near the western margin of the 3-D seis-mic data volume. We find that a translation of1710 m (5610 ft) restores the offset channel tracesto a conformable position (Figure 13); however,given the more linear trace and nebulous seis-mic character of this channel near the fault, we feelthat this restoration measurement is more likely torepresent a near-maximum offset value. Based onthe wavelet and amplitude signatures in the seis-mic data, we estimate that the restoration slip valuehas an uncertainty of +100 or −600 m (+330 or−1970 ft). Although more uncertainty is observed,we feel that the primary results of this channel res-toration are robust. Like the northern channel sys-tem, the sense of offset and translation for this sec-ond channel is consistentwith right-lateral strike-slipmotion. Moreover, the greater magnitude of slipalong this central strike-slip fault in comparison tothe northernmost fault is in accordance with ourearlier observations of a southward-increasing gra-dient in westward-vergent shortening across thefold-and-thrust belt.

Figure 14. Numerically meshed surfaces that represent thefault systems in the study area (Figure 3). The light green surfacerepresents the common detachment level shared by both thethrust and strike-slip faults.

SURFACE RESTORATION AND SLIPPROFILE CALCULATION

We seek to make a more comprehensive assess-ment of slip along the strike-slip faults, althoughthe recognition of offset channels has provided twopoint measurements of slip along the northern tearfaults and supported our conclusion based on theregional transects that the strike-slip faults seg-ment a north–south gradient in shortening. For thisassessment, we use a 2-D, horizon-based struc-tural restoration technique implemented in Gocad,a geological computer-aided design–based model-ing package (Mallet, 1992; Muron et al., 2005).This method simultaneously restores folds andfaults across a deformed horizon and therefore cal-culates a full displacement field for the horizon andthe faults that displace it. We selected for this

restoration the late Oligocene horizon because itrepresents a pretectonically deposited unit en-compassing the full amount of accumulated short-ening and, hence, strike-slip motion, within theregion of interest. After mapping the selected ho-rizon and faults in both the 2-D and 3-D seismicdata sets, we imported the picks into Gocad andused discrete smooth interpolation to generateevenly meshed surfaces. We then used a structuralmodeling workflow that allowed us to make itera-tive refinements to the horizon and fault surfaces toensuremodel consistency. Examining the 3-D faultrelationships during this process provided moresupport for the interpretation of a shallowcommondetachment level for all regional strike-slip andthrust faults (Figure 14).

The 2-D, or map-view, restoration techniquethat we apply is a parametric method that restoresthe faulted and folded surface back to a horizontaldatum while minimizing area change and internalstrain (Muron et al., 2005; Plesch et al., 2007). Tocalculate the displacements and strains needed torestore the deformed surface, the method requiresslip directions, but not magnitudes, on at least someof the faults to be specified. For our restoration, weelected to maintain the strike-slip faults as freesurfaces and thus specify only that the thrust faults

Benesh et al. 477

Figure 15. The de-formed (top) and restored(bottom) surfaces rep-resenting our upper hori-zon of the late Oligocene.The restoration solutionproduces 0.21% contrac-tion when moving fromthe undeformed to thedeformed state. Colorscorrespond to depth onlyin the upper image.

generally slip in a northeast–southwest direction,parallel with the strike-slip faults and consistentwith piercing-point offsets of channels. The smallnormal faults in the northern part of the sectionwere constrained to slip in a purely dip-slip sense.With these constraints and the added specificationof a pinpoint, we then used the restoration tool tocalculate the displacement and strain fields re-quired to flatten the horizon and fully recover itsfault offsets. The initial and restored lateOligocenesurfaces are shown in Figure 15.

In general, the restoration yields a smooth dis-placement field with translation in a direction par-allel with the slip on the thrust faults and the tracesof the tear faults. Moreover, the change in area be-tween the deformed and restored state is modest(0.21%), and the range of local strainmagnitudes issmall. In terms of local dilatation, or area change

478 Geometry, Kinematics, and Displacement Characteristics of

during the restoration, 90% of the surface hasstrains of less than ±4%. Higher strains, as much as±15%, are localized along fault traces. Thus, therestoration seems to perform well in recoveringboth fold and fault offsets while generally main-taining the area of the horizon with geologicallyreasonable magnitudes of local strain.

To further constrain the displacement profilesalong the strike-slip faults, we identify pairs of nodeson the horizon that lie adjacent to each other buton opposite sides of the strike-slip faults in theundeformed (restored) state. We then measurethe offset of these adjacent nodes in the deformedstate, thereby specifying the full displacement pro-files along the faults. These slip vectors allow us todefine both the strike-slip and dip-slip componentsof motion along both the northern (Figure 16) andcentral (Figure 17) strike-slip faults. In these figures,

a Tear-Fault System

Figure 16. Plot of the right-lateral slip (top) and displacement vectors (bottom) for the northern strike-slip fault. The dashed linesrepresent the location of intersecting thrust faults: Lines that extend upward from the dark-gray data points represent faults lying to thenorth, and lines extending downward correspond to thrust faults to the south. The light-gray area reflects uncertainty; the black diamondand error bars represent the measured slip value from the channel restoration (Figure 12). The slip vectors correspond to the movementof the northern block relative to the southern block.

the slip profiles represent right-lateral slip, and eachgray dashed line indicates the location at which athrust fault truncates into the strike-slip fault. Linesthat extend downward from the data points repre-sent thrust faults to the south of the strike-slip fault,whereas lines that extend upward represent thrustfaults on the northern side. The light gray–shaded

region represents the error in these restoration-basedslip measurements. Note that the error does notconstitute a comprehensive evaluation of all pos-sible modeled fault geometries and linkages, but itreflects the uncertainty inherent in the tracking of achosen seismic data horizon and in the generationof fault and horizon meshes based on those seismic

Figure 17. Plot of theright-lateral slip (top) anddisplacement vectors(bottom) for the centralstrike-slip fault in thestudy area. The dashedlines represent the loca-tion of intersecting thrustfaults. The light-gray areareflects uncertainty; theblack diamond and errorbars represent the mea-sured slip value fromthe channel restoration(Figure 13). The slip vec-tors correspond to move-ment of the northernblock relative to thesouthern block.

Benesh et al. 479

Figure 18. Block dia-grams, slip profiles, anddisplacement vectors for aconventional, throughgoingstrike-slip fault (left) andthin-skinned tear fault(right). The illustratedblock diagrams suggestcoeval activity for the strike-slip and thrust faults inthe tear-fault example butdemonstrate the non-contemporaneous natureof thrust-accommodatedshortening and strike-slipmotion in the conventionalview. The slip profiles anddisplacement vectors rep-resent an idealized case forthe traditional strike-slipfault (left) and reflect ourobservations of tear-faultsystems in the Niger Delta(right).

interpretations. The magnitude of this uncertaintyis approximately 125 m (410 ft).

We observe that the slip profiles for both strike-slip faults display a unique stair-step character. Slipis not uniform or smoothly varying but instead jumpsabruptly at each location where the strike-slip faultis met by a thrust fault. These jumps represent thetransition between the footwall and hanging-wallblocks for a given thrust fault. Because footwall andhanging-wall blocks have the opposite direction ofmotion by nature, moving from one to the otherproduces an abrupt change in differential motionalong the strike-slip fault. We also note that thrustfaults extending to the strike-slip fault from thenorth and the south tend to have opposite effects.Naturally, the development of a shortening struc-ture on one side of the fault would increase right-lateral motion, whereas the development of thesame structure on the opposite side would act todecrease right-lateral slip.

We note that the estimates of slip derivedfrom channel offsets accord very well with ourrestoration-calculated slip profiles (Figures 16, 17).For the northern strike-slip fault, the channel-

480 Geometry, Kinematics, and Displacement Characteristics of

measured slip value of 752 m (2470 ft) is 83% ofthe restoration-derived value. For the central strike-slip fault, the channel offset of 1710 m (5610 ft)represents 103% of the restoration-derived value.Both channel offset values fall within our esti-mates of the uncertainties in slip derived fromthe restorations.

Finally, we also note that the rake of the slipvectors and, hence, the proportions of strike-slipand dip (vertical)-slip displacement, vary abruptlyalong the tear faults. Specifically, the rake of the slipvector is nearly horizontal in regions where thrustsheets are not present, reflecting that slip is almostpurely strike-slip in these regions. In contrast, therake of the slip changes abruptly when a thrust faultbounds one or both sides of the tear fault becausethe component of thrust motion induces a locallyhigher component of dip slip on the tear faults. Col-lectively, these patterns of abruptly changing slipmagnitudes and orientations along the tear faultsclearly distinguish them from more continuous dis-placement patterns expected on traditional strike-slip faults (Walsh and Watterson, 1988; Kim andSanderson, 2005; Figure 18).

a Tear-Fault System

CONCLUSIONS

Although tear faults have long been recognized asimportant structural elements in fold-and-thrustbelts, a thorough understanding of their geometricand kinematic relationship to adjacent thrust faultsand their function in accommodating displacementgradients has been lacking. In part, this results fromthe difficulty in observing or imaging the inherently3-D nature of the fault interactions. This study hassought to overcome these limitations by using high-quality 3-D seismic reflection data to constrainmorefully the manner in which these tear faults interactwith thrust sheets and to define their displacementpatterns.

We have shown in an example from the north-western part of the outer fold-and-thrust belt of theNiger Delta that a north–south increase in west-ward displacement and shortening is partitionedby a system of tear faults. The tear faults not onlysegment the gradient in shortening across threelarge regional blocks, but also accommodate dif-ferential motion among the smaller footwall andhanging-wall blocks associatedwith individual thrustsheets. This accommodation produces a unique slipprofile for the tear faults, which exhibit changesin slipmagnitude and orientation occurring at theirintersections with each truncated thrust fault. Wesuggest that this type of slip profile is specific to thedevelopment of tear faults and that it may serve asa useful diagnostic tool that can be used to dis-tinguish tear faults from more traditional strike-slip systems.

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