Geometry, Kinematics, and Displacement

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Geometry, kinematics, and AUTHORS Nathan P. Benesh Department of Earth and displacement characteristics of Planetary Sciences, Harvard University, 20 Oxford Street, Cambridge, Massachusetts 02138; present tear-fault systems: An example address: ExxonMobil Upstream Research Compa- ny, Houston, Texas; [email protected] from the deep-water Niger Delta Nathan P. Benesh is a research geologist in the Struc- ture and Geomechanics Group at the ExxonMobil Upstream Research Company. He previously re- Nathan P. Benesh, Andreas Plesch, and John H. Shaw ceived his Ph.D. in earth and planetary sciences at Harvard University. His research interests focus on geomechanical modeling and the quantitative evaluation of structures at the trap to regional scale. ABSTRACT Andreas Plesch Department of Earth and We use three-dimensional seismic reflection data and new map- Planetary Sciences, Harvard University, 20 Oxford based structural restoration methods to define the displacement Street, Cambridge, Massachusetts; history and characteristics of a series of tear faults in the deep- [email protected] water Niger Delta. Deformation in the deep-water Niger Delta Andreas Plesch is a senior research associate in the is focused mostly within two fold-and-thrust belts that accom- Structural Geology and Earth Resources Group in modate downdip shortening produced by updip extension on the Earth and Planetary Science Department, Harvard University. He received his Ph.D. from the continental shelf. This shortening is accommodated by a Free University, Berlin, Germany. His research in- series of thrust sheets that are locally cut by strike-slip faults. terests revolve around three-dimensional model- Through seismic mapping and interpretation, we resolve these ing and the analysis of structures on the reservoir strike-slip faults to be tear faults that share a common detach- to mountain belt scale with a focus on quantitative aspects. ment level with the thrust faults. Acting in conjunction, these structures have accommodated a north–south gradient in John H. Shaw Department of Earth and westward-directed shortening. We apply a map-based resto- Planetary Sciences, Harvard University, 20 Oxford ration technique implemented in Gocad to restore an upper Street, Cambridge, Massachusetts; [email protected] stratigraphic horizon of the late Oligocene and use this analysis John H. Shaw is the Harry C. Dudley professor of to calculate slip profiles along the strike-slip faults. The slip structural and economic geology and chair of the magnitudes and directions change abruptly along the lengths Department of Earth and Planetary Sciences, of the tear faults as they interact with numerous thrust sheets. Harvard University. Prior to joining the Harvard The discontinuous nature of these slip profiles reflects the man- faculty, Shaw worked as an exploration and pro- ner in which they have accommodated differential movement duction geologist. His research interests include the structural characterization of complex traps between the footwall and hanging-wall blocks of the thrust and reservoirs in both conventional and uncon- sheets. In cases for which the relationship between a strike- ventional petroleum systems. slip fault and multiple thrust faults is unclear, the recognition of this type of slip profile may distinguish thin-skinned tear faults from more conventional deep-seated, throughgoing ACKNOWLEDGEMENTS strike-slip faults. We thank CGGVeritas for providing the seismic data used in this study and Landmark Graphics Corporation for donating the software through its University Grant Program. We also thank Exxon- Mobil for its support of this work and Chevron Corporation for providing additional data sets. The AAPG Editor thanks the following reviewers for Copyright ©2014. The American Association of Petroleum Geologists. All rights reserved. their work on this paper: Christopher F. Elders, Manuscript received January 25, 2011; provisional acceptance March 30, 2011; revised manuscript Stephen J. Naruk, and Sandro Serra. received 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 deltaic deposits on the continental shelf (Wu and Bally, 2000). This updip extension is fed at depth The Niger Delta, situated in the Gulf of Guinea at onto several detachment surfaces within thick over- the southern end of the Cretaceous Benue trough pressured shales of the early to middle Paleogene rift basin, represents one of the largest modern that underlie the postrift deltaic deposits (Bilotti deltas and most productive regions for petroleum et al., 2005; Corredor et al., 2005). Shortening in exploration in the world (Doust and Omatsola, the deep water began in the late Miocene to the 1990; Figure 1). The delta serves as a prime ex- early Pliocene to accommodate the slip that example of gravity-driven tectonic deformation, a tends downdip along these detachments. The characteristic of many deep-water passive margins thrust faults produced by this shortening occur in (Evamy et al., 1978; Doust and Omatsola, 1990). two distinct provinces, termed the “inner fold-and- The delta began to form as sediments that shed thrust belt” and the “outer fold-and-thrust belt” from the Niger River gradually filled the Benue (Connors et al., 1998; Corredor et al., 2005). trough during the opening of the equatorial At- With the advent of petroleum exploration in the lantic, and, by the late Eocene, the delta had be- deep-water Niger Delta in the 1990s, high-quality gun to prograde on top of the continental margin. two-dimensional (2-D) and three-dimensional (3-D) Two distinct fold-and-thrust belts within the delta seismic reflection data have been acquired, which accommodate the shortening and downdip de- have allowed for the investigation of the nature of formation produced by gravity-driven extension these gravity-driven contractional structures. These on the continental shelf. This gravity-driven ex- studies have mainly focused on the analysis of the tension is caused by rapid sediment deposition deep-water thrust faults and fault-related folds, in- that leads to differential loading and the subse- cluding their structural geometries and kinematics quent formation of large normal faults within the (e.g., Connors et al., 1998; Shaw et al., 2004; Suppe

Figure 1. A generalized map of the main structural provinces of the Niger Delta and a schematic diagram of the stratigraphy in the area of interest. Also shown are the locations of the three-dimensional (3-D) seismic reflection data volume and two-dimensional (2-D) seismic survey used in this study. Qua. = Quaternary; Plio. = Pliocene; Oligo. = Oligocene; Paleo. = Paleocene; Cret. = Cretaceous.

466 Geometry, Kinematics, and Displacement Characteristics of a Tear-Fault System et al., 2004; Corredor et al., 2005), and the effects of thrust-fault systems using 3-D seismic reflection high basal fluid pressures (e.g., Bilotti et al., 2005) data that image such structures in the outer fold- and multiple detachment surfaces (e.g., Corredor and-thrust belt of the Niger Delta. The system we et al., 2005; Briggs et al., 2006) on their structural analyze contains multiple strike-slip faults that styles. It is generally accepted that these thrust- work in tandem with the thrust structures to parti- related structures provide the dominant means by tion strain and accommodate a gradient in shorten- which shortening is accommodated in the com- ing across the fold-and-thrust belt. In addition to pressional toe of the delta; however, in this study, analyzing the geometric and genetic relationships we show that transport-parallel strike-slip faults among the faults, we quantify shortening across the are also an important factor. We use both high- region, and, by means of a map-view surface resto- resolution 2-D and 3-D seismic data (Figure 1) to ration, we determine diagnostic slip profiles for the analyze a system of tear faults in the outer fold- strike-slip tear faults. and-thrust belt that partition distal contractional deformation. The term “tear fault” has long been applied to GEOLOGIC SETTING strike-slip faults that abruptly terminate thrust sheets alongstrike (e.g., Twiss and Moores, 1992). The focus of this study is a series of tear faults that The Jacksboro and Russell Fork faults, which bracket occur near the northern termination of the outer thePineMountainthrustsheetinthesouthernAp- fold-and-thrust belt of the Niger Delta. The outer palachian Valley and Ridge Province in the eastern fold-and-thrust belt represents the more distal of United States, provide a well-known classic exam- the two fold-and-thrust belts that accommodate ple of a tear-fault system (Mitra, 1988). Beyond outboard shortening driven by gravitational col- the Appalachians, thin-skinned tear faults that only lapse and extension of the deltaic sequence on the involve the shallow sedimentary section have also continental shelf. For most of the outer fold-and- been noted in the Canadian Rocky Mountains thrust belt, the primary detachment lies within the (Benvenuto and Price, 1979), the Western Foothills Akata Formation (Corredor et al., 2005), a time- of Taiwan (Mouthereau et al., 1999), the Santa transgressive, thick marine shale that generally sits Barbara Channel (Shaw and Suppe, 1994), and the atop an Upper Cretaceous sedimentary sequence, Maracaibo Basin in Venezuela (Escalona and Mann, which itself overlies an Early Cretaceous oceanic 2006), among other localities. These tear faults are crust (Avbovbo, 1978; Knox and Omatsola, 1989; commonly recognized based on surface exposure Wu and Bally, 2000; Figure 1). This shale is be- or interpretations of 2-D seismic lines. The inher- lieved to be one of the major source rocks for hy- ently 3-D nature of these faults, however, has made drocarbons in the delta and also contains some it difficult to fully constrain their geometries, ki- locally developed turbidite sands. Additionally, nematics, and displacement characteristics. Leduc the formation generally exhibits a low seismic et al. (2012) used 3-D seismic data to evaluate a velocity that reflects fluid overpressures that lo- strike-slip system that accommodates motion on cally reach 90% of the lithostatic stress (Bilotti primarily extensional faults on the northern mar- et al., 2005). Above the Akata Formation lies the gin of the Niger Delta, inboard of the outer fold- Agbada Formation. This formation is Eocene to and-thrust belt; however, we know of no other Pleistocene in age and is believed to be the dom- study in which 3-D seismic data have been applied inant petroleum-bearing unit in the delta. In our to carefully examine the full spatial relationship study area, the lowest part of the Agbada consists and displacement profiles for multiple tear faults of channel complexes and basin-floor fans com- and the thrust faults that they more commonly posed of sediments that are believed to be sourced terminate. The aim of this article, based on the work from the Dahomey trough of the onshore Guinea of Benesh (2010), is to more fully characterize the Basin. This unit tapers out southward and is nature of tear faults and their relationships with termed the “Dahomey wedge” (Morgan, 2004;

Benesh et al. 467 Figure 2. A representative thrust fault from the outer fold-and-thrust belt in the northwestern part of the Niger Delta. This structure displays the classic characteristics of a shear fault-bend fold as reflected in the long and shallowly dipping backlimb. The interpreted detachment level for this structure (red dashed line) is above the Akata Formation, within the Dahomey wedge. All seismic data presented here are migrated and depth converted. Data are owned and provided courtesy of CGGVeritas, Crawley, UK.

Briggs et al., 2006; Figure 1). The overlying Benin This type of fold geometry is commonly produced Formation, found in some coastal regions, is not when a weak hanging-wall stratigraphic interval encountered in the deep-water region of our study undergoes bed-parallel simple shear, or pure shear area. localized above the base of the thrust ramp, during fold growth. Corredor et al. (2005) showed that this shear was generally localized in the Akata Formation STRUCTURE and the lowermost part of the Agbada Formation for much of the southern lobe of the outer fold-and- Most of the shortening is accommodated in the thrust belt. We find, however, that, in our northern outer fold-and-thrust belt by thrust sheets, com- study area, shear is limited to the lowermost part of monly referred to as “toe thrusts,” that exhibit a the Agbada Formation, within the weak Dahomey variety of structural styles including detachment, wedge, as the basal detachment for the fold-and- fault-propagation, fault-bend, and shear fault-bend thrust belt has generally risen to the top of the Akata folding (Shaw et al., 2004; Suppe et al., 2004; Formation (Figure 2). As has been modeled and in- Corredor et al., 2005; Higgins et al., 2007; Kostenko ferred in the southern Niger Delta (Cobbold et al., et al., 2008). Many of these folds that develop above 2001, 2009; Mourgues and Cobbold, 2006), shear the thrust faults involve a significant component localized within the Dahomey wedge and the loca- of pure and/or simple shear, reflected in long back- tion of the basal detachment may arise from local limbs that typically dip less than the fault ramp overpressure near the top and the bottom of the (Serra, 1977; Suppe et al., 2004; Shaw et al., 2005). Akata Formation and the Agbada Formation,

468 Geometry, Kinematics, and Displacement Characteristics of a Tear-Fault System Figure 3. A horizontal slice of seismic data at a depth of 4461 m (14,640 ft, left) and an illustrated structural map (right). The location of the seismic data volume is shown in Figure 1. The dashed lines indicate the positions of various figures and regional cross sections dis- cussed in the text. Data are owned and provided courtesy of CGGVeritas, Crawley, UK.

respectively (Bilotti et al., 2005; Briggs et al., to backthrusts (west-dipping faults; Bilotti et al., 2006; Guzofski, 2007). 2005). We find, in fact, a much higher percentage A migrated and depth-converted seismic profile of backthrusts compared to forethrusts in the study from a 3-D seismic volume is presented in Figure 2. area. In addition to the thrust faults, we have These seismic data show a typical toe-thrust struc- mapped a small set of normal faults in the northern ture, or shear fault-bend fold, from the study area. part of our area and three primary strike-slip faults The interpreted version of the profile also displays that crosscut the region striking northeast–south- the four primary stratigraphic horizons that we west (Figure 3). Notably, most of the thrusts in the mapped across the region and used for our structural area terminate into one or more of these strike-slip characterization. Starting with the deepest level, the faults. As noted previously, this truncation of horizons represent the top of the Akata Formation, shortening structures is a defining characteristic of the top of the Dahomey wedge, a prominent Agbada tear faults (Twiss and Moores, 1992). Formation reflection of the late Oligocene, and an- With the availability of 3-D seismic reflection other prominent Agbada Formation reflection of data, we were able to directly constrain the 3-D ge- the late Miocene. Aided by these mapped horizons, ometry of the tear-fault systems using a combina- which we will refer to as the “AF,”“DW,”“LO,” tion of vertical sections (inlines and crosslines) and and “LM” horizons, we can see that the inter- time and depth slices. As with thrust or normal preted structure displays the classic character- faults, we used abrupt fold limb (kink-band) ter- istics of a shear fault-bend fold; it possesses a minations and horizon-fault cutoffs to precisely de- backlimb that dips less than the fault ramp and has fine the position of the strike-slip fault traces in these a width much greater than the forelimb of the fold seismic sections (Figures 4,5). and greater than the amount of slip on the thrust Vertical seismic sections provide the best means ramp (Suppe et al., 2004; Shaw et al., 2005). of constraining the downdip extent of the tear-fault A very low bathymetric slope is observed in systems. The section displayed in Figure 6 represents the distal part of the outer fold-and-thrust belt; thus, a typical image for any of the three primary strike- no significant propensity exists for regional fore- slip tear faults that crosscut the study area. We ob- thrusts (east-dipping faults) to develop in preference serve significant vertical offsets across the strike-slip

Benesh et al. 469 Figure 4. Seismic data illustrating the common indicators (kink-band and horizon terminations) that are commonly used to identify strike-slip faults in map view. These data are from a horizontal slice at a depth of 4461 m (14,640 ft). Data are owned and provided courtesy of CGGVeritas, Crawley, UK.

Figure 5. A second example of the interpretation of strike-slip faults in map view when using three-dimensional (3-D) seismic reflection data. These data are from a horizontal slice at a depth of 4461 m (14,640 ft). Data are owned and provided courtesy of CGGVeritas, Crawley, UK.

470 Geometry, Kinematics, and Displacement Characteristics of a Tear-Fault System Figure 6. A representative cross section of the strike-slip faults in the study area. Note the vertical offset apparent for the LM, LO, and DW horizons that does not continue past the AF reflection. The red dashed line represents the likely detachment level. Data are owned and provided courtesy of CGGVeritas, Crawley, UK.

faults for the Dahomey wedge, late Oligocene, and termination of the thrust sheets (Figures 2, 7). This late Miocene horizons; however, these offsets do not observation supports the interpretation of the fold- extend to the top Akata Formation horizon. In and-thrust belt as a thin-skinned system and sug- Figure 6, a vertical offset of approximately 0.25 km gests that the tear-fault systems serve a function in (0.16 mi) observed at the level of the DW hori- accommodating displacement gradients on the basal zon decreases to no discernable offset at the AF detachment that are perpendicular to the general horizon, which lies 0.5 km (0.3 mi) deeper. This east–west transport direction. abrupt downward decrease in separation suggests Perhaps the best constraints on the 3-D geom- that the tear faults do not extend below the top etry of the tear faults are provided by the time and Akata Formation. This interpreted fault termina- depth slices, where the strike-slip faults are typically tion corresponds directly with the basal detach- imaged as discrete linear zones of low coherency. ment horizon interpreted from the downward Structural and stratigraphic features, such as folds,

Benesh et al. 471 Figure 7. Seismic cross section of a thrust fault in proximity to the southern strike-slip fault restraining bend. The dark- blue dashed line shows the division between strata deposited before and during growth. Data are owned and provided courtesy of CGGVeritas, Crawley, UK.

thrust faults, and channel systems, are abruptly ter- deposited syntectonically thins abruptly onto struc- minated across these strike-slip fault traces. We tural highs and includes stratigraphic onlaps and developed a 3-D representation of the tear faults other features that indicate that the units were by mapping their traces in a series of closely spaced deposited in the presence of bathymetry gener- time and depth slices, ranging from the sea floor to ated by the growth of the underlying folds and the travel times and depths corresponding with faults. Notably, the sections deposited during the the basal detachment level. The faults have nearly growth of the toe thrusts and tear faults are co- vertical dips along most of their extents, with sig- incident (Figures 7, 8), further supporting our nificant changes in fault dip occurring in regions of interpretation that the tear-fault systems are an fault stepovers (Harding, 1985; Sylvester, 1988). important factor in accommodating displacement Both extensional releasing and contractional re- gradients in the toe-thrust systems. straining bends are common along these tear-fault systems. The timing of the deformation of these strike-slip faults is constrained by syntectonic growth REGIONAL SHORTENING strata deposited across these restraining and releasing bend systems (Figure 8). In general, an To discern how the patterns of shortening in the upper Miocene horizon that sits approximately outer fold-and-thrust belt are influenced by the 0.5 km (0.3 mi) stratigraphically higher than our strike-slip faults, we estimated the total shorten- mapped late Miocene reflection marks the tran- ing using three cross-sectional transects across the sition from strata deposited pretectonically to syn- region (see Figure 3 for map locations). The north- tectonically. The pretectonically deposited deltaic ern transect (AA′) is located north of the primary section is characterized by laterally continuous strike-slip faults and encounters only two thrust stratigraphic horizons with stratigraphic thick- faults: one backthrust and one forethrust (Figure 9). nesses that vary gradually. In contrast, the section Relative to the Akata Formation reflection, which

472 Geometry, Kinematics, and Displacement Characteristics of a Tear-Fault System Figure 8. A seismic cross section through a restraining bend of the southern strike-slip fault examined in Figure 5.The division between pretectonically and syntectonically deposited strata is marked by the dark-blue dashed line. This horizon marks the beginning of the section deposited during the growth of both the restraining bend and adjacent thrust faults (Figure 7). Data are owned and provided courtesy of CGGVeritas, Crawley, UK.

lies below the basal detachment, the overlying hori- The central transect (BB′, Figure 10) is located zons are all shortened, with a maximum of 0.5 km between the northern and central strike-slip faults (0.3 mi) of shortening reached at the level of the and crosses the greatest number of thrust faults. late Oligocene reflection. Based on the palinspastic Like the AA′ line, most of the faults in this section restoration of these sections and shear fault-bend sole into the Dahomey wedge; however, several folding theory, we assess that most of this short- smaller faults terminate either between the late ening results from displacement on the detach- Oligocene and Dahomey wedge horizons or at the ment and ductile deformation or shear within the Dahomey wedge horizon. This transect has under- Dahomey wedge, with lesser amounts of shear gone considerably more shortening than the AA′ between the Dahomey wedge and late Oligocene line. Along the late Oligocene horizon, we measure horizons. 3.0 km (1.9 mi) of shortening. As with AA′, most

Figure 9. Uninterpreted and interpreted regional seismic profile along transect AA’. The colored horizons represent the AF reflection (blue), the likely detachment level (red, dashed), the DW reflection (green), the LO reflection (orange), and the LM reflection (dark red). A maximum of 0.5 km (1600 ft) of shortening is measured along the LO horizon for this transect. Data are owned and provided courtesy of CGGVeritas, 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 measured along 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 the Oligocene horizon, CC′C″ exhibits a maximum of Dahomey wedge and is reflected in the consid- 3.8 km (2.4 mi) of shortening that is primarily pro- erable visible thinning and thickening within that duced by ductile shear within the Dahomey wedge. interval. The shear above the Dahomey wedge As illustrated by these transects, the contrac- horizon also contributes some amount to the mea- tional structures in this region accommodate a gra- sured maximum shortening. dient in westward-vergent shortening that increases The southernmost transect (CC′C″)contains from north to south. This gradient is segmented fewer faults than section BB′ but more total short- by the two northern strike-slip faults to produce a ening (Figure 11). Because the toe-thrust systems northern low-shortening block, a central transition extend westward of the 3-D seismic coverage in this block, and a southern high-shortening block. Relative region, we extended the section using constraints from to the northern low-shortening block, deformation 2-D seismic reflection data. Measured along the late extends farther to the west in the transition block

Figure 11. Seismic profile for transect CC′C″. The left part of the profile between C′ and C″ represents an extrapolation of surface geometries from two-dimensional (2-D) seismic lines. For this transect, we measure a maximum of 3.8 km (2.4 mi) of shortening along the LO horizon (orange). Data are owned and provided courtesy of CGGVeritas, Crawley, UK.

474 Geometry, Kinematics, and Displacement Characteristics of a Tear-Fault System Figure 12. An offset channel of the middle to late Miocene (top), restored (left) and interpreted (right). Restoration of the offset indicates that the fault has experi- enced 752 (±140) m (2470 [±460] ft) of right-lateral displacement at this location. Data are owned and provided courtesy of CGGVeritas, Crawley, UK.

and farther still in the southern high-shortening locations along the strike-slip faults. To this end, we block. This westward extension of the deformation have identified in the 3-D seismic data two chan- front, coupled with the north–south gradient in nel systems that formed in the middle Miocene to shortening, produces net right-lateral motion along late Miocene that cross and are offset by the two the strike-slip faults. northern primary strike-slip faults. These channels occur in the oldest part of the syntectonically deposited section. Thus, we recognize that their paths RESTORATION OF CHANNEL OFFSETS may have been influenced by the initial formation of the fault system. As a result, apparent channel In an effort to validate our interpretation of the sense offsets might overestimate true fault slip if the of slip on the strike-slip faults and to define the fault- channels traveled along the traces of the faults. To slip magnitude, we sought to determine piercing avoid this pitfall, we selected sections of channels points that directly constrain the accumulated slip at with bends and meanders that are not aligned along

Benesh et al. 475 Figure 13. A channel of the middle to late Mio- cene that is offset by the central strike-slip fault (top), restored to a conformable geometry (left) and interpreted (right). The restored offset for this channel indicates 1710 (+100 or −600) m (5610 [+330 or −1970] ft) of right-lateral fault slip. Data are owned and provided courtesy of CGGVeritas, Crawley, UK.

the traces of the faults and thus provide more dis- our restoration measurement is derived from two tinct piercing-point offsets. The first of these chan- sources. First, the inherent limitation in the reso- nels crosses the most northern strike-slip fault and is lution of seismic reflection data at depth (~50 m composed of two truncated arms of a 180° chan- [160 ft]) produces some uncertainty in identifying nel bend (Figure 12). We find that a translation of and tracing the specific amplitude or wavelet that 752 (±140) m (2470 [±460] ft) along the strike- corresponds to the impedance contrast produced slip fault trace restores the bend and channel arms by the presence of the channel. Second, given the to a conformable position. The sense of translation amount of fault-related deformation that has oc- agrees with right-lateral fault slip as inferred from curred since the formation of the channel, we rec- the gradient in shortening across the fold-and-thrust ognize that not all parts of the channel trace are belt. The estimate of uncertainty that is included in preserved as they cross the fault. Thus, the restoration

476 Geometry, Kinematics, and Displacement Characteristics of a Tear-Fault System measurement reflects our best attempt to align restoration the late Oligocene horizon because it wavelet signatures that we believe were contiguous represents a pretectonically deposited unit en- or nearly contiguous in a pretectonic setting, within compassing the full amount of accumulated short- the limits of the data resolution. ening and, hence, strike-slip motion, within the The second channel crosses the central strike- region of interest. After mapping the selected ho- slip fault near the western margin of the 3-D seis- rizon and faults in both the 2-D and 3-D seismic mic data volume. We find that a translation of data sets, we imported the picks into Gocad and 1710 m (5610 ft) restores the offset channel traces used discrete smooth interpolation to generate to a conformable position (Figure 13); however, evenly meshed surfaces. We then used a structural given the more linear trace and nebulous seis- modeling workflow that allowed us to make itera- mic character of this channel near the fault, we feel tive refinements to the horizon and fault surfaces to that this restoration measurement is more likely to ensure model consistency. Examining the 3-D fault represent a near-maximum offset value. Based on relationships during this process provided more the wavelet and amplitude signatures in the seis- support for the interpretation of a shallow common mic data, we estimate that the restoration slip value detachment level for all regional strike-slip and has an uncertainty of +100 or −600 m (+330 or thrust faults (Figure 14). −1970 ft). Although more uncertainty is observed, The 2-D, or map-view, restoration technique we feel that the primary results of this channel res- that we apply is a parametric method that restores toration are robust. Like the northern channel sys- the faulted and folded surface back to a horizontal tem, the sense of offset and translation for this sec- datum while minimizing area change and internal ond channel is consistent with right-lateral strike-slip strain (Muron et al., 2005; Plesch et al., 2007). To motion. Moreover, the greater magnitude of slip calculate the displacements and strains needed to along this central strike-slip fault in comparison to restore the deformed surface, the method requires the northernmost fault is in accordance with our slip directions, but not magnitudes, on at least some earlier observations of a southward-increasing gra- of the faults to be specified. For our restoration, we dient in westward-vergent shortening across the elected to maintain the strike-slip faults as free fold-and-thrust belt. surfaces and thus specify only that the thrust faults

SURFACE RESTORATION AND SLIP PROFILE CALCULATION

We seek to make a more comprehensive assessment of slip along the strike-slip faults, although the recognition of offset channels has provided two point measurements of slip along the northern tear faults and supported our conclusion based on the regional transects that the strike-slip faults segment a north–south gradient in shortening. For this assessment, we use a 2-D, horizon-based structural restoration technique implemented in Gocad, a geological computer-aided design–based modeling package (Mallet, 1992; Muron et al., 2005). This method simultaneously restores folds and Figure 14. Numerically meshed surfaces that represent the faults across a deformed horizon and therefore cal- fault systems in the study area (Figure 3). The light green surface culates a full displacement field for the horizon and represents the common detachment level shared by both the the faults that displace it. We selected for this thrust and strike-slip faults.

Benesh et al. 477 Figure 15. The deformed (top) and restored (bottom) surfaces rep- resenting our upper horizon of the late Oligocene. The restoration solution produces 0.21% contrac- tion when moving from the undeformed to the deformed state. Colors correspond to depth only in the upper image.

generally slip in a northeast–southwest direction, during the restoration, 90% of the surface has parallel with the strike-slip faults and consistent strains of less than ±4%. Higher strains, as much as with piercing-point offsets of channels. The small ±15%, are localized along fault traces. Thus, the normal faults in the northern part of the section restoration seems to perform well in recovering were constrained to slip in a purely dip-slip sense. both fold and fault offsets while generally main- With these constraints and the added specification taining the area of the horizon with geologically of a pinpoint, we then used the restoration tool to reasonable magnitudes of local strain. calculate the displacement and strain fields re- To further constrain the displacement profiles quired to flatten the horizon and fully recover its along the strike-slip faults, we identify pairs of nodes fault offsets. The initial and restored late Oligocene on the horizon that lie adjacent to each other but surfaces are shown in Figure 15. on opposite sides of the strike-slip faults in the In general, the restoration yields a smooth dis- undeformed (restored) state. We then measure placementfieldwithtranslationinadirectionpar- the offset of these adjacent nodes in the deformed allel with the slip on the thrust faults and the traces state, thereby specifying the full displacement pro- of the tear faults. Moreover, the change in area be- files along the faults. These slip vectors allow us to tween the deformed and restored state is modest define both the strike-slip and dip-slip components (0.21%), and the range of local strain magnitudes is of motion along both the northern (Figure 16)and small. In terms of local dilatation, or area change central (Figure 17) strike-slip faults. In these figures,

478 Geometry, Kinematics, and Displacement Characteristics of 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 lines represent the location of intersecting thrust faults: Lines that extend upward from the dark-gray data points represent faults lying to the north, and lines extending downward correspond to thrust faults to the south. The light-gray area reflects uncertainty; the black diamond and error bars represent the measured slip value from the channel restoration (Figure 12). The slip vectors correspond to the movement of the northern block relative to the southern block.

the slip profiles represent right-lateral slip, and each region represents the error in these restoration-based gray dashed line indicates the location at which a slip measurements. Note that the error does not thrust fault truncates into the strike-slip fault. Lines constitute a comprehensive evaluation of all pos- that extend downward from the data points repre- sible modeled fault geometries and linkages, but it sent thrust faults to the south of the strike-slip fault, reflects the uncertainty inherent in the tracking of a whereas lines that extend upward represent thrust chosen seismic data horizon and in the generation faults on the northern side. The light gray–shaded of fault and horizon meshes based on those seismic

Figure 17. Plot of the right-lateral slip (top) and displacement vectors (bottom) for the central strike-slip fault in the study area. The dashed lines represent the location of intersecting thrust faults. The light-gray area reflects uncertainty; the black diamond and error bars represent the measured slip value from the channel restoration (Figure 13). The slip vectors correspond to movement of the northern block relative to the southern block.

Benesh et al. 479 Figure 18. Block diagrams, slip profiles, and displacement vectors for a conventional, throughgoing strike-slip fault (left) and thin-skinned tear fault (right). The illustrated block diagrams suggest coeval activity for the strike- slip and thrust faults in the tear-fault example but demonstrate the non- contemporaneous nature of thrust-accommodated shortening and strike-slip motion in the conventional view. The slip profiles and displacement vectors represent an idealized case for the traditional strike-slip fault (left) and reflect our observations of tear-fault systems in the Niger Delta (right).

interpretations. The magnitude of this uncertainty measured slip value of 752 m (2470 ft) is 83% of is approximately 125 m (410 ft). the restoration-derived value. For the central strike- We observe that the slip profiles for both strike- slip fault, the channel offset of 1710 m (5610 ft) slip faults display a unique stair-step character. Slip represents 103% of the restoration-derived value. is not uniform or smoothly varying but instead jumps Both channel offset values fall within our esti- abruptly at each location where the strike-slip fault mates of the uncertainties in slip derived from is met by a thrust fault. These jumps represent the the restorations. transition between the footwall and hanging-wall Finally, we also note that the rake of the slip blocks for a given thrust fault. Because footwall and vectors and, hence, the proportions of strike-slip hanging-wall blocks have the opposite direction of and dip (vertical)-slip displacement, vary abruptly motion by nature, moving from one to the other along the tear faults. Specifically, the rake of the slip produces an abrupt change in differential motion vector is nearly horizontal in regions where thrust along the strike-slip fault. We also note that thrust sheets are not present, reflecting that slip is almost faults extending to the strike-slip fault from the purely strike-slip in these regions. In contrast, the north and the south tend to have opposite effects. rake of the slip changes abruptly when a thrust fault Naturally, the development of a shortening struc- bounds one or both sides of the tear fault because ture on one side of the fault would increase right- the component of thrust motion induces a locally lateral motion, whereas the development of the higher component of dip slip on the tear faults. Col- same structure on the opposite side would act to lectively, these patterns of abruptly changing slip decrease right-lateral slip. magnitudes and orientations along the tear faults We note that the estimates of slip derived clearly distinguish them from more continuous dis- from channel offsets accord very well with our placement patterns expected on traditional strike- restoration-calculated slip profiles (Figures 16,17). slip faults (Walsh and Watterson, 1988; Kim and For the northern strike-slip fault, the channel- Sanderson, 2005; Figure 18).

480 Geometry, Kinematics, and Displacement Characteristics of a Tear-Fault System CONCLUSIONS contractional fault-related folds: An AAPG seismic atlas: AAPG Studies in Geology 53, p. 103–104. Briggs, S. E., R. J. Davies, J. A. Cartwright, and R. Morgan, Although tear faults have long been recognized as 2006, Multiple detachment levels and their control on important structural elements in fold-and-thrust fold styles in the compressional domain of the deep wa- belts, a thorough understanding of their geometric ter west Niger Delta: Basin Research, v. 18, p. 435–450, doi:10.1111/j.1365-2117.2006.00300.x. and kinematic relationship to adjacent thrust faults Cobbold, P. R., S. Durand, and R. Mourgues, 2001, Sandbox and their function in accommodating displacement modeling of thrust wedges with fluid-assisted detach- gradients has been lacking. In part, this results from ments: Tectonophysics, v. 334, p. 245–258, doi:10.1016 the difficulty in observing or imaging the inherently /S0040-1951(01)00070-1. Cobbold, P. R., B. J. Clarke, and H. Løseth, 2009, Structural 3-D nature of the fault interactions. This study has consequences of fluid overpressure and seepage forces sought to overcome these limitations by using high- in the outer thrust belt of the Niger Delta: Petroleum quality 3-D seismic reflection data to constrain more Geoscience, v. 15, p. 3–15, doi:10.1144/1354-079309 fully the manner in which these tear faults interact -784. Connors, C. D., D. B. Denson, G. Kristiansen, and D. M. with thrust sheets and to define their displacement Angstadt, 1998, Compressive anticlines of the mid-outer patterns. slope, central Niger Delta: AAPG Bulletin, v. 82, no. 10, Wehaveshowninanexamplefromthenorth- p. 1903. Corredor, F., J. H. Shaw, and F. Bilotti, 2005, Structural western part of the outer fold-and-thrust belt of the styles in the deep-water fold and thrust belts of the Niger Niger Delta that a north–south increase in west- Delta: AAPG Bulletin, v. 89, p. 753–780, doi:10.1306 ward displacement and shortening is partitioned /02170504074. by a system of tear faults. The tear faults not only Doust, H., and E. Omatsola, 1990, Niger Delta, in J. D. Edwards and P. A. Santogrossi, eds., Divergent/passive margin ba- segment the gradient in shortening across three sins: AAPG Memoir 48, p. 201–238. large regional blocks, but also accommodate dif- Escalona, A., and P. Mann, 2006, Tectonic controls of the ferential motion among the smaller footwall and right-lateral Burro Negro tear fault on Paleogene struc- hanging-wall blocks associated with individual thrust ture and stratigraphy, northeastern Maracaibo Basin: AAPG Bulletin, v. 90, no. 4, p. 479–504, doi:10.1306 sheets. 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482 Geometry, Kinematics, and Displacement Characteristics of a Tear-Fault System