Analysis of 28.5 km² of three-dimensional (3-D) seismic reflection data from the triangle zone of the Ouachita fold-and-thrust belt and the foreland Arkoma basin reveals structural details not recognized previously in conventional two-dimensional (2-D) seismic data. The data indicate that the frontal Kiowa syncline in the Arkoma basin has been passively uplifted by blind thrusting at the Morrowan Wapanucka Limestone level, and that smaller wavelength folds are produced by thrusting at shallower levels in the Atoka Formation. Faulting at deeper levels in the Hunton and Arbuckle groups has been traditionally interpreted as normal, but our analysis of this data set indicates that, in this area, normal faults were reactivated during the Ouachita orogeny as reverse aults, and the changes in fault separation can be followed along strike. These faults show the same trend as the overlying thrusts and are normal or have minor inversion where the overlying thrusts have small displacement. These faults have been completely inverted where the overlying thrusts have more displacement, suggesting a genetic relation between the Wapanucka thrusts and the inversion of the Hunton and Arbuckle faults.

Four reflections were chosen for analysis: one reflection in the lower Atoka Formation, two reflections repeated in the Wapanucka Limestone, and a fourth reflection in the Hunton Group. All of these surfaces exhibit the same geometry with the fold axes plunging to the southwest. Variations in bearing and plunge of fold axes in the Wapanucka Limestone can be directly correlated to changes in displacement and ramp height along strike. The similarity between surface geometries suggests that the last deformation took place at deeper levels in the Hunton and Arbuckle groups and folded the overlying thrusts. Reactivation of Atokan normal faults at deeper levels in the Arkoma basin and Ouachita subthrust play may be more widespread than previously recognized.

INTRODUCTION

The Ouachita system is a late Paleozoic orogene that extends from the southern end of the Appalachian Mountains to west Texas. The Ouachita Mountains and the southern part of the Arkoma basin are the main outcrop regions of the late Paleozoic collisional orogene along the North American craton (Arbenz, 1989). The boundary between the frontal zone of the Ouachita Mountains and the foreland Arkoma basin is drawn along the trace of the Choctaw fault. The Arkoma basin is a mildly compressed fold belt characterized by open folds with minor faulting, whereas the frontal zone of the Ouachita Mountains is defined by imbricated thrust faults with tight to overturned folds. The transition from fold-and-thrust belt to foreland basin is marked by a classic triangle zone (Hardie, 1988).

Exploration objectives in the area include (1) Atokan sandstones in shallow folds; (2) Spiro Sandstone and Wapanucka Limestone reservoirs in thrust-related structures (Berry and Trumbly, 1968), and (3) Cambrian-Ordovician Arbuckle carbonates on fault-bounded blocks (e.g., Wilburton field). The major emphasis is presently on Spiro-Wapanucka and Arbuckle plays, which require high-quality seismic data to accurately define the extent of structures and location of faults and fold crests (Bertagne and Leising, 1989).

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With the development of 3-D seismic technology, a more detailed image of the subsurface geology is possible. Migration of 3-D data reduces sideswipe and places dipping and curvilinear reflections in their proper vertical and horizontal positions. One of the most important advantages of a 3-D seismic survey is that the data provide a volume that can be examined in various ways: vertical slices in any arbitrary direction, time slices, chair displays, and isometric views. Thus, a feature that may not be clear in one type of a section may be evident in another. The time slice is very useful for structural interpretation because it shows the structural position of the reflections, very much like a geologic map.

Our study uses a 28.5-km² 3-D seismic survey from the triangle zone between the frontal Ouachita Mountains and southern Arkoma basin to produce a detailed 3-D picture of the blind thrusting and block faulting under the frontal syncline of the triangle zone. The survey is located in southeastern Oklahoma, in Pittsburg County, 10 km southeast of McAlester (Figure 1) and 2 km northwest of the trace of the Choctaw fault. The survey

Fig. 1. Location map showing the study area in the Ouachita Mountains and Arkoma basin. The surface traces of the main faults are shown for reference. The Choctaw fault separates the Arkoma basin and the Ouachita Mountains in Oklahoma.

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area is rectangular, with the long dimension parallel to the southwest structural trend.

GEOLOGIC SETTING

The Ouachita Mountains in southeastern Oklahoma and western Arkansas are part of a mostly buried late Paleozoic fold-and-thrust belt that extends from Alabama to northern Mexico. In Oklahoma, the Ouachita Mountains and the Arkoma basin can be divided into four tectonic provinces (structural regions) on the basis of different structural styles (Arbenz, 1989; Suneson and Campbell, 1990). From north to south (Figure 1) they are (1) the Arkoma foreland basin, a mildly compressed fold belt of Pennsylvanian rocks, (2) the frontal thrust zone, which lies between the Choctaw and Windingstair faults and consists of severely shortened, north- and northwest-vergent imbricated thrusts and tight folds of mainly Pennsylvanian strata, (3) the central thrust zone, characterized by broad open syncline separated by tight, typically thrust-cored anticlines of mainly Mississippian and Lower Pennsylvanian turbidites, and (4) the Broken Bow uplift, which consists of isoclinally folded and faulted Lower Ordovician to Lower Mississippian strata of mostly deep-water origin.

The tectonic history of the Oklahoma portion of the Ouachita orogene can be summarized as follows. During the late Precambrian and Early Cambrian, opening of the Iapetus ocean produced an irregular rifted margin of the North American craton (Thomas, 1991). Subsequently, a broad, southward-dipping continental shelf formed on the North American craton during the Early Cambrian through Early Pennsylvanian, where shallow-water clastics and carbonates accumulated (Houseknecht, 1986). Outboard of this continental shelf, "Ouachita facies" deep-water sediments were deposited in a starved basin (Suneson and Campbell, 1990). Continental convergence began in the Late Mississippian between North America and the colliding tectonic terranes (collectively called the Sabine plate) along a southward-d pping subduction zone. The subsequent orogeny culminated in the Middle Pennsylvanian, first causing down-to-the-south normal faulting of the North American plate, perhaps due to loading (Houseknecht, 1986; Sutherland, 1988). Regional tectonic transport in the Ouachita fold-and-thrust belt was north-northwestward, approximately perpendicular to present orientations of fold axis and fault traces (Hardie, 1988).

The southern part of the Arkoma basin and the Ouachita Mountains north of the Ti Valley fault are stratigraphically indistinguishable, with the exception that north of the Choctaw fault the foreland sediments of the Krebs Group are present (Suneson and Campbell, 1990). The stratigraphy of the area is summarized in Figure 2. South of the Choctaw fault, in the frontal zone, the northwest-vergent imbricate thrusts involve mainly the Morrowan Wapanucka Limestone and the Atoka Formation.

The main structural features in the study area are the northwest-verging Choctaw fault and the frontal Kiowa syncline that plunges southwest (Figure 3). In the southeastern limb of the Kiowa syncline and north of the Choctaw fault are two minor folds, the Craig anticline and the Haileyville- Hartshorne syncline, that form an anticline-syncline

Fig. 2. Stratigraphic column for the triangle zone of the Ouachita Mountains and Arkoma basin (modified from Suneson et al., 1990) showing major detachments. Arrows pointing to the right correspond to north-vergent thrusts. The arrow pointing to the left is the upper detachment for the underlying Wapanucka imbricates. Ouachita facies sediments are not shown in this stratigraphic column.

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pair parallel to the Choctaw fault. These two folds can be traced for about 15 km, and the Kiowa syncline is a major fold that can be traced to the southwest for more than 40 km (Marcher and Bergman, 1983). The study area is a few kilometers southwest of the Wilburton gas field, which produces from the Atoka Sandstone, Spiro Sandstone, Wapanucka Limestone, and Arbuckle Group carbonates (Tilford, 1990).

Figure 4 is a schematic cross section showing the position of the 3-D interpretation in the triangle zone. The formation of the Kiowa syncline is produced by deformation at two different levels: a duplex system involving the Wapanucka Limestone and blind thrusts within the Atoka Formation that produce small folds. The Carbon fault flattens with depth below the Kiowa syncline, detaching the middle and lower Atoka Formation (Milliken, 1988). This detachment in the lower Atoka Formation separates the two deformation levels and serves as the roof thrust (Mitra, 1986) for the Wapanucka duplexes.

Triangle Zone

Triangle zones are a common structural element at the leading edge of some fold-and-thrust belts. These zones are located between the last exposed thrust and the frontal syncline in the foreland. This type of structure has been described in the Rocky Mountains Foothills in Alberta (Jones, 1982), the west Mackenzie Mountains (Canada), Pakistan (Banks and Warburton, 1986), Peru, Alaska (Vann et al., 1986), and the Magallanes thrust-and-fold belt in Chile (Alvarez-Marron et al., 1993). Jones (1982) was the first to thoroughly describe the main elements of a triangle zone.

Arbenz (1984) first described this style of deformation in the frontal Ouachita thrust belt in western Arkansas, showing foreland-directed blind thrusting north of the Choctaw fault. Hardie (1988) was the first to describe in detail the transition of the frontal Ouachita fold-and-thrust belt to the foreland Arkoma basin as a triangle zone. By using surface and subsurface data, he concluded that the structural transition from the Ouachita Mountains into the Arkoma basin is an incipient triangle zone and that a more mature and deeply eroded triangle zone exists farther south, within the frontal Ouachita. He proposed two regional detachments, one at the base of the Springer Shale and the other at the base of the Woodford Shale.

Arbenz (1989) used seismic sections across the structural front of the Ouachita Mountains in Pittsburg County, Oklahoma, to illustrate a well-developed triangle zone with underthrusted and upturned Atokan and Desmoinesian strata. Bertagne and Leising (1989) identified this area as the Ouachita frontal fairway and described a structurally complex zone extending approximately 19 km north and south of the surface trace of the Choctaw fault. They examined conventional 2-D seismic data and indicated that sideswipe is a common problem encountered in the frontal fairway.

Fig. 3. Geologic map of the study area showing the location of the 3-D seismic survey, the approximate location of in lines and cross lines, and cross section XX^prime.

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Tilford (1990) also used seismic and well data to describe their "wedge zone" as allochthonous, sometimes overturned, thrust sheets of Spiro Sandstone and Wapanucka Limestone, bounded by Atokan and Morrowan shales. The wedge zone occurs in the interval between the overlying rocks of the Ouachita overthrust and the underlying autochthonous units of the Arkoma basin. Tilford (1990) described the faulting in the wedge zone as imbricate, northward-directed sole thrust faults with additional southward-directed backthrusts and antithetic relaxation faults. He also reported that some wells in the wedge zone have documented overturned bedding in the Spiro and Wapanucka units. Suneson and Campbell (1990) identified the Spiro-Wapanucka-Cromwell blind and imbricate thrusts north of the Choctaw a a possible exploration play.

Perry and Suneson (1990) also examined a seismic-reflection profile across the frontal zone of the Ouachita thrust belt near Hartshorne and confirmed that it is a triangle zone. They concluded that the frontal thrusting is younger than the Hartshorne Formation of late Middle Pennsylvanian (Desmoinesian) age, the youngest Paleozoic unit preserved along the seismic profile. Perry and Agena (1992) determined that the triangle zone and associated imbrication represent as much as 10 km of shortening. Wilkerson and Wellman (1993) relied on seismic and well data to construct nine cross sections through the frontal zone in Latimer and Pittsburg counties. They identified two blind thrust systems below the Choctaw fault and named them the Gale and Buckeye systems, respectively.

Atokan Normal Faults

The Arkoma basin is a mildly compressed fold belt that is decoupled from the underlying substratum in the lower Atoka Formation (Arbenz, 1989). In the southern part of the basin, near the Choctaw fault, the lower Atokan decoupling level serves as the upper detachment for the triangle zone, and the lower detachment is in the Springer and Woodford shales (Figure 2). Faulting below this detachment in the Hunton Group has been traditionally interpreted as normal on 2-D seismic profiles (Bertagne and Leising, 1989; Perry and Suneson, 1990; Reeves et al., 1990; Wilkerson and Wellman, 1993). These are the same lower and middle Atokan basement-involved growth faults that were later overridden by the thrust sheets from the south. The predominant trend of these normal faults is east-northeast-w st-southwest and down-to-the-south, although northeast-southwest and north-south trends are also seen (Arbenz, 1989). These faults apparently were caused by flexural bending of the foreland crust related to a subduction zone to the south, and to tectonic loading of the growing thrusts, also to the south (Houseknecht, 1986).

Tilford (1990) suggested that some of these faults were reactivated as reverse faults during thrust emplacement. Camp and Ratliff (1988) interpreted a deep gas-producing structure in the Wilburton field as the hanging wall of a high-angle, south-dipping reverse fault in the Arbuckle Group. Based on thickness changes of Pennsylvanian-lower Atokan sediments, and by

Fig. 4. Schematic cross section XX^prime through the triangle zone of the Ouachita Mountains and Arkoma basin showing the location of the 3-D seismic survey (see Figure 3 for section location).

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analogy to comparable extensional faults to the north, they suggested that this fault may be a reactivated normal fault. They also suggested that at least some of the movement on the Arbuckle reverse fault appears to postdate the overlying thrusts.

3-D SEISMIC DATA SET

The migrated data set has 268 southeast-northwest in-line profiles and 102 southwest-northeast cross-line profiles, for a total of 27,336 bins (common cell gathers). The spacing between bins is 32 m; the length in the cross-line direction is 8.54 km and in the in-line direction 3.33 km, for a total of 28.45 km² (Figure 4). The data were acquired in eight-line swaths, each consisting of eight receiver lines 256 m apart. Each swath has a three-line overlap with those on either side, for a total of 33 receiver lines. Each receiver line has 50 receiver groups; one every 64 m. Five source lines spaced an average of 800 m apart run approximately perpendicular to receiver lines; sources along each line are an average of 64 m apart.

The quality of the data varies according to the fold coverage. The maximum fold reached in the central part of the data was 21 and decreased toward the edges of the survey. There is an artifact produced by migration near the edges of the data, which is more evident on the in-line profiles and may produce spurious reflections.

One of the main advantages of using a 3-D data volume is that the interpreter can select the slice that best exhibits a given feature. For example, most of the faults trend southwest-northeast, and hence are difficult to pick to the cross-line direction but are clearly seen on the in-line profiles. Thus, most of the faults were picked on the in-line profiles and later correlated on the cross-line profiles. In several examples, some features are clearly seen only on a specific type of slice.

STRUCTURAL INTERPRETATION

Figure 5 presents three representative southeast-northwest in-line profiles. In-line profile 35 is near the southwest end of the survey area, and profile 250 is toward the northeast end (Figure 3). The

Fig. 5. Uninterpreted variable density displays of in-line profiles 35, 164, and 250 from 0 to 3 s. The strong reflections around 2.0 s in in-line profile 164 are repeated Spiro-Wapanucka sections. The other high-amplitude reflection at 2.4 s is the Hunton Group.

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upper 1.5 s of the sections present northwest-dipping parallel reflections from the southern limb of the Kiowa syncline. Most of these reflections correspond to the Atoka Formation and the lower part of the Krebs Group. The strong reflections between 2.0 and 2.2 s on in-line profile 35 correspond to repeated Spiro-Wapanucka sections. On in-line profiles 164 and 250 (Figure 5), the Wapanucka thrust sheet has more displacement and is separated from the footwall section. The other high-amplitude reflections between 2.2 and 2.5 s correspond to the Hunton Group. The main structure seen in the data is the northwest-vergent fault-bend fold that repeats the Wapanucka Limestone below the southern limb of the Kiowa syncline.

Cross line 46 (Figure 6) shows these structures along strike. The upper 1.5 s show the Atoka Formation and the lower part of the Krebs Group plunging to the southwest (see also the geologic map of Figure 3). Around 2.0 and 2.2 s are the repeated Wapanucka sections, and between 2.3 and 2.5 s is the Hunton Group.

In-line profile 164 (Figure 7) crosses the site of well A that reached a first Spiro-Wapanucka contact at 3380 m (1.86 s); a thrust fault was found at 3654 m and a second Spiro-Wapanucka contact was reached at 3663 m, which is the strong reflection at 2.0 s. A second well (B), northwest of well A and toward the edge of the data (Figure 3), was drilled to a total depth of 3650 m, and remained in the Atoka Formation without reaching the Spiro-Wapanucka.

Reflection A (Figure 7) is the last clear reflection of the lower Atoka Formation that could be traced throughout the data set. Reflection A separates the undeformed limb of the Kiowa syncline from the more structurally complex zone underneath. The deformation in the Wapanucka Limestone exhibits the typical northwest-vergent thrusting of the frontal Ouachita Mountains. Three northwest-vergent thrusts offset the Wapanucka Limestone and are labeled from top to bottom W1, W2, and W3 (Figure 7). The Wapanucka thrust sheet above thrust W1 has a horizontal displacement of at least 1.6 km in this profile, whereas thrusts W2 and W3 record a limited shortening of a few tens of meters.

Neither of the wells reached the strong reflector at 2.3 s (Figure 7). The stratigraphic position and a good correlation with a structure map in an adjacent area to this 3-D survey (Wilkerson and Wellman, 1993) support the interpretation that this reflector is the top of the Hunton Group. The Hunton Group shows a more complex faulting pattern, including northwest-vergent thrusts (H1) and a backthrust (HB). Reflection D is a detachment in the Woodford Shale that separates deformation at the Wapanucka and Hunton levels.

Cross-line profile 46 (Figure 8), from southwest to northeast, intersects in-line profile 164 at well A and illustrates the structural features in the strike

Fig. 6. Uninterpreted variable density display of cross-line profile 46 from 0 to 3 s. The Spiro-Wapanucka reflections are between 2.0 and 2.2 s. The Hunton Group is between 2.3 and 2.5 s.

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direction. The limb of the Kiowa syncline is plunging to the southwest and flattens to the southwest. Above reflection A, parallel continuous and relatively low-amplitude reflections are seen in the lower Atoka Formation. The area between the repeated Wapanucka section and reflection A lacks strong reflections, although some weak reflections parallel to A are observed.

The two reflections from the Wapanucka Limestone in Figure 8 are dipping toward the southwest, similar to the reflections from the overlying syncline. W1 is the main thrust that repeats the Wapanucka Limestone throughout most of the cross-line profile and appears to be folded. Thrust W2, which shows minor displacement on the in-line profiles, reveals very limited extent and dies out laterally. Thrust W3 merges with detachment D, and both appear to be folded.

Reverse faults that affect the Hunton Group (Figure 8) are labeled H1 and H2. Thrust H2 does not show any apparent displacement in this perspective, whereas thrust H1 offsets the Hunton Group and merges upsection with the Woodford detachment D. Cross-line profile 46 shows these structures plunging to the southwest, and the two sections of the Wapanucka Limestone and Hunton Group, including the Woodford detachment, appear to be folded.

One of the advantages of 3-D seismic data is that the time slices provide a view very much like a geologic map. The principal reflections can be mapped in sequential sections to outline structures in three dimensions. The position of a reflection in successive time slices is related to its dip. The higher the dip, the narrower it will appear, and conversely, the lower the dip, the thicker it will appear. Variations in reflection amplitude, however, can have the same effect as dip changes in a constant amplitude reflection (Brown, 1991).

Three time slices (Figure 9) illustrate these structures in map view. The time slice at 1860 ms shows the Wapanucka thrust sheet forming an anticline bearing S40°W (Figure 9a). The time slice at 2000 ms shows the Wapanucka thrust sheet shifted to the southwest and the footwall Wapanucka beginning to emerge in the core of the anticline (Figure 9b). Thrust W1 that separates the reflections is also folded, suggesting that the formation of this anticline postdates the thrusting that repeats the Wapanucka Limestone.

At 2000 ms, the bearing of the anticline is S65°W, more westerly directed. Thrust W3 offsets the footwall Wapanucka and has a relatively straight southwest-northeast trend, suggesting that it is younger and responsible, in part, for the folding of the overlying anticline. The reflection from the backlimb of the fault-bend fold has very low amplitudes or is absent, probably due to increased convexity that disseminated the energy, or to a steeper dip that reflected the energy out of the geophone array. The time slice at 2400 ms at the Hunton level is not as clear as the shallower slices, but serves to illustrate the trend of the northwest-vergent thrusts and the backthrust (Figure 9c).

Upper Detachment

The triangle zone model requires the presence of an upper detachment or passive roof thrust

Fig. 7. In-line profile 164 from 1.1 to 2.6 s showing the main structural features of the study area. The two reflectors near 1.8 and 2.1 s are two sections of Wapanucka limestone. The strong reflector at 2.3 s is the Hunton Group. A = reflection in the lower Atoka Formation; W1, W2, and W3 = northwest-vergent thrusts; H1 = northwest-vergent thrust; HB = backthrust in the Hunton; D = detachment in the Woodford that separates the thrusting at the Wapanucka and Hunton levels.

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(Banks and Warburton, 1986) that separates strata of the frontal syncline from the underlying duplexes. This upper detachment is localized in the lower Atoka Formation, but does not have a clear seismic expression, probably because it is parallel to the bedding of the syncline and is localized within shales that do not have any significant acoustic impedance contrast that would generate a reflection. The upper detachment of the triangle zone should be close to reflection A and parallel to the bedding of the frontal syncline (Figure 9c).

Thrusting in the Wapanucka Limestone

The most prominent structure in the data is the fault-bend fold (Suppe, 1983) that repeats the Wapanucka Limestone. The horizontal displacement on the underlying thrust W1 progressively increases from southwest to northeast, and varies from 0.83 km on in-line profile 35 to 1.5 km on in-line profile 164; on in-line profile 250 the displacement is more than 1.5 km because the leading edge is outside of the data volume (Figure 5). The increase in displacement along strike is also accompanied by an increase in the ramp angle toward the northeast end of the data. The detachment for thrust W1 is located about 60 ms below the hanging-wall Wapanucka Limestone in the Springer Shale. The calculated dip angles for W1 range from approximately 11° on in-line profile 164 to 20° on in-line profile 250. The detachment for W2 is also in the Springer Shale, whereas W3 has its detachment above the Hunton Group in the Woodford Shale.

The faults that offset the Hunton Group were interpreted mainly as reverse faults. The interpretation of these faults as reverse was ambiguous in many in-line profiles, but the interpretation of the whole survey demonstrated that there are repeated sections of the Hunton. The reverse motion of these faults is seen more clearly in some cross-line profiles. Cross-line profile 10 (Figure 10), on the northwest side of the survey (Figure 4), shows clearly the reverse motion of faults H1 and H2 that uplift the two overlying Wapanucka sections. The displacement on these faults is not great, so the higher resolution of 3-D seismic was required to identify them.

Fault H2 is reverse on cross-line profile 10, but on in-line profile 35 (Figure 11), 2 km to the southwest, fault H2 is interpreted as a normal fault. The time slices are very useful in correlating these faults along strike, even though they change their throw (Figure 9c). This evidence suggests that these faults, interpreted as reverse, were normal faults reactivated during the Ouachita orogeny, as proposed by Tilford (1990).

The normal separation of fault H2 and the almost negligible reverse motion of H1 at the southwestern end of the survey coincide where the overlying Wapanucka thrust W1 has the least displacement. At the northeastern end of the survey, the Hunton faults have reverse separation where displacement on the Wapanucka thrust W1 is greatest, suggesting a genetic relation between

Fig. 8. Cross-line profile 46 from 1.4 to 2.9 s illustrating the main reflectors along strike. W1, W2, and W3 = thrust faults at the Wapanucka level; WL = a tear fault; H1 and H2 = thrust faults at the Hunton level.

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the amount of compression and the reactivation of the normal faults.

Tear Fault WL

At the southwestern end of cross-line profile 46 (Figure 8), tear fault WL marks the southwest extent of the deformation of the hanging-wall and footwall Wapanucka Limestone. Southwest of WL, the lower Wapanucka Limestone seems to be undisturbed. Fault WL is seen in cross-line profile 46 as a reverse fault offsetting the footwall Wapanucka and in cross-line profile 10 (Figure 10) as a normal fault. This change in fault-plane dip may have several explanations. First, this fault may have been a normal fault that was reactivated as a reverse fault during the Ouachita orogeny. Another possible interpretation is that the change in fault-plane dip is a product of rotation along a tear fault. In either case,

Fig. 9. Time slices at (a) 1860, (b) 2000, and (c) 2400 ms.

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this fault seems to have been formed prior to the thrusts and acted as a buttress during compression.

Woodford Detachment

Reflection D is located in the stratigraphic position of the Woodford Shale (Figure 10). The Woodford detachment (Hardie, 1988; Wilkerson and Wellman, 1993) separates the allochthonous Wapanucka thrust sheets from the underlying autochthonous in some areas of the triangle zone. Although major translation occurs along W1 and detaches the Wapanucka from the Springer Shale in this area, a detachment (D) in the Woodford Shale seems to accommodate some displacement. Fault W3 appears to sole out at this level, and faults H1 and H2 do not cut this reflection, suggesting that they merge there and their displacement is taken by this detachment (Figure 10).

In some published seismic reflection profiles from the triangle zone, the normal faults that offset the Hunton and Arbuckle groups do not continue upward to offset the Wapanucka Limestone, although these normal faults are interpreted to be younger (Bertagne and Leising, 1989; Wilkerson and Wellman, 1993). This scenario can be seen on in line 35 (Figure 11), where fault H2 does not reach the Wapanucka Limestone. The most likely explanation is that the Woodford detachment postdates the Atokan normal faults and decapitated normal faulted blocks, explaining why fault WL (Figures 8, 10) does not continue into the underlying Hunton Group.

Small-Wavelength Folds in the Frontal Syncline

The triangle zone model explains the uplift of the limb of the frontal syncline by development of duplexes below. However, between the Kiowa syncline fold axis and the Choctaw fault is an anticline-syncline pair with a wavelength of about 1 km (Figure 3). The Craig anticline is partially imaged by this data set. In-line profile 250 (Figure 5) shows that the reflections from the Atoka Formation around 1.2 s are dipping less than in in-line profiles 35 and 164. A closer look to the upper part of in line 250 (Figure 12) shows that the Atoka reflections above 1 s are steeper to the southeast and are slightly offset by a steep fault. Displacement along this fault is lost upsection. The structural style of these shallower folds was not studied in detail, but they appear to be similar to oth r seismic sections in this area presented by Perry and Suneson (1990) and Reeves et al. (1990) that show faulting involving only Atokan strata.

3-D SUBSURFACE STRUCTURAL GEOMETRY

Figure 13a is an amplitude and time-contour map for the hanging-wall Wapanucka thrust sheet. The variations in reflection amplitude are attributed mainly to reflector curvature. Higher amplitudes are associated with the axial portion of the fold, where the dip is gentle. The amplitude of the backlimb of the fold is very low, where the reflector is more convex. Minor variations in amplitude can be

Fig. 10. Cross-line profile 10 illustrating the along-strike reverse faulting of H1 and H2 in the Hunton Group.

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related to lithological variations or fluid content. The structurally higher part of the fold is located northeast of the area, and the structurally lower part of the fold is to the southwest.

The amplitude and time-contour map for the footwall Wapanucka Limestone (Figure 13b) shows a very good correlation between blocks of different amplitudes and the fault traces. The higher part of the unit is located in the northeastern part of the area and has an overall shape of an antiform plunging to the southwest. Fault H1 in the amplitude and time contour map of the Hunton Group (Figure 13c) separates a southwest-northeast-trending higher amplitude hanging-wall block from the lower amplitudes to the northwest. Fault H1 and the backthrust HB bound a block, with the shallower part in the northeastern corner of the area and the deeper part to the southwest.

Figure 14 shows perspective views of the surfaces of reflection A, the Wapanucka thrust sheet, the lower Wapanucka, and the Hunton Group. This

Fig. 11. In-line profile 35 from 1.4 to 2.9 s. H2 is a normal fault and H1 shows very small reverse motion. In this area the overlying thrust W1 has less displacement.

Fig. 12. In line 250 from 0.3 to 2.4 s. The faulting in the Atoka Formation at the southeastern end of the line produces the Craig anticline. The geometry of reflection A is complicated by the overlying faulting in the Atoka Formation and by the increase in height of the Wapanucka ramp.

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view is from the south-southwest and at an angle of 30°. From this perspective, one can clearly see that the southern limb of the Kiowa syncline (reflector A) has been uplifted by underlying duplexes, in agreement with the triangle zone model. This similarity between surface geometries suggests that they were

Fig. 13. Amplitude and time-contour maps of (a) the Wapanucka thrust sheet, (b) the footwall Wapanucka, and (c) the Hunton Group. Amplitude color scale varies for each reflector.

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involved in the same folding event; therefore, the youngest faults underlie the Hunton Group.

Fold Axes Data

The time-contour maps were converted to depth using the same velocity function for the entire survey to calculate the bearing and plunge of the folds for the hanging wall and footwall of the Wapanucka Limestone and the Hunton Group (Figure 15). The data from the three surfaces indicate plunging from 2 to 10° to the southwest, and the Kiowa syncline plunges an average of 14°, also to the southwest (S60°E). This similarity supports that they were involved in the same deformational event.

Although the Wapanucka thrust sheet was refolded by an underlying fault, variations in the bearing and plunge of the fault-bend fold (Figure 13a) can be correlated to variations in fault geometry along

Fig. 14. Three-dimensional perspective views of the four reflectors interpreted from the south at an angle of 30°.

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strike, as seen in the in-line profiles (Figure 5). Some of the possible causes are changes along the strike of the ramp cutoff angle, differential transport, and changes in ramp height (Wilkerson et al., 1991). Ramp angles for W1 appear to be fairly constant along strike (around 11°), but at in-line profile 250 the angle increases to about 20° (Figure 12). Differential transport along strike increases from southwest to northeast. In in-line profile 35 (Figure 5) the displacement is 0.8 km, in in-line profile 164 displacement is 1.5 km, and in in-line profile 250 the leading edge of the thrust sheet is out of the volume, with a minimum transport of about 1.5 km. The height of the ramp is fairly constant along most of fault W1 (110 ms), but around in-line profile 250 the ramp length increases to 250 ms (Figure 12).

The effects of differential transport on fold axis geometry are illustrated in a schematic block diagram using area-balanced similar fault-bend folds (Figure 16a) (Wilkerson et al., 1991; Medwedeff, 1992). Cross section C marks the transition from the crestal uplift stage to the crestal broadening stage (Shaw et al., 1994). In the crestal broadening stage C-D, the forelimb anticline trends toward the fold termination and the plunge remains constant. The seismic profiles show that most of the fold is in the crestal broadening stage, which agrees with the fold axis data that display a fairly constant plunge (Figure 15). In the crestal uplift stage A-C, the fold widens and plunges toward the fold termination. This is also observed in the contour map of the Wapanucka thrust sheet (Figure 3a), suggesting that the southwestern part of the fold is in the crestal uplift stage (in line 35, Figure 5).

The combined effects of differential transport and increase in the ramp height seen in in line 250 are shown schematically in Figure 16b. The increase in ramp height (cross sections C, D, and E) would accentuate the change in trend of the fold axes, which would explain the scatter of the fold axes data (Figure 15). Also, there would be an associated increase in fold plunge, which is believed to be the cause of the change in trend and the steepening of the Wapanucka thrust sheet to the northeast end of the study area (Figure 13a).

SEQUENCE OF DEFORMATION

Deformation began in the foreland basin with normal faulting in the early and middle Atokan (Houseknecht, 1986; Sutherland, 1988). The first thrust to develop was W1, which formed as a fault-bend fold with its detachment in the Springer Shale. This initiated the passive uplift of the overlying Atokan and younger section. Thrusts W2 and W3 followed, slightly folding the overlying Wapanucka section. The detachments for these thrusts are in the Springer Shale and in the lower part of Woodford Shale. These detachments may have truncated and transported the Atokan normal-faulted blocks.

The seismic data suggest that the triangle zone in the Oklahoma portion of the Ouachita Mountains formed by thrusting at different stratigraphic levels with independent detachments that may vary along strike. The dominant shortening in this area was accommodated by duplexes in the Wapanucka Limestone that uplifted the frontal syncline, and a smaller zone of thrusting involving middle and upper Atokan strata formed the smaller wavelength folds. The timing of the deformation at these two stratigraphic levels is not clear, but may be coeval.

The normal faults that offset the Hunton Group and deeper strata were partially reactivated as reverse faults during the later stages of thrust emplacement. These faults show greater reverse separation, where the overlying Wapanucka thrust has more displacement, and are still normal, or the inversion is less to the southwest, where the Wapanucka thrust W1 has less displacement. This evidence suggests a direct relation between the Wapanucka thrusting and the inversion of the Hunton faults. The Hunton faults appear to have

Fig. 15. Fold axes data (lower hemisphere projection).

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been reactivated when the Wapanucka thrust sheet was being emplaced; however, the Hunton faults continued moving and subsequently folded the entire overlying sequence. This movement agrees with the theory that foredeep or forebulge normal faults, such as the Atokan faults, are usually inverted late in the deformation history of a fold-and-thrust belt (Hayward and Graham, 1989).

Faulting in the Hunton Group and deeper units has been traditionally interpreted as normal (Bertagne and Leising, 1989; Perry and Suneson, 1990; Suneson et al., 1990; Wilkerson and Wellman, 1993). The conclusions drawn from this study agree with Tilford (1990), who proposed that some of the Atokan normal faults were reactivated as reverse faults during the Ouachita orogeny. Camp and Ratliff (1988) generated a balanced cross section through the Wilburton field and interpreted a deep gas-productive structure in the Arbuckle Group as a high-angle, south-dipping reverse fault. They also suggested that at least some movement on the reverse fault appears to postdate the overlying thrusts in the Wapanucka Limestone. The observations in this study are in agreement with the conclusions of Camp and Ratliff (1988) that some of the deeper faults are reverse and postdate the overlying Wapanucka thrusts.

CONCLUSIONS

The interpretation of this 3-D survey has provided a more detailed structural picture of a portion of the triangle zone of the frontal Ouachita, previously unattainable with 2-D seismic and well data. This area is a triangle zone (Jones, 1982) with northwest-vergent blind thrusting under the frontal Kiowa syncline. The southern limb of the Kiowa syncline has been passively uplifted by the blind thrusting at deeper levels, with three distinct levels of deformation: (1) reverse faulting of small offset in the upper Atoka Formation, (2) thrusting in the Wapanucka Limestone, and (3) inversion of the Atokan normal faults at the Hunton and Arbuckle level.

The triangle zone that generates the frontal syncline in this area has its lower detachment in the Springer Shale and probably the Woodford Shale, and the upper detachment in the lower Atoka Formation. The faulting in the Wapanucka Limestone and the underlying Hunton Group is separated by a detachment in the Woodford Formation, which has been mapped based on the termination of faults.

The amplitude-horizon maps are consistent with the interpretation of the traces of the main faults. The variations in geometry of the Wapanucka thrust sheet are reflected in variations in fold axis bearing and plunge. These variations are attributed to increase in ramp height and displacement changes of the thrust sheet along strike. The correspondence among the geometry of the limb of the Kiowa syncline, the hanging wall and footwall of the Wapanucka, and the Hunton Group suggests that they were involved in the same compressional events. Therefore, the youngest structures would be at the deeper levels in the Hunton Group and Arbuckle Group. The deformations of these older sequences uplift and fold the overlying sequence.

The Hunton faults were interpreted as reactivated Atokan normal faults that were inverted in the final stages of the Ouachita orogeny, folding the overlying strata, including the Wapanucka thrusts. The correlation between the amount of shortening observed in the Wapanucka thrust and the inversion of the Hunton faults supports this observation. The reactivation of the Atokan normal faults at deeper levels in the Arkoma basin and Ouachita subthrust play may be more widespread than has been previously recognized.

Fig. 16. Schematic block diagrams using similar fault-bend fold models illustrating changes in fold axis bearing and plunge with (a) differential transport (modified from Wilkerson et al., 1991; Medwedeff, 1992) and (b) differential transport and increase in ramp height (cross sections C-E).