Orientale Basin is the youngest and best-preserved large impact basin on the Moon with at least four topographic rings contained within the topographic rim marked by the Cordillera Ring (diameter = 930 km). Its well-exposed interior makes this basin a prime location to study basin formation processes. Forward mechanical modeling of basin ring topography shows that the outermost rings, the Cordillera Ring (CR) and Outer Rook Ring (ORR) are large-scale normal faults with displacements (D) of 0.8 to 5.2 km, fault dip angles (δ) of 54° to 80°, and vertical depth of faulting (T) between 19 and 37 km with most faults having T = 30 ± 5 km. These faults and the distribution of maria inside the basin suggest that the transient crater, important for determining many impact-related characteristics such as projectile size, was contained entirely within the ORR and likely had a diameter between 500 and 550 km. The difference in crustal thickness between the western and eastern sides of the basin is not a result of the basin-forming event, which indicates the formation of the hemispheric crustal thickness asymmetry was likely before the formation of Orientale Basin 3.68 to 3.85 Ga.
 Orientale Basin, with a diameter in excess of 900 km (Figure 1), is the best-preserved and youngest multi-ring basin on the Moon [Hartmann and Kuiper, 1962; Head, 1974a; Moore et al., 1974; McCauley, 1977; Spudis, 1993], with age estimates of the basin-forming event ranging from 3.85 Ga [Wilhelms, 1987] to 3.68 Ga [Whitten et al., 2011]. Centered at approximately 265°E, 20°S, it is located on the Moon's western limb [Hartmann and Kuiper, 1962; Head, 1974a; Spudis et al., 1984] in the transition region between thin nearside and thick farside crust (Figure 2) [Ishihara et al., 2009]. Understanding the formation of multi-ring basins is central to lunar and planetary science because the distribution of their ejecta is critical to interpreting lunar stratigraphy [Head, 1974a; Moore et al., 1974] and the geologic context of the Apollo [Head, 1974a] and Luna samples. Orientale Basin is particularly interesting because its interior remains relatively unobscured by mare deposits unlike most of the prominent nearside basins. The exposed structures can, therefore, be used to test concepts of basin formation that will be applicable to other basins on the Moon and elsewhere in the solar system.
 The basin interior contains at least four topographically defined, roughly concentric rings (Figure 1) [Hartmann and Kuiper, 1962; McCauley, 1977]. The outermost ring scarp, called the Cordillera Ring (CR), is the most prominent basin ring both topographically and morphologically and, thus, defines Orientale's diameter of 930 km [e.g., Head, 1974a; Spudis, 1993]. The interior ring structures, the Outer Rook Ring (ORR) and Inner Rook Ring (IRR), have diameters of 620 and 480 km, respectively [Head, 1974a; McCauley, 1977]. An inner ring (IR) with a diameter of about 320 km contains a flat, low albedo unit, known as Mare Orientale [Head, 1974a], which appears to partially fill the center of Orientale Basin.
 The cratering processes that produce multi-ring basins remain poorly understood, and their resolution is one of the science priorities targeted by the National Research Council . Several classes of competing hypotheses for the formation of the rings of Orientale and similar structures in other basins have been suggested. These include the hydrodynamic or tsunami hypothesis [e.g., Baldwin, 1949, 1963, 1972, 1974, 1981], the megaterracing hypothesis [Hartmann and Yale, 1968; Head, 1974a, 1977; Howard et al., 1974; McCauley, 1977], the ring tectonic hypothesis [Melosh and McKinnon, 1978; McKinnon and Melosh, 1980; McKinnon, 1981; Melosh, 1989], and the nested melt cavity hypothesis [Head, 2010]. This study tests aspects of these diverse models, and the results may be applied to further studies of impact basin formation mechanisms. We show that the Cordillera and Outer Rook Rings are large-scale normal fault scarps, which likely formed as a result of the collapse of the transient cavity walls to form the basin equivalent of a complex crater modification zone during basin formation.
2 Orientale Basin
 Impact basins represent a class of structures characterized as depressions with widespread concentric-radial lineament systems [Gilbert, 1893; Baldwin, 1942, 1943, 1949; Dietz, 1946; Hartmann and Wood, 1971] having diameters in excess of ~300 km for the Moon [Wilhelms, 1987; Spudis, 1993]. In the following, we briefly summarize the basin topography, ring characteristics, impact and post-impact deposits, and crustal thickness, which provide geologic context for our measurements and models.
2.1 Basin Topography
 Figure 1b shows topographic data (512 px/deg) collected by the Lunar Orbiter Laser Altimeter (LOLA) [Smith et al., 2010] (onboard the Lunar Reconnaissance Orbiter (LRO)) draped over a shaded relief model. On average, elevations are ~6 km higher on the western side of the basin than on the east. The four topographic rings of Orientale are prominent as approximately concentric circles (Figure 1b). In profile, the basin has a stair-step shape, with the highest elevation on the western rim at about 6.5 km, stepping down to the lowest elevation in the basin-interior mare of around −3 km. Low topographic slopes (~1–3°) exist between the ORR and CR with the elevation decreasing toward the CR and then abruptly increasing at the CR scarp by ~4 km.
 The Cordillera Ring (diameter = 930 km) consists of a generally continuous inward-facing scarp and rises up to 4 km above the surrounding plains [Head, 1974a]. In places, it takes on a saw-toothed appearance [Head, 1974a], which has been attributed to the preexisting “lunar grid” [Fielder, 1961; Head, 1974a, 1974b] where the ring structures may have formed along preexisting fractures oriented in the northwest–southeast and northeast–southwest directions. The Outer Rook Ring (diameter = 620 km) is composed of kilometer-scale massifs with steep slopes facing the basin interior [Head, 1974a] and is the most continuous and topographically rugged of the rings [McCauley, 1977]. Linear portions of the ring parallel those of the Cordillera Ring [Head, 1974a] in the west. As reported for the Cordillera Ring, the Outer Rook Ring height is variable [Head, 1974a] and ranges from 1 to 5 km in elevation. Spectroscopic studies of the ORR suggest a composition ranging from noritic anorthosite to anorthositic norite [Spudis et al., 1984], although shocked anorthosite has also been observed [Bussey and Spudis, 1997, 2000; Hawke et al., 2003; Pieters et al., 2009].
 In the southwest where the concentric trends of the rings are lost, the Cordillera and Outer Rook Rings are generally indistinguishable (Figure 1d) [Scott et al., 1977] using imagery alone. The complicated structures have been suggested to be related to an oblique basin-forming impact, orientation of preexisting crustal weaknesses [Scott et al., 1977], the presence of a pre-Orientale basin [Schultz and Spudis, 1978; Spudis, 1993; Wood and Collins, 2011], or increasing lithospheric thickness towards the west [Head and Solomon, 1980]. The Cordillera and Outer Rook Rings do not show any significant difference in crater density relative to the ejecta blanket [Hartmann and Wood, 1971], indicating that these rings formed contemporaneously with the Orientale basin-forming event and with each other.
 The Inner Rook Ring (diameter = 480 km), characterized by disconnected peaks that range in height from 1 to 3 km and 2 to 10 km in width [Head, 1974a], is well developed on the northwest, southwest, and southeast sides of the basin [McCauley, 1977]. The eastern portions of the IRR are interpreted to be composed of essentially pure anorthosite of both shocked and nonshocked varieties, in contrast to the generally more mafic compositions of other Orientale units [Spudis et al., 1984; Head et al., 1993, 2010; Bussey and Spudis, 1997, 2000; Hawke et al., 2003; Ohtake et al., 2009; Pieters et al., 2009], implying that the material that comprises this ring is likely derived from the upper crust [e.g., Spudis and Davis, 1986]. The IRR has been variously interpreted as marking the location of the rim of the transient cavity [Floran and Dence, 1976], a central uplift analogous to central peak rings [e.g., Head, 1974a; Moore et al., 1974; McCauley, 1977; Solomon and Head, 1980; Head et al., 1993], and the surface expression of the crust-mantle boundary [Wilhelms et al., 1977; Hodges and Wilhelms, 1978] (meaning that the formation of this ring is the result of the rheological layering of the target).
 The Inner Ring (diameter = 320 km) is discontinuous and consists of a rounded step-like scarp that separates the lowest parts of the inner basin from the more rugged terrain outside [McCauley, 1977]. In the south to southwest, the Inner Ring scarp may consist of small steep-faced fault segments in contact with the mare; to the northeast, the ring is expressed as elongated fractured ridges [McCauley, 1977]. The Inner Ring may delineate the deepest part of the original cavity [McCauley, 1977] into which basalt was extruded but from which it was later partially withdrawn [Scott et al., 1977], causing the inner part of the basin to collapse. Alternatively, the depression bound by the Inner Ring may be the result of thermal contraction and subsidence of the impact melt sheet and substrate [Bratt et al., 1985; Head et al., 1993]. The inward-facing scarp of the Inner Ring has also been suggested to represent a major strength discontinuity in the lunar subsurface [Scott et al., 1977].
 In addition to the four well-defined topographic rings (Figure 1), at least two rings external to the Cordillera Ring have also been suggested, with diameters of 1300 [Hartmann and Kuiper, 1962] and 1900 km [Pike and Spudis, 1987]. They appear to have subdued scarp-like morphology [Spudis, 1993], possibly from obscuration due to deposition of ejecta on top of these structures. A possible exterior ring, with a diameter of 1460 km, was noted by van Dorn . A possible ring interior to the IR may exist as a roughly basin-concentric wrinkle ridge system in western Mare Orientale [Scott et al., 1977; Solomon and Head, 1980].
2.3 Impact-related Deposits
 The Orientale Group includes all materials produced by and deposited contemporaneously with the basin-forming event: the Hevelius, Montes Rook, and Maunder Formations [McCauley, 1977; Scott et al., 1977]. The Hevelius Formation, including the inner (Iohi), transverse (Ioht), outer (Ioho), and secondary crater (Iohs) facies (Figure 1c), lies mostly outside the Cordillera Ring [McCauley, 1977; Scott et al., 1977]. It has been interpreted as an early-stage ejecta blanket and consists of hummocky, lineated, and swirl-textured deposits [McCauley, 1977; Scott et al., 1977; Spudis, 1993]. The Hevelius Formation extends at least one basin diameter beyond the Cordillera Ring [Spudis et al., 1984; Head et al., 1993], and its thickness has been estimated to be ~3.6 km [Moore et al., 1974; Scott et al., 1977] or ~2.9 ± 0.3 km [Fassett et al., 2011] at or near the CR. The Cordillera Ring is draped by the Hevelius Formation over ~80% of its circumference; this has been interpreted to indicate that the CR formed before the emplacement of the ejecta [Howard et al., 1974; McCauley, 1977]. Head [1974a], however, notes that no Orientale ejecta has been deposited against the Cordillera Ring scarp, which may imply that the formation of the scarp occurred after and/or contemporaneously with the deposition of ejecta.
2.4 Mare Deposits
 Three major mare units occur within Orientale Basin [Scott et al., 1977] (Eratosthenian/Imbrian mare material: EIm; Figure 1c). In decreasing areal extent, these are Mare Orientale, Lacus Veris, and Lacus Autumni. Basin volcanism is preferentially concentrated along the interior of basin rings and in the inner part of the basin [Hartmann and Kuiper, 1962]. Mare Orientale is located in the basin center and encompassed almost entirely by the Inner Ring. Lacus Veris is located between the Inner and Outer Rook Rings, and Lacus Autumni is contained between the Outer Rook and Cordillera Rings (Figure 1a). Based on crater counting studies [Greeley et al., 1993; Whitten et al., 2011], mare volcanism occurred significantly later than basin formation, as indicated by the lower relative crater density of the mare when compared to the basin ejecta blanket [Hartmann and Wood, 1971]. Mare Orientale is the oldest identified in Orientale Basin, with model ages of 3.7–3.45 Ga [Greeley et al., 1993; Whitten et al., 2011]. Lacus Veris and Lacus Autumni have estimated age ranges of 3.69–3.20 and 3.47–1.66 Ga, respectively [Greeley et al., 1993; Whitten et al., 2011], consistent with previous estimates of the duration of lunar volcanism [e.g., Hiesinger et al., 2011].
2.5 Crustal Thickness
 The Orientale Basin straddles the nearside–farside crustal thickness asymmetry (Figure 2), with thicker crust present on the western side of the basin in the lunar highlands [Ishihara et al., 2009]. Estimates of crustal thickness have been obtained from inversion of lunar gravity and topography data [Hikida and Wieczorek, 2007; Ishihara et al., 2009]. Here, the term crust refers to the upper compositional stratum of the Moon and is defined in these models by the density of crustal materials (e.g., anorthosite and basalt).
 The thickness of the lunar crust in the vicinity of Orientale ranges from 20 to 90 km [Hikida and Wieczorek, 2007; Ishihara et al., 2009]. The thickest crust in the Orientale Basin (~80 km) occurs in the northwestern, western, and southern sections of the ORR [Ishihara et al., 2009]. The crust in the basin interior is ~20 km thick [Ishihara et al., 2009], although it may be as thin as 0.7 km [Hikida and Wieczorek, 2007]. Most of the crust in the Orientale Basin region, however, is ~70–80 km thick [Ishihara et al., 2009]. The crustal thickness notably decreases with a gradient of 20 m/km from the west to the east (Figure 2).
3 Overview of Basin Formation Models
 The variety of basin ring morphologies on the terrestrial planets and icy satellites suggests that several mechanisms may be responsible for ring formation in impact basins [McKinnon and Melosh, 1980]. While there is no consensus on the formation of structures inside the transient cavity, i.e., peak rings and central peaks, there is general agreement that the collapse of the central uplift is important [e.g., Melosh, 1989; Melosh and Ivanov, 1999; O'Keefe and Ahrens, 1999; Morgan et al., 2000; Collins et al., 2002]. Here, we focus our brief discussion on the hypotheses for the formation of the rings outside the transient cavity; for Orientale Basin, we consider these to be the Cordillera and Outer Rook Rings.
 Previous hypotheses for the formation of outer rings in lunar impact basins can be divided into several classes of models: the hydrodynamic or tsunami model [e.g., Baldwin, 1949, 1963, 1972, 1974, 1981; van Dorn1968, 1969], the ring tectonic model [Melosh and McKinnon, 1978; McKinnon and Melosh, 1980; McKinnon, 1981; Melosh, 1989], the nested melt cavity model [Head, 2010], and the megaterracing model [Hartmann and Yale, 1968; Head, 1974a, 1977; Howard et al., 1974; McCauley, 1977]. These hypotheses share the idea that stresses in the Moon, built up due to violent dissipation of energy imparted to the lunar surface during basin formation, result in the formation of concentric ring structures [Hartmann and Wood, 1971] but differ in the manner(s) in which these stresses are relieved and predictions on the presence and type of faults occurring at the basin rings.
 Ring formation in the hydrodynamic or tsunami model as proposed by Baldwin [1949, 1963, 1972, 1974, 1981] results from impact-induced shock modification of rock, causing the target material to behave as a fluid-like rubble; as stresses decay, the rock no longer behaves as a fluid, forming rings as anticlines and synclines when impact-induced tsunami-like shock waves “freeze” in place [Baldwin, 1949, 1963, 1972, 1974, 1981] or from repeated rebound and collapse (i.e., oscillation) of the central uplift [Murray, 1980]. This model gives no predictions on the presence or absence of faults at basin rings.
 In the ring tectonic model, basin rings are normal fault scarps along which crustal blocks move radially inward toward the basin center; material on the basinward side of these scarps is downthrown relative to the pre-impact surface [McKinnon and Melosh, 1980; Melosh, 1989]. This model predicts that the rings of basins formed on bodies with thick lithospheres such as the Moon are composed of antithetic, approximately circumferential normal faults induced by inward asthenospheric flow (asthenosphere forming a low-viscosity channel) [Melosh and McKinnon, 1978; McKinnon, 1981; Melosh, 1989]. These normal faults are assumed to form when the depth of the transient cavity exceeds the thickness of the lithosphere at the time of the basin formation [Melosh, 1989; c.f. McKinnon and Melosh, 1980].
 The nested melt cavity model [Head, 2010] for the formation of basin rings is based on the observation that the proportion of impact-produced melt increases with increasing transient crater size [e.g., Cintala and Grieve, 1998]. After impact, a melt cavity forms at the sub-impact point, where the boundary between the melt zone and the displaced zone consists of material that experienced high shock pressures but is still solid [Head, 2010]. The highly shocked rocks of the displaced zone rebound to form the expanded peak ring, moving upward and inward, displacing the impact melt in the central depression, which results in melt coating the collapsing cavity floor and ponding of melt in the central crater [Head, 2010]. Deep-seated radially inward listric normal faulting is initiated along the base of the displaced zone, propagating outward to the base of the structurally uplifted rim, which becomes an additional ring with an inward-facing fault scarp [Head, 2010]. Collapse of the rim forms a megaterrace [Head, 1974a, 1977, 2010], which may be analogous to the CR in Orientale.
 The most commonly proposed mechanism for basin ring formation is the megaterracing model [Hartmann and Kuiper, 1962; Hartmann and Yale, 1968; McCauley, 1968, 1977; Mackin, 1969; Hartmann and Wood, 1971; Head, 1974a, 1977; Howard et al., 1974; Scott et al., 1977]. In this model, outer rings of Orientale and other multi-ring basins form as large normal faults, where the interior of the basin is displaced downward relative to the preexisting lunar surface. In particular, on the basis of the morphology similar to fault scarps with steep inner faces [Hartmann and Kuiper, 1962], the Cordillera Ring has been interpreted to represent a large-scale normal fault scarp [e.g., Hartmann and Wood, 1971; Head, 1974a, 1977; Howard et al., 1974].
 As most hypotheses for the formation of basin rings require or predict normal faulting, we will test these by performing mechanical modeling of Orientale CR and ORR cross-sectional topography, as described in section 4.
4 Modeling Approach
 To test the fault-related models of basin ring formation, we initially assume that the ORR and CR scarps are normal faults and adopt a standard technique that utilizes the inversion of fault-related topography [e.g., Cohen, 1999; Schultz and Lin, 2001] to determine if the rings can be successfully modeled as normal faults. Models of this type are used to calculate surface displacements due to underlying faults with prescribed geometries and displacement magnitudes [Schultz and Lin, 2001]. Forward mechanical modeling has been used successfully to model the surface displacements from faults on Mercury [Watters et al., 2002], Earth [e.g., King et al., 1988; Toda et al., 1998; Cohen, 1999; Muller and Aydin, 2005; Resor, 2008], asteroids [Watters et al., 2011], and Mars [e.g., Schultz, 2000; Schultz and Lin, 2001; Schultz and Watters, 2001; Grott et al., 2007]. This approach provides remarkably good fits to the structural topography above a fault for a relatively narrow range of parameters [e.g., Cohen, 1999; Schultz and Lin, 2001]. As shown below, a good correspondence between the output model displacements and observed LOLA topography would suggest that the fault parameters obtained from modeling are representative of the characteristics of the putative ring-forming faults [e.g., Schultz and Lin, 2001].
4.1 LOLA Topography across the Rings of Orientale Basin
 Several sets of topographic profiles were derived from the 512 pixel/deg (~60 m/px at the equator) LOLA digital elevation model (DEM) [Smith et al., 2010] perpendicular to ring scarps (although not necessarily always basin radial) in each location of inferred normal faulting (CR and ORR; Figure 3), with profiles A through J shown in Figures 4 and 5. Additional profiles (K–N in Figure 3) were derived from IRR and shown in Figure 6 for comparison (see below). The interior of the basin is to the left in most profiles; those that have a different orientation are noted in Figure 4. The mean topography for each set of profiles, calculated by stacking and averaging individual profiles, is shown as heavy black lines in Figures 4 and 5. The number of profiles averaged and the distances over which these are spread are given in the corresponding figure captions. Thin black lines indicate the spread of one standard deviation. Where a regional slope of ~1° was apparent (e.g., profiles C, D), it was subtracted from the average profiles [e.g., Grott et al., 2007] prior to modeling.
Table 1. Best-fit Model Parameters for Faults in Average Profiles for the Cordillera Ringa
 The main topographic features evident in the suite of profiles are the scarp faces, having slopes of 2° to 24° (accounting for vertical exaggeration), and the more gently dipping footwall back scarps, having slopes of less than 1° to 4°. The primary criteria for identification of potential faults in the topographic profiles are steep slopes occurring near or at ring boundaries, nonlinearly sloping backscarps, elevation offset, and elevations leveling off away from the scarp.
 As ejecta deposition significantly contributes to the morphology of impact basins and the surrounding regions, possible effects on the resultant scarp topography must be estimated. Assuming fault formation occurred prior to ejecta deposition [Howard et al., 1974; McCauley, 1977; Scott et al., 1977], the shape of any footwall could have been significantly modified by the deposition of ejecta. The difference in topography and decrease in ejecta thickness with distance was calculated at the ORR and CR based on the equation derived by Fassett et al. . Fassett et al.  estimate the thickness of ejecta deposited at the CR to be on the order of 2.9 km and up to ~9 km at the ORR. However, the latter value is heavily dependent on the presumed diameter of the transient crater. Although ejecta deposition drastically changes the topography of the region surrounding the transient crater, to first-order, no significant difference in the shape of the topographic profiles results from these calculations as the slope and concavity of the decrease in topography with distance due to faulting and ejecta deposition are roughly similar. Indeed, removal of the ejecta from the topographic profiles slightly decreases the angle of the backslope. Comparison of the model results using this topography yields model parameters within ~15% of the reported values. Thus, the effect of ejecta deposition is generally minor with respect to the model fits. A caveat to this is that the deposition of ejecta on top of the fault topography would increase the elevation of the scarps, which may lead to artificially high values of displacement on each fault determined from our models. Thus, the results reported here are likely maximum values of displacements along the ring-forming faults.
 On the other hand, if the formation of the CR and ORR scarps occurred after the deposition of ejecta [Head, 1974a], the present-day topography of the footwalls closely approximates the topography shortly after faulting occurred. In addition, slopes due to ejecta deposition calculated from Fassett et al.  are 1° and 0.7°, determined from the CR out 10 and 100 km, respectively. Thus, to first-order, complications associated with potential ejecta modification of structural topography can be neglected when performing forward mechanical modeling of fault topography.
 Shown in Figure 6 are representative profiles across the IRR for comparison with those taken across the CR and ORR (Figures 4 and 5). These profiles illustrate that typical cross-sectional views of the massifs in the IRR do not show the characteristics of normal faulting (listed above) as are evident in profiles A–J. Instead they show single (profiles L and N) or double peaks (profiles K and M) with sharp to sloping scarps where the profile crosses the mapped IRR ring boundary as well as on both sides of the IRR massif peaks. Therefore, this indicates that the IRR did not form from normal faulting, and accordingly, the IRR profiles are not included in the modeling.
4.2 Model Details
 We use the forward mechanical dislocation modeling program Coulomb (the software, which requires MATLAB to run, can be downloaded from http://earthquake.usgs.gov/research/modeling/coulomb/overview.php) [Lin and Stein, 2004; Toda et al., 2005] to model surface displacements associated with normal faulting. Stress and material displacement calculations are made in an elastic half-space with uniform isotropic elastic properties following the equations derived by Okada .
 In our models, a fault is idealized as a rectangular plane with the sense of slip (i.e., normal, thrust, strike-slip, or oblique), magnitude of displacement, fault dip angle, depth of faulting, and fault length specified (Figure 7). We use a constant value of pure dip-slip displacement (no strike-slip component) [Schultz and Lin, 2001] in both the strike and dip directions along each modeled fault. While a nonconstant slip distribution can be prescribed in Coulomb in both the strike and dip directions, the way in which the slip is distributed is unknown and cannot be determined from the data currently available for the Moon. For example, some studies recommend a triangular slip distribution [e.g., Cowie and Scholz, 1992; Dawers et al., 1993; Manighetti et al., 2005], while others suggest an elliptical slip distribution better approximates natural faults [e.g., Pollard and Segall, 1987; Bürgmann et al., 1994; Willemse et al., 1996]. Thus, while a tapered slip distribution is more representative of the way faults behave, imparting a slip distribution to the faults modeled here would add another layer of uncertainty. Therefore, we choose to model the faults with as few assumptions as possible for simplicity. Using a tapered slip distribution, which is more realistic for natural faults, would likely result in deeper depths of faulting (T) than the method used here.
 Good fits to the LOLA topography were obtained by iteratively adjusting the values of fault dip angle, displacement, and depth of faulting in the model. The initial displacement magnitude is estimated from the relief of the scarp and adjusted based on model output. Final model parameters were determined based on visual fits to the shape of the footwall between observed (measured LOLA) and predicted (modeled) topography [Watters et al., 2002], as the shape of the footwall uplift is characteristic of normal fault topography [e.g., Jackson and McKenzie, 1983]. On the Earth, the uplift of extensional rift flanks has been shown to be the result of isostatic rebound of the lithosphere following normal faulting; the shape of the uplift forms at the time of faulting and represents permanent deformation of the lithosphere [Jackson and McKenzie, 1983; Weissel and Karner, 1989]. Applying this to the Moon and lunar impact basin large-scale normal faults, the present-day topography likely is representative of the original structural topography as modification of the initial topography by erosion on the Moon is minor. However, mare deposits have often infilled the bases of the fault scarps which further emphasizes that the often poor fits between the topography of the hanging wall and the model are not a major concern; the footwall preserves the original fault topography much better than the hanging wall.
 It should be noted, however, that flexure of the lithosphere is a long-term, slow, viscoelastic process, and this model does not and cannot model this type of behavior. Given the strain rates associated with impact structure formation (i.e., orders of magnitude faster than geologic strain rates [e.g., Key and Schultz, 2011]), brittle elastic processes are dominant. A sufficiently thick lithosphere, such that it does not flow and allow stress relaxation on short timescales, like that for the Moon, would remain rigid, and footwall uplift would be negligible at the surface during impact basin formation. Neglecting the effects of viscous deformation that has taken place since the formation of the basin means that our calculated displacement values should be regarded as minima.
 This modeling approach is not sensitive to the removal of regional slopes (i.e., detrending) carried out during the LOLA topographic data processing [e.g., Grott et al., 2007]. Although small variations in the parameters are permitted by the topographic data, a remarkably good match between the models and data is obtained for a relatively narrow range of the fault parameters.
 A Young's modulus E of 83 GPa [Turcotte and Schubert, 2002], Poisson's ratio ν of 0.25, and coefficient of friction μ of 0.6 are assumed for the anorthositic rock mass for the pre-impact surface [Schultz, 1995, 1996; Schultz and Lin, 2001]; these values were held constant throughout the modeling process as changes in these parameters do not have significant effects on the resultant fault-related topography. The primary variables that affect the shape of the modeled displacement are the fault dip angle δ, vertical depth of faulting T, and the magnitude and sense of displacement D. Briefly, variations in the fault dip angle affect both the amplitude and shape of the fault-related topography [Schultz and Lin, 2001] (Figure S1a in the Supporting Information), increasing the magnitude of displacement increases the structural relief (Figure S1b), and the shapes of the footwall uplift and hanging wall are affected by changes in the vertical depth of faulting [Schultz and Lin, 2001] (Figure S1c). A more in-depth discussion of the effects of changing these parameters is presented in the Supporting Information.
 Modeling using an elastic half-space minimizes the deformation that would (or did) occur in a plate with a finite thickness (such as the lithosphere/crust of a planetary body). Thus, misfits between the model output and the measured LOLA topography are expected; additional sources of misfits may come from the simplistic approach to fault mechanics in this model. For example, fault block rotations and changes in fault dip with depth (i.e., listric fault geometry) usually associated with normal faults are not accounted for in the Coulomb model. Future work, which applies finite element models of finite thickness plates, may be able to clarify the roles of fault block rotation, listric, or otherwise nonplanar fault geometries and tapered fault slip distribution and their effects on the determination of important fault parameters. Thus, the work presented here represents an important first step in determining the characteristics of the ring-forming faults at depth.
 Values for the best-fit parameters to the LOLA topography across the CR and ORR scarps are listed in Tables 1 and 2, respectively. In general, the depth of faulting T ranges from 19 to 37 km, fault dip angle δ varies between 54° and 80°, and fault displacement D varies between 0.8 and 5.2 km. For the CR, the depth of faulting T ranges from 19 to 37 km, fault dip angle δ varies between 61° and 75°, and fault displacement D varies between 0.8 and 5.0 km. For the ORR, the depth of faulting T ranges from 20 to 30 km, fault dip angle δ varies between 54° and 80°, and fault displacement D varies between 1.6 and 5.2 km. This relatively constant depth of faulting may correlate to some sort of mechanical layer thickness (perhaps similar to the lithosphere) during the impact event. Rheology of geological materials has been shown to affect the ways in which rock behaves when subjected to different strain rates (i.e., the strength envelope) [e.g., Brace and Kohlstedt, 1980]. Thus, under these high strain rate conditions, the rock at depth may have behaved mechanically homogenously down to about 35 km. Given the inherent uncertainty in the approach of forward modeling techniques, these results represent the best-fitting solutions to the topography data and are likely not unique solutions. However, the fits of the model outputs match the averaged topography well, as shown in Figures 4 and 5, and thus, the values for the best-fit parameters are significant.
 Profiles A, B, C, and E (Figure 4) and G, H, and I (Figure 5) show individual normal faults, with the uplifted footwall to the right and the down-dropped hanging wall to the left. In these cases, best-fit models are chosen based on the match to the footwall uplift alone, with the exception of profile I (Figure 5). The reasoning is twofold; the shape of the footwall uplift is more characteristic of normal fault topography than the shape of the hanging wall [e.g., Jackson and McKenzie, 1983], and the model outputs material displacements relative to an original flat, horizontal datum to which displacements are referenced. As observed in profiles A, B, C, E, G, and H, this is reflected by the best-fit model having higher elevations and plotting above the LOLA topography on the hanging wall side. The shape of the model may mimic the shape of the hanging wall as in profile C (Figure 4) or match the hanging wall fairly well (profile I; Figure 5), indicating that the method can accurately calculate the hanging wall displacements but not the elevation offset as a result of fault motion.
 The remaining profiles show more complicated normal fault geometries. Profile F (Figure 4) shows a horst with the master fault, fault 1, on the basinward side. Profile D (Figure 4) shows a complicated section of the western Cordillera Ring structure over 250 km long and encompasses a minimum of four synthetic normal faults. Profile J (Figure 5) shows at least two synthetic normal faults dipping toward the basin interior. The topography of fault 2 is well matched by the best-fit model, but the topography of fault 1 is not. This may be due to the presence of a small fault at approximately 60 km. Models that fit portions of the fault 1 topography had unrealistic fault parameters (e.g., T = 10 km, D = 5 km), and models with three faults also did not produce satisfactory fits. The remaining possibilities to explain the misfit are that the topography of fault 1 was modified during ejecta emplacement after fault formation or that fault 2 is the only fault transected by profile J. The remarkable fit of the model to profile D between faults 1 and 2 and 2 and 3 and in profile F between faults 1 and 2 demonstrates the robustness of this method.
 Figure 8 shows a map view of the modeled faults in Orientale. There are likely many other faults present, but without confirmation by modeling or unambiguous interpretations of imagery and topography, only those faults successfully modeled are shown. A cross-sectional view of Orientale with fault locations and dip angles determined from modeling profiles A and D is shown in Figure 8.
6 Discussion and Implications
6.1 Insights from a Terrestrial Analog: Chicxulub
 As the Chicxulub impact structure, located on the Yucatán Peninsula, Mexico, is the largest (diameter ≈ 180 km), youngest multi-ring impact basin on Earth [e.g., Morgan and Warner, 1999], it represents the best terrestrial analog for large-scale impact structures on the Moon and the terrestrial planets. The structure has been probed by multiple boreholes, scanned with subsurface imaging techniques involving gravity and magnetic surveys, seismic reflection and refraction studies, and modeled with hydrocode. Those results show that the final crater rim is defined, in part, by an inward dipping normal fault scarp [Morgan and Warner, 1999], which is one of several produced during the collapse of the ~100 km diameter transient crater [Kring, 1995; Morgan et al., 1997], forming a modification zone and the final basin. The central uplift collapsed to form a ~90 km diameter peak ring whose radially outward movement produced a collision with and overlapping of the inward collapsing transient cavity wall [Morgan and Warner, 1999; Collins et al., 2002; Ivanov, 2005; Morgan et al., 2011]. Seismic data reveal a vertical offset of stratigraphy of ~3 to 6 km along the normal faults at the basin rim [Morgan et al., 1997; Morgan and Warner, 1999], with single displacements up to 2.5 km [Morgan and Warner, 1999]. An additional circumferential fault system is characterized by outward-verging thrust faults occurring beyond the final crater rim with a diameter of ~250 km [Morgan and Warner, 1999]. The structures in the Chicxulub basin are most similar to those associated with the megaterracing model [Hartmann and Yale, 1968; Head1974a, 1977; Howard et al., 1974; McCauley, 1977; Morgan and Warner, 1999], although the outermost ring may have formed by the process described by the ring tectonic model [Melosh and McKinnon, 1978; McKinnon and Melosh, 1980; McKinnon, 1981; Morgan and Warner, 1999].
 Forward mechanical modeling of the Outer Rook and Cordillera Ring topography performed in this study indicates that these rings were formed by large-scale normal faults for which the vertical extent of faulting T ranges from 19 to 37 km, fault dip angle δ varies between 54° and 80°, and fault displacement D varies between 0.8 and 5.2 km. These results are consistent with observations at the Chicxulub impact crater. As such, it has been suggested that the ORR and CR of Orientale are analogous to the crater rim and outer ring of Chicxulub, respectively [Morgan and Warner, 1999].
6.2 Transient Crater Location and Dimensions
 An integral stage in impact crater formation is the production of a transient crater, the idealized initial cavity formed at the end of the excavation stage [Gault et al., 1968]. The size (depth, diameter, volume) of the transient crater is used to determine many fundamental crater characteristics, including the size of the projectile, the amount of impact melt produced, and the depth of the final crater [e.g., Collins et al., 2005 and references therein]. Currently, there is no consensus on the location of the rim of the transient crater for Orientale, although the majority of authors interpret the ORR as at least the approximate location of the transient crater rim [e.g., Head, 1974a; Moore et al., 1974; Scott et al., 1977; Head et al., 1993; Fassett et al., 2011; Table 3]. Previous transient crater diameter estimates range from 100 to 620 km [Head, 1974a; Table 3], and all four major topographic rings have been suggested to mark the location of the transient crater rim. However, there is no physical reason to assume that any of the observed rings should approximate the transient crater rim [e.g., Howard et al., 1974; Pike and Spudis, 1987].
 Because the ORR is a fault scarp of the type produced during the modification phase of impact cratering, the transient crater must be interior to it. If the CR represents the final crater diameter, then traditional scaling [Schmidt and Housen, 1987] suggests the transient crater had a diameter of ~500 km, well within the ORR. If the transient crater extended to the current location of the ORR, the morphology of the ring would not be controlled by a deep normal fault with its characteristic footwall topography as our modeling implies, but instead brecciated material at the location of the ORR would have collapsed into the transient cavity floor, and the terrace-like modification of the transient cavity would have resulted in faulting beyond the present location of the ORR.
 As described above (sections 2.2 and 4.1 ; Figure 6), the IRR has a different morphology than the ORR and CR, being instead composed of massifs. In the Chicxulub structure, that type of peak ring structure has been associated with the collapse of the central uplift onto the margins of the transient cavity and a collision with material collapsing inward from the modification zone [e.g., Morgan and Warner, 1999; Collins et al., 2002; Ivanov, 2005; Kring, 2005; Morgan et al., 2011]. If that analogy applies to Orientale, then the margin of the transient crater had an approximate diameter greater than 480 km. The distribution of post-impact mare fill is therefore consistent with the IRR and the ORR bounding the transient crater. Sharply defined circumferential deposits (e.g., Lacus Veris at the base of the ORR) would be produced from magmas propagating up well-defined faults, as is common on Earth [e.g., Smith and Bailey, 1968; Pitcher and Bussell, 1977], whereas the more distributed Mare Orientale erupted through a fractured floor beneath and breccia fill within the remnants of the transient cavity (e.g., Figures 9d and 9e).
 Here, we propose that the transient crater lies within the Outer Rook Ring but interior to Lacus Veris, with a diameter of 500–550 km. Our interpretation of the transient crater diameter differs from the commonly held view that the ORR marks the greatest plausible extent of the transient cavity (Table 3). Of the transient crater size estimates, our results are most compatible with those of Spudis , Spudis et al. , and the numerical modeling with thermal profile 2 (mantle not reaching solidus) of Potter et al.  but are notably larger than, for example, the diameter estimate of ~400 km based on the Orientale gravity anomaly [Wieczorek and Phillips, 1999; Hikida and Wieczorek, 2007], the <400 km estimate by Melosh , or the 352 km numerical model estimate based on Potter et al.'s  thermal profile 1 (mantle reaching solidus).
6.3 Crustal Thickness
 The crustal thickness in eastern Orientale, derived from inversion of gravity and topography data, is ~12 km thinner than in the west, consistent with the regional gradient of crustal thickness derived from profile A in Figure 2. This suggests that the difference in crustal thickness may be a primary structure, existing prior to the impact event and did not occur as a result of the impact and basin-forming processes. Thus, this evidence may provide a constraint on the timing of the formation of the crustal thickness asymmetry, which had to be in place before the estimated time of Orientale Basin formation: 3.85 Ga [Wilhelms, 1987] to 3.68 Ga [Whitten et al., 2011].
6.4 Relationship between Normal Faults and Maria
 Further evidence for normal faulting of the rings comes in the form of the distribution of locations and ages of mare deposits within Orientale Basin. The crust in the basin center has been significantly thinned and fractured due to material excavation and impact shock, respectively (Figure 2b), favoring magma ascent there (Figure 9d); thus, the materials in Mare Orientale erupted earliest and are the oldest, consistent with published age estimates [Greeley et al., 1993; Whitten et al., 2011]. The central mare load may have exerted tension on the lithosphere, causing dilation of the impact-induced ring faults and created discrete conduits for magma ascent to the surface [e.g., Hartmann and Kuiper, 1962; McGovern and Litherland, 2011]. Simultaneously, compressional stresses were induced below the basin, closing off previously utilized conduits [McGovern and Litherland, 2011], stopping additional magma from erupting as lava in Mare Orientale. As lava erupted on the surface along the ORR, more weight was exerted on the crust, and the zone for favorable magma ascent and lava eruption may have been diverted to the nearest outer structural weakness, the CR. This sequence of faulting and loading from mare fill may account for the decrease in mare ages from the basin center outward [Greeley et al., 1993; Whitten et al., 2011] as well as providing support for our hypothesis that the extent of the transient crater lies entirely interior to the Lacus Veris mare ponds. Additionally, the crustal thickness asymmetry (Figure 2) may be a factor in the preferential location of mare materials on the eastern side of the basin where the crust is ~10–30 km thinner than on the west, likely influencing fault and ring formation and, therefore, locations of discrete conduits available for magma ascent.
6.5 Formation of Basin Rim Topography
 The topographic data and modeled structures indicate that the presently observed CR is reminiscent of a final complex crater rim that has slumped in a manner broadly similar to the terrace formation in complex craters. This can be seen, for example, in profile D in Figure 3, where several normal faults are present on the southwestern side of Orientale in the location where individual rings are not easily discerned. We suggest that this normal faulting, similar in principle to the formation of terraces in complex craters, is sufficient to cause the modification of the final crater rim into the observed Cordillera Ring and Outer Rook Rings with accompanying smaller normal faults without a need to invoke formation of a single megaterrace far beyond the uplifted rim [Head, 1974a, 1977]. Nevertheless, further faulting beyond the final topographic rim is possible and, in the case of Orientale, may have resulted in the formation of the 1300 km diameter outer ring [e.g., Hartmann and Kuiper, 1962; Hartmann and Wood, 1971; Pike and Spudis, 1987]. Testing this hypothesis is, however, beyond the scope of the present study. As the faults forming both the ORR and the CR scarps are deep (Figure 8), uplift of the elastic lithosphere was probably an important part of the structural uplift process forming the topographic rings. Thus, in addition to ejecta, a structural component is also clearly required to form the observed topography of the ORR and CR.
 In addition, as we have shown above (Figure 6), the Inner Rook Ring displays topography unlike the normal fault-dominated ORR and CR (Figures 4 and 5), implying that the IRR formed by a different mechanism. We consider this to support the interpretation that IRR is analogous to peak rings in peak-ring craters [e.g., Head, 1974a, 1977; McCauley, 1977; Scott et al., 1977; Head et al., 1993] like that also seen in Chicxulub [Morgan and Warner, 1999; Collins et al., 2002; Ivanov, 2005; Kring, 2005; Morgan et al., 2011]. If the IRR (diameter = 480 km) is a peak ring, then its size relative to that of the CR (930 km) is similar to the ~0.5 value expected [e.g., Wood and Head, 1976; Pike and Spudis, 1987; Baker et al., 2011]. Because peak rings are composed of material uplifted from depth, this interpretation is fully consistent with the spectral signature of partially shocked and uplifted plagioclase (anorthosite) in the IRR [Spudis et al., 1984; Head et al., 1993, 2010; Bussey and Spudis, 1997, 2000; Ohtake et al., 2009; Pieters et al., 2009], which is distinct from the noritic spectral signature of the outer basin.
 To summarize, we suggest the following scenario for the formation of the three main rings of the Orientale Basin (Figure 9). The IRR is a peak ring formed by the collapse of the central uplift, with probable contribution from the collapsing transient cavity rim material. The CR is analogous to final complex crater rims, with the Cordillera Ring scarp marking the location of a deep, inwardly dipping, normal fault and the ring topography being mainly due to ejecta deposition and uplift induced by the deep faulting.
 The ORR is located outside the transient cavity, and the scarp marks the location of the second major normal fault in the Orientale Basin. The topography of the ORR is also the result of ejecta deposition and uplift induced by the deep faulting, with probable contribution from the rotation of the block between the ORR and CR. The collapse of the transient cavity took place mostly as deep normal faults, with additional shallow normal faults particularly important in the southwestern portion of the basin where the morphologic and topographic ORR and CR scarps are difficult to distinguish.
 This formation model is consistent with the observed ring morphology, topography, spectral properties of the rings, location of the mare and the lacūs, the origin of the Montes Rook Formation as the deepest ejecta deposited just outside the transient crater, peak-ring formation models, IRR/CR diameter ratio, and the results of forward mechanical modeling of the ORR and CR scarps.
6.6 Comparison with Other Formation Hypotheses
 The observed topography of the ORR and CR matches that expected from ejecta deposition and deep normal faulting and is inconsistent with features predicted by the tsunami model [van Dorn, 1968, 1969]. Thus, we consider Baldwin's  statement that the CR appears “to be a ripple, not just a ring fault” to be invalid. In addition, the predicted locations of faults by the nested melt cavity model [Head, 2010] do not match observations and modeling and therefore is not considered to be a viable formation mechanism for large impact basins on the Moon.
 Compared to the ring tectonic-based approach by Melosh , our model differs by having a notably larger transient crater diameter (<400 km versus 500–550 km; see Table 3). If the IRR is a peak ring [e.g., Head, 1974a; Moore et al., 1974; McCauley, 1977; Solomon and Head, 1980; Head et al., 1993], a transient crater diameter of ~400 km or less [Melosh, 1989; Wieczorek and Phillips, 1999; Hikida and Wieczorek, 2007; Table 3] is in stark contrast with formation models in which peak rings result from the outward collapse of the central peak combined with the inward collapse of the transient cavity [e.g., Morgan and Warner, 1999; Morgan et al., 2000, 2011; Collins et al., 2002]. If the transient crater had a diameter of ~400 km or less [Melosh, 1989; Wieczorek and Phillips, 1999; Hikida and Wieczorek, 2007; Table 3], the IRR (diameter = 480 km) could not be a peak ring formed by the outwardly collapsing central peak and inwardly collapsing transient cavity model.
 Although in many respects broadly similar, the hypothesis presented in this study differs in two important ways from the megaterrace hypothesis: (1) The dimensions of the transient crater are different, and the reason for placing it in this location is that the magma conduits that facilitated the formation of the lacūs are deep faults caused by the collapse of the transient cavity, and thus, the transient cavity has to have been inside the lacūs; and (2) the formation processes of complex crater rims and the Cordillera Ring do not have to be drastically different. Rather, there is a continuum from complex crater terraces to basin rings, as shown by the highly complex faulting in the southwest part of the basin, transitioning to other parts of the basin where there typically is at least one major fault accompanied by several smaller ones.
 Forward mechanical modeling of ring topography reveals that the Outer Rook and Cordillera Rings are large-scale normal faults with the vertical depth of faulting T from 19 to 37 km, with most faults having T = 30 ± 5 km, fault dip angle δ between 54° and 80°, and fault displacement D between 0.8 and 5.2 km.
 The collapse of the transient cavity rim took place by normal faulting, either by several smaller normal faults roughly similar to complex crater terraces as in the southwest part of the Orientale Basin (e.g., profile D in Figure 4) or mostly by two deep normal faults forming the ORR and CR scarps, as shown by forward mechanical modeling. The Cordillera Ring is morphologically [e.g., Moore et al., 1974; Head, 1977; Wilhelms et al. 1977; Wilhelms, 1987] and topographically similar to final complex crater rims, suggesting a similar formation mechanism.
 The distribution of mare deposits inside Orientale Basin suggests that the CR and ORR normal faults were used as conduits for magma ascent subsequent to their formation during or slightly after the collapse of the transient cavity.
 Our results generally agree with the models that predict normal faulting, such as megaterracing [Hartmann and Yale, 1968; Head, 1974a, 1977; Howard et al., 1974; McCauley, 1977] and ring tectonics [Melosh and McKinnon, 1978; McKinnon and Melosh, 1980; McKinnon, 1981; Melosh, 1989], although details of these models compared to ours may differ.
 The Inner Rook Ring does not display characteristic normal fault topography, implying that the IRR formed by a different mechanism, supporting the interpretation that IRR is analogous to peak rings in peak-ring craters.
 The crustal thickness difference between the eastern and western sides of the basin is likely preexisting, attributable to the global crustal thickness asymmetry, and not the result of basin formation processes. The formation of the hemispheric crustal thickness asymmetry can then be placed before the formation of Orientale Basin 3.68 to 3.85 Ga.
 The transient crater rim was located inside the Outer Rook Ring and likely had a diameter of ~500–550 km.
 The authors thank M. Weller (Rice University) for discussions about fault modeling using Coulomb, R. Schultz (ConocoPhillips) for detailed discussions regarding faulting behavior, C. Mercer (LPI and USGS Denver) and P. McGovern (LPI) for discussions about magma ascent around impact basins, R. Potter (LPI) for discussions regarding hydrocode models, Y. Ishihara (National Astronomical Observatory of Japan) for sharing GIS-compatible crustal thickness data, L. Gaddis (USGS), the USGS ISIS team, and B. Fessler (LPI) for valuable computer support for ArcMap and ISIS. We are also grateful for the data collected and provided by the LRO LOLA team. The authors thank Jeff Andrews-Hanna and Christian Klimczak for thorough and detailed comments that greatly improved the manuscript. This research was partially funded by NASA under the LPI Cooperative Agreement NNX08AC28A, NASA Lunar Science Institute contract NNA09DB33A (PI David A. Kring), and NASA Outer Planets Research grant NNX09AP33G (PI B. R. Smith-Konter). This is LPI contribution 1712.