We present the first model results showing that some core complex detachment faults are strong and that their strength has to be in a narrow range to allow certain extensional structures to develop. The structures we simulate are kilometer-scale “rider blocks” that are particularly well observed on some oceanic core complexes as well as continental metamorphic core complexes. Previous numerical simulations of lithospheric extension produced the large-offset, core complex-forming, normal faults only when the faults were weaker than a given threshold. However, our new, high-resolution simulations indicate that rider blocks only result when the faults are stronger than a given level. A narrow range of fault weakening, relative to intact surrounding rock, allows for a consecutive series of rider blocks to emerge in a core complex-like geometry. Our results show that rider blocks develop when the dominant form of weakening is by reduction of fault cohesion while faults that weaken primarily by friction reduction do not form distinct rider blocks.
 Faults must be weaker than surrounding rocks to explain observed localization of strain on faults. There is disagreement over just how weak faults are and particularly whether they can be characterized as having normal versus low values of friction. Laboratory measurements indicate that for most rocks, the friction coefficient is between 0.6 and 0.8 [Byerlee, 1978] which also predicts relatively high angles for active normal faults formed under subvertical maximum compressive stress, consistent with observed dips of active, seismogenic normal faults that range between ~45° and 60° [Jackson, 1987; Collettini and Sibson, 2001], and stress differences measured in boreholes [McGarr and Gay, 1978; Brace and Kohlstedt, 1980; Townend and Zoback, 2000].
 The recognition of large-offset normal faults, or detachments, in metamorphic core complexes [Coney, 1980] that presently dip at a low angle (<30°), or are flat, has been used as an argument that these faults have a very low friction coefficient [e.g., Hayman et al., 2003; Axen, 2004; Numelin et al., 2007]. Several questions about low-angle normal faults are debated including whether they originate with low dips [Wernicke, 1981; Yin, 1989; Forsyth, 1992] or are rotated into that orientation [Buck, 1988; Wernicke and Axen, 1988]. Some normal faults do appear to be active with a low dip angle, though they may have inherited a low-friction fault zone [Collettini et al., 2009]. However, the question of the dip angle for the formation of oceanic detachments has been firmly resolved in favor of high-angle initiation based on the large magnitude of rotation indicated by paleomagnetic studies of drill cores from the footwalls of two oceanic core complexes [Morris et al., 2009; MacLeod et al., 2011].
 Here we consider the implications for fault strength of structures called rider blocks, seen in many continental and oceanic core complexes. Rider blocks are pieces of hanging wall (i.e., from above the fault plane) riding on the master normal fault (Figure 1) of core complexes [Coney, 1980; Rehrig and Reynolds, 1980; Davis et al., 1986; Reston and Ranero, 2011]. They were first recognized on continental core complexes (Figure 1a), and recent observations from oceanic core complexes have prompted renewed interest in rider block formation. The initial discovery of oceanic core complexes relied on the mapping of corrugated detachment surfaces that are not covered by rider blocks, but seismic imaging indicates that many oceanic detachments are buried by rider blocks as shown in Figure 1b. Such buried detachments may exist along the as much as half of slow-spreading ridges [Escartin et al., 2008; Reston and Ranero, 2011] while corrugated surfaces are seen on a much smaller fraction of ridges. Thus, rider blocks may cover vast areas of crust formed at slow-spreading centers [Reston and Ranero, 2011].
2 Previous Work
 Many core complex detachments are clearly rotated to lower dip angles, or are even overturned, by isostatic adjustment to the topographic loads produced by fault offset [e.g., Spencer, 1984]. Models of the regional isostatic response to offset assumed to occur on a single normal fault show that the inactive, upper part of these faults could rotate from initially high dip angle to be nearly flat or overturned as long as the fault offset was greater than the brittle layer thickness. Also, model rider blocks could form if high-angle splay faults periodically grow out of the active faults [e.g., Buck, 1988]. These simple models did not consider the range of fault strengths that would explain two questions: (1) How could a single fault develop a very large offset and (2) when would splay faults bounding rider blocks form?
 The first of these questions was addressed using analytic and numerical models that came to a somewhat unsurprising conclusion. Namely, for large offset and such large fault rotations to develop, a fault had to be weaker than a given value [e.g., Forsyth, 1992; Buck, 1993; Lavier et al., 2000]. The inactive upper part of such model large-offset faults rotates to domal shapes that compare well to the observed geometry of continental and oceanic core complexes [Lavier et al., 1999]. If the fault were too strong, then a series of normal faults develop with no fault accruing sufficient offset to produce the flat faults seen in core complexes.
 A theoretical treatment of the second problem [Choi and Buck, 2012] suggests that core complex rider blocks only form when the master fault weakening, relative to the surrounding rocks, is in a narrow range. If the fault strength is too low, no rider blocks form since the master fault can slip even if it has rotated to a very low dip. This analysis also predicts that if the fault loses strength primarily by friction reduction, then discrete rider blocks cannot be created. Because the analysis ignored complications, such as changes in stress orientations due to fault offset or partial basin filling, these predictions can only be a rough guide to the conditions needed for rider block formation.
3 Model Formulation
 Here we use numerical experiments to investigate the generation of large-offset normal faults and associated rider blocks with a minimum of simplifying assumptions. We follow the numerical procedure employed in some earlier studies of normal fault evolution [Lavier et al., 2000] but include two new features essential to simulate rider block development. First, because rider blocks often have dimensions smaller than the brittle layer thickness, the grid spacing needed to resolve them is 5–10 times greater than in earlier studies. Second, the blocks are composed largely of sedimentary and volcanic material that fills the fault-generated basin. Thus, we assume that the basin stays filled up to a depth Di with respect to the initial surface—a procedure similar to that used in previous studies of effects of sedimentation [e.g., Burov and Poliakov, 2001; Bialas and Buck, 2009].
 We consider extension of an idealized brittle (Mohr-Coulomb) layer as depicted in Figure 2a. The layer floats on an inviscid substratum while the top surface is stress free. Bands of localized plastic strain develop through strain weakening and are considered to represent faults. The process of strain weakening is approximated by reducing cohesion and friction coefficient proportional to the amount of plastic deformation. Previous numerical treatment of fault strain weakening show that results can be made largely independent of mesh size by reducing friction and cohesion as a function of a characteristic amount of fault offset [Lavier et al., 2000; Gerya, 2013]. We adopt 1.5 km for the characteristic offset in this study, which has been shown to promote large-offset faulting [Lavier et al., 2000]. Practically, plastic parameters that are affected by strain weakening are linearly reduced from an initial value to a final value as plastic strain increases to a characteristic value. The characteristic plastic strain is given by the characteristic offset divided by an approximate thickness of shear band (~300 m, 3 times the grid resolution).
 The density of the brittle layer is fixed at 2800 kg/m3. Hydrostatic pore fluid pressures are assumed with a water density (1000 kg/m3). Material filling in the depression created by fault offset is represented by infill depth (Di) and has the properties as the rest of the brittle layer except the density is 2400 kg/m3. As inviscid material beneath the brittle layer ascends to 10 km depth, it takes on all properties of that brittle layer as may occur through ductile-to-brittle transition due to hydrothermally assisted cooling [Lister, 1980; Phipps Morgan and Chen, 1993; Lavier and Buck, 2002].
 A suite of models were run with different values of parameters such as the initial or final cohesion and the depth of infill. Since previous work shows that a brittle layer thickness around 10 km gives the observed wavelength of doming of core complexes [e.g., Lavier et al., 1999; Rey et al., 2009; Le Pourhiet et al., 2012], the same brittle layer thickness is employed here. The initial friction coefficient is set to be 0.58 but allowed to evolve to different final values through prescribed strain weakening. Values of initial cohesion are in the range of 10–40 MPa, and different final values of cohesion were considered.
 A case that produced a sequence of sizeable rider blocks is illustrated in Figure 2 (also see the dynamic content Movie S1 in the supporting information). This reference case has an initial cohesion of 20 MPa and an infill depth of 1000 m. The final cohesion is 4 MPa but friction remains unchanged. Snapshots for 3 to 40 km of extension are shown in Figures 2b–2d. The first normal fault to form has a dip of 60°, consistent with the friction coefficient (Figure 2b). As extension proceeds, the footwall is uplifted due to unloading and the master fault bends and rotates. As a result, the fault has a dip of about 45° at 10 km of extension (Figure 2c). With further rotation, the fault locks at depths ≤ ~3 km and a new splay fault forms. Offset of this splay produces a well-defined rider block, composed of the former basin infill and hanging wall crust (Figure 2d). Subsequent rider blocks do not take as long to form because the active master fault around the depth of 3 km remains close to the locking orientation after the first rider block forms. Consequently, their cross-sectional areas are smaller than that of the first block. By extension of 30 km, two more rider blocks are created (Figure 2e) and the system appears capable of producing more rider blocks with continued extension (Figure 2f).
 Faulting patterns in our numerical models are sensitive to many parameters such as initial and final cohesion/friction coefficient and infill depth (for an overview, see the supporting information), but we here present some representative cases. For much greater strain weakening than in the reference, model rider blocks do not form. As the initial high-angle normal fault rotates to a low dip at intermediate to shallow depths, it continues to accommodate extension without locking. For an initial cohesion of 20 MPa, final cohesions less than 4 MPa and final friction coefficients less than 0.32 make the initial fault too weak for rider block formation no matter the thickness of infill (Figure 3a). The size of rider blocks depends on fault strength. When a fault is slightly stronger than in the reference model (e.g., the final cohesion equal to 8 MPa), the fault locks after a less amount of rotation as well as at a shallower depth, making the size of and the interval between rider blocks smaller (Figure 3b). A much stronger fault with a final cohesion greater than 10 MPa produces even smaller rider blocks that are difficult to recognize given the current model resolution (Figure 3c).
 The effects of variation in cohesion and infill depth on rider block formation are shown in Figure 4a for cases where the fault friction is maintained. The plot shows under what combinations of infill depth and initial cohesion rider blocks can form. Also shown is the cross-sectional area of the first block (Figure 4b). Rider blocks are bigger for greater cohesion loss and for smaller infill depth. This trend is roughly consistent with the prediction by Choi and Buck . However, there is also substantial discrepancy between numerical results and theory in terms of the block sizes as well as the formation conditions. For example, with intermediate amounts of infill (e.g., infill depth ~ 1000 m), rider blocks emerge for a narrower range of cohesion in the analytical treatment compared to the results of this study. The presence of added basin infill changes the stress field, and as a consequence, the shape of the master fault in ways that promote rider block formation. Nevertheless, the range of fault weakening leading to large-offset faults with rider blocks is very restricted. Models considering a wide range of parameters are discussed in the online supporting information.
 For models with an initial cohesion of 20 MPa and an infill depth of 1 km (Figures 2 and 3), we find that rider blocks only form when a master fault has a friction coefficient greater than 0.4 and a cohesion reduction between about 12 and 20 MPa. Qualitatively, a rider block-producing fault must have high friction but low final cohesion.
5 Discussion and Summary
 Rider blocks generated in our reference model (Figure 2) are reminiscent of the inferred geometry of master and splay faults as well as associated fault blocks seen in continental and oceanic core complexes (Figure 1). However, some core complexes have no rider blocks. Erosion could remove rider blocks in some continental areas though this should not occur for oceanic core complexes. Our results suggest either that the detachments in these complexes have a friction coefficient lower than 0.4 or that the amount of infill is not sufficient to form rider blocks even though friction coefficient is greater than 0.4. In the former case, such low values of friction are consistent with the measured values (< 0.3) for weak minerals like talc found on the corrugated surface [Escartin et al., 1997; Escartín et al., 2003; Moore et al., 2004; Schroeder and John, 2004; Boschi et al., 2006; Karson et al., 2006; Dick et al., 2008; Picazo et al., 2012]. The latter case, insufficient infill, has also been suggested as an explanation of the lack of rider blocks on the Atlantis massif, which is located at a volcanic infill-poor ridge-transform intersection [Reston and Ranero, 2011].
 This is the first study to place upper and lower bounds on the strength of normal faults. Our self-consistent numerical models indicate that large-offset, low-angle normal faults with sizable rider blocks are frictionally strong and have rotated to a low angle from the optimal orientation predicted by Andersonian fault mechanics. Rider blocks emerge with a core complex-like geometry in high-resolution simulations only for a narrow range of fault weakening, relative to intact surrounding rock. Furthermore, they develop when the dominant form of weakening is by reduction of fault cohesion while faults that weaken primarily by friction reduction do not form distinct rider blocks. Our models require that some large-offset faults have values of friction coefficient close to 0.6. Though we have focused on a specific fault type, our results may have implications for faults in general: i.e., faults have “normal” levels of friction, and altered minerals like talc must be present to explain the apparent low-strength features such as core complexes without rider blocks.
 E. Choi and W. R. Buck were partly supported by the U.S. National Science Foundation (NSF) through grant EAR-0911565. E. Choi and L. L. Lavier received partial support from the NSF Continental Dynamics program under grant EAR-0607588. Computations for this study were performed using the HPC resources provided by the Texas Advanced Computing Center at The University of Texas at Austin under TeraGrid grant TG-EAR100019.
 The Editor thanks Julia Morgan and an anonymous reviewer for their assistance in evaluating this paper.