Dynamic Models for Metamorphic Core Complex Formation and Scaling: the Role of Unchannelized Collapse of Thickened Continental Crust

Home , Exhumation (geology), Metamorphic core complex

ARTICLE IN PRESS TECTO-124557; No of Pages 9 Tectonophysics xxx (2009) xxx–xxx

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Tectonophysics

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Dynamic models for metamorphic core complex formation and scaling: The role of unchannelized collapse of thickened continental crust

Rebecca Bendick ⁎, Julia Baldwin 1

Department of Geosciences, University of Montana, United States article info abstract

Article history: Metamorphic core complexes at collisions between cratons and softer terranes, such as in the northern North Received 15 May 2008 American Cordillera, share a set of characteristic features including spatial and temporal association of Received in revised form 23 January 2009 ductile mid-crustal deformation with brittle normal faulting, spatial coincidence with prior crustal Accepted 19 March 2009 thickening, characteristic spatial scaling and limited duration and extent of deformation. These properties Available online xxxx are reproduced in numerical solutions for gravity-driven collapse of a viscous crustal region under conditions where vertical stress is continuous through thickened lithosphere (rigid, deformable conditions). Such Keywords: Metamorphic core complex solutions allow inversion for effective mechanical properties and crustal geometry from direct observations Crustal ﬂow of aspect ratio and exhumation velocity; in the northern Rockies, core complex geometry is consistent with a Continental dynamics twofold decrease in viscosity of the thickened Cordilleran crustal welt. Gravitational collapse © 2009 Elsevier B.V. All rights reserved.

1. Introduction This study focuses in particular on the northern North American Cordillera (Fig. 1), where metamorphic core complexes (Table 1) share Metamorphic core complexes occur in orogenic belts worldwide a set of common physical characteristics: and offer important opportunities to examine exposures of middle to lower continental crust in regions that have undergone large-scale 1. Crustal exhumation is spatially associated with brittle normal extension, uplift, and surface erosion (Crittenden, 1980; Armstrong, faulting. (Normal faults bound zones of observed ductile 1982). Much previous work on metamorphic core complexes has exhumation.) focused on the mechanisms and timing of detachment faulting and 2. Localization of exhumation is spatially associated with the edge of a exhumation of footwall rocks through integrated structural, petrolo- craton. (Highly exhumed exposures align between the isotopic gic, and geochronologic studies (e.g. Parrish et al., 1988; Hodges and signature of cratonic material at depth and surface exposures of Walker, 1992; House et al., 1997; Foster et al., 2007). continental craton. See Fig. 1.) However, the term ‘metamorphic core complex’ is presently used 3. Localization of exhumation is spatially associated with a thick for a variety of different structures, ranging from low-angle normal crustal welt. (Highly exhumed exposures are associated with initial faults with associated mylonitic shear zones (e.g. Coney, 1980), to crustal thicknesses N50–60 km.) migmatite-cored gneiss domes that record significant near-vertical 4. Exhumation follows crustal thickening and lasts for a limited time. exhumation (e.g. Whitney et al., 2004). We are particularly interested (Peak exhumation appears to last for 10–15 Myr.) in a group of metamorphic core complexes in settings of convergence 5. The length scale of core complex exhumation is limited, and between stiffer and softer continental packages. Examples of this 6. Crustal exhumation is localized to a region of characteristic width specific tectonic setting include the North American Cordillera, the to depth aspect ratio. northeastern Pamir in China (Robinson et al., 2004, 2007), and within the Alpine–Himalaya Belt, including core complexes of the eastern In this paper, we consider the evolution of metamorphic core Mediterranean and central Iran (Lister et al., 1984; Whitney and Dilek, complexes with these characteristics, including the related changes in 1997; Verdel et al., 2007). Extension in these regions has previously the shape and position of crustal rocks. We make the assumption fi been attributed to vertical extrusion due to topographic collapse or that a signi cant part of this process occurs in continental materials fl backarc extension due to slab rollback. that deform continuously and may be investigated by recourse to uid dynamics. Other recent work on tectonic dynamics of continental lithosphere has similarly borrowed tools from fluid dynamics (e.g. England and McKenzie, 1982; Royden, 1996; Beaumont et al., 2004; Flesch et al., 2005) to describe the spatial distribution of both stress ⁎ Corresponding author. Tel.: +1 406 243 5774; fax: +1 406 243 4028. and strain in continents. Unlike these previous efforts, however, we E-mail addresses: [email protected] (R. Bendick), [email protected] (J. Baldwin). develop dynamic solutions that allow vertical variations in strain 1 Tel.: +1 406 243 5778; fax: +1 406 243 4028. and strain rate (in contrast to thin viscous sheets) and coupled

Please cite this article as: Bendick, R., Baldwin, J., Dynamic models for metamorphic core complex formation and scaling: The role of unchannelized collapse of thickened continental crust, Tectonophysics (2009), doi:10.1016/j.tecto.2009.03.017 ARTICLE IN PRESS

2 R. Bendick, J. Baldwin / Tectonophysics xxx (2009) xxx–xxx

Fig. 1. Map of the northern Rockies showing the distribution of Eocene metamorphic core complexes, location of the Idaho batholith, the initial 87Sr/86Sr=0.706 line marking the boundary between accreted terranes and craton, the Lewis and Clark fault zone, and the limit of the Sevier thrust belt (modified from Coney, 1980). deformation across crustal boundaries (in contrast to channel flows). materials, including quartz (Brace and Kohlstedt, 1980), feldspars None of the fluid formulations for continents actually imply that the (Zavada et al., 2007), and sedimentary rocks (Schmid et al., 1977; continents are liquid, only that deformation in continental rocks is Zhang et al., 1993). broadly distributed and smoothly varying (hence continuous) at least at the longest length and time scales. Nor do these formulations imply 2. Geological setting of the northern North American that the continental lithosphere is absolutely weak. Successful fluid metamorphic core complexes dynamical descriptions of continental deformation allow effective lithospheric viscosities greater than 1020 Pa s (Bendick et al., 2008), Numerous structures in the northern Cordilleran region of North consistent with results from rock mechanics for common continental America (Fig. 1) have been identified as metamorphic core complexes

Table 1 Characteristics of northern Rockies metamorphic core complexes.

Name Location Width (km) Max P (kbar) Depth (km) Max T (°C) Metamorphism (Ma) Extension (Ma) Frenchman's Cap B.C., Can. 30–35 12a 40 800a 77–59a 59–53a Valhalla B.C., Can. 20–30 8b 26 820b 70–57c 51–49c Thor-Odin B.C., Can. 10–15 8–10d 26–33 750–800d 75–56e 55–45f Okanogan WA 55 9–10g,h 30–33 700–850g,h 85–70; 61–49 54–47i Kettle Dome/Grand Forks WA/B.C., Can 25–30 5–8j 20 750–850j 89–78; 74–56j 56–51j Priest River ID/WA 20–30 7–11 k 23–33 770–930k 85–55k,l 55–43m,n,o Clearwater ID 30–35 8–11 p,q 26–36 650–750p,q 82–80; 74–72; 64–55p,o 53–46pr Bitterroot ID/MT 30–35 6–8s,t 20–26 650–750s,t 80–75t 55–39t,u Anaconda MT 15–20 4–5v 13–16 600–650v 79o 53–40o Pioneer ID 15–17 3.5w 12 680w 79w 54–45w

a Armstrong et al. (1991). b Spear and Parrish (1996). c Gordon et al. (2008). d Norlander et al. (2002). e Carr (1992). f Vanderhaeghe et al. (1999). g Hansen and Goodge (1988). h Harvey (1994). i Kruckenberg et al. (2008). j Laberge & Pattison (2007). k Doughty and Price (2000). l Doughty et al. (1998). m Doughty and Price (1999). n Miller and Engels (1975). o Foster et al. (2007). p Doughty et al. (2007). q Grover et al. (1992). r Burmester et al. (2004). s House et al. (1997). t Foster et al. (2001). u Chase et al. (1983). v Haney (2008). w Silverberg (1990).

R. Bendick, J. Baldwin / Tectonophysics xxx (2009) xxx–xxx 3 on the basis of their structural and petrologic characteristics. These complicated mixed conditions, which strongly affect the spatial include low-angle normal faults bounding a localized region of pattern and magnitude of stress, strain, and strain rate. footwall rocks of higher metamorphic grade, generally characteristic For this investigation, we impose rigid, deformable boundary of middle crustal depths. conditions on an irregular fluidlike lower crustal region. McKenzie Crustal contraction during the Mesozoic and early Cenozoic in et al. (2000) first defined rigid, deformable boundary conditions to western North America resulted from Farallon plate subduction. This investigate lower crustal flow in simple extensional settings. These contraction involved a complex and protracted period of subduction- conditions entail fixed horizontal velocities and balanced (lithostatic) related deformation and plutonism. Crustal shortening during the vertical stresses on horizontal boundaries at the top and bottom of a Sevier orogeny affected a 200-km-wide zone extending from Canada modeled viscous region. Vertical boundaries at the edges of the region to northern Mexico, resulting in the development of the Cordilleran have velocity conditions in both directions. By setting vertical fold and thrust belt (Armstrong, 1968). Within the hinterland of the boundary conditions on horizontal boundaries to a state of stress Sevier orogen, a 50 to 60-km-thick crustal welt formed during the late balance instead of a particular velocity, rigid-deformable conditions Cretaceous to early Tertiary (Coney and Harms, 1984; Parrish et al., allow for deformations of these boundaries (and imply deformation in 1988; Constenius, 1996; Foster et al., 2001; Kalakay, 2001; Lageson surrounding material) along with the viscous region of interest in et al., 2002). response to a combination of boundary forces and gravitational body Although localized extension may have occurred during the forces. These conditions imply vertical mechanical coupling through Mesozoic, major extension in the Cordillera occurred between the lithosphere. For the case of a viscous middle crust, therefore, approximately 80 and 50 Ma (Coney and Harms, 1984). In many crustal flow stimulated by gravitation or boundary tectonic forces may places within the Cordillera, the onset of this Tertiary extension is promote both horizontal and vertical advection of material. The latter marked by the development of metamorphic core complexes (Coney effect is of particular interest in the case of metamorphic core and Harms, 1984). The occurrence of core complexes along the part of complexes, because core complex rocks appear to directly record the orogen where crustal thicknesses were at their maximum has led vertical advection of mid-crustal rocks relative to the surface of the many workers to hypothesize that gravitational collapse was the cause Earth. of extension (Sonder et al., 1987; Livaccari, 1991; Liu and Shen, 1998; In order to justify these boundary conditions, we must demon- Dilek and Moores, 1999; Sonder and Jones, 1999; Liu, 2001; Rey et al., strate that the stiffness contrast between the uppermost elastic crust 2001). Crustal extension overlapped in time with magmatism in the and the viscous part of the crust is small and that the stiffness contrast North America Cordillera, but the causal relationship between between the viscous part of the crust and the mantle lithosphere is magmatism, extension, and the development of metamorphic core also small (Bendick et al., 2008). By small, we mean that stresses complexes is not resolved (Wernicke et al., 1987; Armstrong and generated by crustal flow are sufficient to also drive deformation in Ward, 1991; Foster and Fanning, 1997; Foster et al., 2001; House et al., the uppermost crust and the mantle lithosphere (i.e. across the upper 2002). and lower boundaries of a viscous crustal layer). In the alternative North of the Snake River plain, metamorphic core complexes show case, corresponding to channel or pipe flow, where the mechanical a prolonged metamorphic history, lie inboard of the initial 87Sr/ contrast is large across the boundaries, stresses due to crustal flow are 86Sr=0.706 line, and are spatially associated with major Cordilleran supported by the stiffness of the surrounding material, decoupling batholiths (Coney, 1980). In western North America, the limit of the deformation of the crust and mantle. For the case of the northern craton at depth is defined by initial (age corrected) 87Sr/86Sr isotope Rockies, the stiffness contrast between the uppermost crust and the ratios in igneous rocks that track the transition from plutons emplaced mid-crust is very small at wavelengths N50 km, because the effective into oceanic lithosphere on the western (accreted terrane) side to elastic thickness of western North American crust is small (Das and those that intrude continental lithosphere on the eastern (craton) side Nolet, 1998; Gilbert and Sheehan, 2004; Flesch et al., 2007). Therefore, (Armstrong et al., 1977). The northern complexes also have a common at the length scale of dynamic topography from flow in the mid-crust, asymmetric, domal structure. Peak metamorphic conditions are the uppermost elastic lid of the crust simply flexes. This is not to amphibolite facies, with maximum crustal depths of around 25– suggest that the uppermost crust has no strength. Indeed, localized 35 km in the most deeply exhumed complexes. Migmatitic footwall stresses at short length scales clearly result in brittle failure of the rocks are common. Metamorphosed footwall rocks include units elastic lid, as demonstrated by the existence of large numbers of active within Proterozoic crystalline basement as well as the sediments of and senescent faults in the region. The thin elastic lid is sufficiently the Belt Supergroup. Peak metamorphic conditions were achieved 89– strong in the horizontal direction to allow the fixed horizontal velocity 49 Ma, which overlaps in some areas with magmatism in the condition used in the model. The stiffness contrast between the lower Cordilleran batholiths (64–56 Ma). Widespread complex-related crust and the mantle lithosphere also appears to be relatively small, extension occurred 56–39 Ma, with several core complexes recording based on arguments from thin viscous sheet estimates of the mean an initial rapid phase of extension at c. 50 Ma followed by more lithospheric viscosity (Flesch et al., 2007). Although standard litho- protracted, slower exhumation (Table 1). spheric strength profiles suggest a large stiffness contrast at the Moho (Brace and Kohlstedt, 1980), in settings with high geothermal gradients or particular compositional anomalies, especially the 3. Model formulation presence of small amounts of water, rock mechanics results allow for a small change in stiffness across this boundary. We therefore The process of implementing the Navier–Stokes equation, the consider that rigid-deformable conditions on crustal flow are reason- standard formulation of equilibrium in a fluid, for tectonic dynamics able for models of the northern Cordillera, and indeed offer significant entails two fundamental tasks. The first is identifying the appropriate advantages in cases where observations require vertical displace- scales and location for its application. In general, the longest length ments of crustal material. and time scales are best approximated by continuous formulations. In The geometry of the model (Fig. 2) is designed to reflect the particular, such formulations are predicated on integration over difference in mechanical properties between accreted terranes and length scales much larger than individual faults and time scales continental craton at continental sutures. In western North America, much longer than a seismic cycle, since faults indisputably exist and the limit of the craton is defined by the 0.706 line. To the east of this are indisputably elastic and brittle. The second is identifying the line, the lithosphere is old, thick, cold, and very stiff. West of the line, appropriate boundary conditions on the continuously deforming the lithosphere is younger, thinner, warmer, and softer. However, the region. Many different boundary conditions are allowed, including 0.706 line is offset from surface exposures of continental craton,

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Fig. 2. (Top) Formulation of the numerical model space. The top and bottom boundaries have horizontal velocity boundary conditions and vertical stress boundary conditions, the left boundary has a finite horizontal velocity and zero vertical velocity, the right boundary has Couette flow conditions (horizontal velocity depends on z with zero vertical velocity), and the block labeled ‘rigid’ has zero vertical and horizontal velocity conditions. The modeled viscous region has constant viscosity and density everywhere. The total thickness of the viscous region is h, the thickness of the rigid region is a, hence the indenter ratio, s,isa/h. (Bottom) Analogous geometry of a model cross section in the northern Cordillera. Cratonic material at depth is delimited by the Sr isotope ratio of partial melts sampled at the surface. This limit of cratonic material also coincides with maximum crustal thickening during orogenesis, and the localization of exhumation during collapse. indicating that some material from accreted terranes has moved over to boundary forces in the system (McKenzie et al., 2000). Thus, a the top of the craton during collision. We therefore include additional viscous region with a large Argand number deforms primarily in boundary conditions incorporating a step of arbitrary height repre- response to gravitational body forces, and a region with a small senting a mechanical contrast embedded within the crust. This step, Argand number deforms primarily in response to tectonic boundary made of craton, is rigid and undeformable relative to the continuously forces. deforming material within the model space. Using the conventions of For the generic case of constant Argand number and indenter ratio, the previous paragraph, the craton is sufficiently stiff that it can the collision between the rigid and viscous regions results in net support any stresses generated by flow in the accreted region without convergence between the viscous region and the cratonic indenter itself deforming. We allow viscous material to move over the top of accommodated by crustal thickening. Particles within the viscous the stiff step in accordance with the observation from North America region move toward the front of the indenter, where they are then (and Tibet) that the deformation front at the surface is inboard of the deflected vertically to build dynamic surface topography and a crustal edge of cratonic material at depth. That is, the Laramide frontal thrusts root, hence crustal thickening associated spatially with a suture are a few 100s of kilometers to the east of the limit of cratonic (Fig. 3). This thickened crust is always in isostatic equilibrium contamination of melts. We assume a simple rectangular geometry for (McKenzie et al., 2000). The steady-state slope angle, symmetry, the craton edge in the absence of any detailed evidence for other and length scale of thickened crust depend on both the Argand geometries. Sensitivity tests for edge geometry in other settings number and the indenter ratio (Bendick et al., 2008). (Bendick and Flesch, 2007) show that other suture shapes have only For the purpose of investigating core complex dynamics, we run small effects on the associated dynamic topography and flow field. We the model with static parameters for a finite time to produce an initial consider a 2D model in this work because there is little evidence for crustal welt, for a range of initial indenter ratios and Argand numbers. along-strike variations in suture geometry, boundary conditions, or This welt approximates Laramide crustal thickening. Using the mechanical variations. We also assume Newtonian viscosity. thickened crustal welt as our initial condition, we then model a We use the 2D finite element solver rheolef (Saramito et al., 2006) to calculate solutions of Stokes' equation subject to these boundary conditions and conditions of internal incompressibility. The same numerical methods were used in Bendick et al. (2008) and are described in detail in that work. In these solutions, velocity, stress within the deformable viscous region, and dynamic topography on the region's boundaries depend only on two dimensionless parameters, the Argand number and the ratio between the height of the rigid step and the height of the viscous ρgh2 ρ region, called the indenter ratio. The Argand number, ηU , where is the density of the viscous region, g is gravitational acceleration, h is Fig. 3. Model streamlines during the initial continental convergence phase of the model run. Material in the viscous region is advected horizontally toward the indenter front by the height (thickness) of the viscous region, η is the effective viscosity collision, where it is then deflected to excite surface topography and a corresponding of the viscous region, and U is the convergence velocity between the crustal root. Some viscous material also moves over the top of the rigid indenter block. viscous region and the rigid craton, describes the ratio of gravitational The grey box marks the region immediately at the indenter front shown in Fig. 4.

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observations of core complexes in the northern Rockies in the following section. As discussed above, the juxtaposition of rigid and viscous materials stimulates flow in the vicinity of the rigid indenter front (Fig. 3). This is true for all Argand numbers and indenter ratios, although the length scale of significant vertical flow varies with these two parameters. Following the change in the Argand number imposed on all models, the flow field changes markedly near the indenter front for a limited time until the entire viscous region approaches a new steady-state with scaling appropriate to the new Argand number (Fig. 4). For an instantaneous increase in the Argand number (equivalent to a Fig. 4. (Left) Velocity vectors for selected points on the upper boundary of the modeled decrease in effective viscosity, convergence velocity, or both), the viscous region immediately following an instantaneous increase in the Argand number thick crustal welt collapses gravitationally. Like the growth of the welt of the model space. The region shown is only that within the gray box in Fig. 3. Because itself, this perturbation is excited at the boundary between rigid and the numerical model is dimensionless, the spatial scale and magnitude of velocity vectors depend on the parameters for a particular case. For rescaling using crustal viscous materials, so is always located near the indenter front. The density of 2900 kg/m3, gravitational acceleration of 10 m/s2, and a 40 km-thick crustal spatial correlation among metamorphic core complexes, crustal layer with initial viscosity of 1021 Pa s, the region shown is approximately 20 km thick, thickening, and the craton edge is one of the characteristic features and the velocities are of order cm/yr. The predominant velocity of surface points is that we sought to reproduce with a dynamic model. downward, consistent with a gravity-driven decrease in elevation, but horizontal For small changes in Argand number (less than one order of extension is also excited near the indenter front. (Right) Streamlines for the same model region and time interval. Material is rapidly exhumed in a localized region magnitude), the region of gravitational collapse is characterized by immediately adjacent to the indenter. strongly localized vertical advection of mid-crustal material (Fig. 4), producing rapid exhumation of a narrow zone of mid-crustal material. The scaling of this exhumation zone is discussed in more detail below, range of instantaneous increases in the Argand number. In this but the model solutions do produce highly localized vertical particular continental context, such a change in Argand number displacements of mid-crustal material, another characteristic feature represents a decrease in the convergence velocity, a decrease in the that we sought to reproduce dynamically. effective viscosity of the viscous region (such as by heating), or both. Also coincident in space with the zone of gravitational collapse and For the specific purpose of comparison with core complexes of the rapid exhumation is a highly localized region of large horizontal North American Cordillera, we confine the initial Argand number and extensional stress (Fig. 5). Maximum extensional stress occurs at the indenter ratio around values that produce a crustal welt with the same uppermost part of the viscous region, therefore immediately at the scaling characteristics as the pre-Tertiary Laramide Rockies. This welt base of any overlying elastic lid. The stress decays rapidly with depth, had a minimum elevation of 4 km (Mulch et al., 2004), and a approaching the background state of stress within the viscous region horizontal length scale of ~100 km (DeCelles, 2004). The best initial over ~10 km. This scaling varies slightly with the change in Argand parameters are an Argand number of 30 and an indenter ratio near 0.8. number (ΔAr) and indenter ratio, but the high-stress region is always For a 40 km-thick deformable crustal region, these correspond to a localized to the uppermost part of the model domain adjacent to the layer 10–20 km thick of crustal material overriding the craton, indenter front. Rescaled values for the maximum extensional stress effective crustal viscosities of order 1021 Pa s, and convergence are of the order of GPa, an order of magnitude greater than the stress velocities of order 10 mm/yr, although these values cannot uniquely required to initiate brittle failure in most crustal rocks (Byerlee, 1978). be determined, since they trade-off within the Argand number. Therefore, the localized extensional stress produced by an instantaneous change in the Argand number of viscous middle crust is ample 4. Model results to initiate normal faulting in the elastic upper crust coincident with the zone of viscous crustal exhumation. Again, this spatial correlation Results from numerical solutions to the problem of a collision of craton edge, rapid exhumation, and brittle normal faulting is a between a viscous body and a rigid body including an instantaneous characteristic quality of the targeted metamorphic core complexes. change in the Argand number can be separated into qualitative Finally, vertical velocity within the viscous region decays with a observations and quantitative scaling rules. Both of these types of time constant of approximately 5 Ma (for rescaling using crustal results are used to assess the relevance of the solutions to the case of density of 2900 kg/m3, gravitational acceleration of 10 m/s2, and a metamorphic core complex formation in convergent, mechanically 40 km-thick crustal layer with initial viscosity of 1021 Pa s) as the heterogeneous settings. We explicitly compare the model results with system approaches its new characteristic form, in agreement with

Fig. 5. Large horizontal extensional stresses also arise at the indenter front following the instantaneous increase in Argand number. Dimensionless values from the numerical model are rescaled here to give standard units for horizontal distance, depth, and stress using a viscous region density of 2900 kg/m3, gravitational acceleration of 10 m/s2, and a 40 km- thick viscous region. Recall that depth 0 in the model solutions represents the crustal brittle–ductile transition, not the surface of the earth.

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observations that core complexes do not exhume or extend indefi- able properties of solutions, including exhumation zone width (we), nitely. Thus, the simple dynamic model proposed here appears to depth of exhumation (de), and mean exhumation velocity (ve) and reproduce our observation of a finite duration for complex extension. their relationship to the two independent parameters, the change in For larger changes in Argand number, extension occurs throughout the Argand number (ΔAr) and the indenter ratio (s)(Fig. 6). the viscous region diffusely rather than localizing near the indenter For all small ΔAr solutions, the exhumation zone width scales front. This produces a very broad zone of extensional stress with low linearly with the depth of exhumation. The two values are therefore strain, and relatively little vertical advection of material. As in the combined into a single dimensionless measure, aspect ratio (A). We small ΔAr case, velocities related to gravitational collapse decay over use the convention A = we. We observe that only a limited range of de time until reaching a new steady-state. Without nonlinear effects aspect ratios is allowed in the entire calculated solution space. No (that we do not calculate here), such a system does not produce an reasonable values of ΔAr or s produce model core complexes of aspect identifiable localized core complex with mid-crustal rocks exposed at ratio less than 0.5 or greater than 8. A strong prediction of this the surface. proposed model of core complex dynamics is therefore that no We undertake a more quantitative comparison of model results observed core complexes of our target subtype may have substantially with field observations by systematically evaluating simple measur- different aspect ratio. We fit second-order polynomials relating aspect

Fig. 6. Scaling rules for core complexes from the numerical solutions. (a) Aspect ratio measurements from individual model runs, (b) exhumation velocity measurements from individual model runs, (c) minimum rms polynomial approximation of aspect ratio as a function of step ratio and change in Argand number, (d) minimum rms polynomial approximation of exhumation velocity as a function of step ratio and change in Argand number, (e) difference between (a) and (c), (f) difference between (b) and (d).

R. Bendick, J. Baldwin / Tectonophysics xxx (2009) xxx–xxx 7 ratio and mean exhumation velocity to ΔAr and s,tofind that the to be minimum constraints on the maximum exhumation depths since aspect ratio is described by in some case earlier higher pressures may have been achieved. We assume that the calculated pressures represent the minimum depth of X2 X2 equilibration under lithostatic pressures, and thus correspond to the lnðÞA = A xmyn mn depth of the rocks now exposed at the surface. Table 1 indicates a range m =0 n =0 of pressure estimates for most core complexes, indicating the – when x=ln(ΔAr) and y=ln(s). The coefficients that minimize the uncertainty in such measurements on the order of 5 10 km. Critically, rms difference from the numerical simulations are this depth is the absolute depth of the material relative to the surface of the earth, so records the total thickness of both viscous and elastic : ; : ; : A00 =1581 A10 =05389 A01 =23735 crust. However, the numerical models in this study only reproduce : ; − : ; : A11 =09369 A20 = 0 0897 A02 =60492 deformation within the viscous part of the crust, and allow an elastic A21 = A12 = A22 =0 lid with a limited range of possible thicknesses. For comparisons between observations and numerical results, we assume an elastic lid For the same x and y, mean exhumation velocity is described by of 10 km in all the targeted core complexes. We therefore translate observed depth to model space depth for aspect ratio calculation by X2 X2 subtracting 10 km from the petrologic estimate of depth. This is lnðÞv = B xmyn e mn certainly only a coarse approximation, since 10 km is the current mean m =0 n =0 estimate of elastic thickness from seismic, gravity and stress inversions fi with minimum rms coefficients: (e.g. Gilbert and Sheehan, 2004; Flesch et al., 2007) after signi cant Basin and Range thinning. In addition, the elastic lid thickness may − : ; − : ; : B00 = 0 1243 B10 = 0 2946 B01 =38159 have varied slightly from region to region. The uncertainty in thickness − : ; : ; : B11 = 0 1499 B20 =00143 B02 =28702 of the elastic lid during the end of Laramide orogenesis is comparable B21 = B12 = B22 =0 in magnitude to the uncertainty in peak pressure estimates from metamorphic mineral assemblages, so we consider this assumption to Inverting these relations therefore allows us to use observations of be nominally acceptable for this preliminary interpretation. aspect ratio and exhumation velocity to calculate the geometry of a Finally, mean exhumation velocity is estimated for the target core region along with its change in Argand number. The latter value can be complexes by dividing the rescaled viscous depth from the previous further utilized to estimate the change in effective viscosity or step by the duration of rapid exhumation generally estimated by Ar– convergence velocity required for core complex formation, if other Ar cooling ages. Most complexes record an initial phase of rapid parameters like the thickness and density of the viscous part of the exhumation around 53–48 Ma defined by these cooling ages, which crust can be estimated independently. Predicted values of indenter translates to initial rapid exhumation rate on the order of 1.5–6 km/ ratio are especially useful for ‘sanity checks’ of the model, because the Myr. Older ages for the onset of extension in Table 1 are considered thickness of the whole crust, the thickness of cratons, and the thickness maximum ages and are generally constrained by cross-cutting of imbricated, overriding orogenic materials can all be independently intrusions. The lower end of the range of estimated exhumation estimated from existing seismic and gravity observations. durations varies considerably from complex to complex, partly as a function of dating methods. Of particular importance are the 5. Scaling of core complexes in North America thermochronometers used, since each has different blocking tem- peratures (e.g. Ar–Ar vs. U–Th–He or fission track) and thus younger Given the relatively strong constraints on core complex aspect ages may record a protracted phase of exhumation related to later ratio and mean exhumation velocity provided by the numerical erosional processes rather than extension. solutions, we compile published observations of footwall width, exhumation depth, and mean exhumation velocity from the targeted 6. Discussion northern Rockies core complexes for comparison. Core complex width was estimated from published geologic The term “metamorphic core complex” is traditionally used to mapping as the maximum width of exposure of high grade describe structures that contain relatively high grade metamorphic metamorphosed footwall rocks between east-dipping low-angle rocks exposed along low-angle normal faults. However, other char- detachments on the eastern side of the complexes and west-dipping acteristic features of such structures are not universal, and range from ‘rolling-hinge’ detachments on the foreland side of the core complexes complexes that are melt-absent with upper greenschist to lower (Teyssier et al., 2005)(Table 1). Uncertainty in the core complex width amphibolite facies metamorphic rocks, to complexes that contain estimate arises from two sources. First is the observation that the diapir-like gneiss domes of high grade upper amphibolite facies rocks rolling-hinge detachments are sometimes not well defined or within larger core complexes, such as those in British Columbia. Adding exposed, in which case the boundary between high grade footwall to the confusion is the description of some exposures of ultrahigh- rocks and lower grade to unmetamorphosed hanging wall rock was pressure eclogite contained within lower-grade host rock as core used. Second, the method of estimating width assumes that the complexes. Not only do these systems vary in structure and petrology, current exposure of footwall rocks is entirely the result of the initial they vary considerably in dynamic setting and tectonic context. We dynamics driving core complex formation, and that no additional believe that these broad categories of metamorphic core complexes exhumation by erosion has occurred since complex formation. This should be subdivided to reflect both the diversity of characteristics and assumption is probably robust where mylonite zones have been the diversity of operative tectonic processes. mapped, since surface processes expanding the width of footwall We propose one particular subdivision based on tectonic setting, exposure would have to remove the mylonite. We assume here that where normal-fault-bounded exposures of ductile middle crust are the erosional contribution is negligible. spatially associated with a prior collision between a coherent unit of Minimum constraints on the maximum exhumation depths were continental craton and accreted terranes. This subdivision would estimated using standard geothermobarometric methods applied to include the core complexes of the northern North American Cordillera peak metamorphic assemblages in the footwall, recognizing that the in the western U.S. (Fig. 1), and similar complexes in the Chinese depth recorded by most metamorphic assemblages is typically the Pamir (Robinson et al., 2007). These complexes share a set of simple pressure at the thermal maximum. We therefore infer these pressures structural and petrologic characteristics including a crustal welt built

8 R. Bendick, J. Baldwin / Tectonophysics xxx (2009) xxx–xxx during the initial period of collision, low-angle normal faulting of the predictions are in agreement with observations, at least to the upper crust, ductile footwall fabrics, mid-crustal footwall maximum resolution of current published data. In some cases, however, the pressures, and characteristic aspect ratios. exhumation history of footwall rocks is not very well constrained by We further propose that the tectonic setting of this class of existing petrological data, so future work will serve as a better test. In metamorphic core complexes is responsible for their structural and addition, the unchannelized collapse model explains the very limited petrologic characteristics, because they undergo very particular spatial distribution and timing window for core complexes in the dynamics. In the numerical solutions presented here, core complex western U.S. even in the presence of signi ficant past and ongoing formation depends upon three critical conditions. First, the structural regional extension probably related to “excess” gravitational potential. geometry of the crust must contain both vertical and lateral The assumptions used in this paper mean that our numerical mechanical heterogeneity. That is, the cratonic material must be solutions provide only upper bounds on changes in crustal properties, rigid compared to accreted crust, and crustal material must be able to since thickness of viscous crust and effective viscosity trade-off within move over the top of the craton during collision. Second, the the Argand number. Furthermore, non-Newtonian viscosities and 3D boundaries of the middle crust must be rigid and deformable. That geometry certainly would generate a wide variety of nonlinear is, the stiffness contrast with the uppermost crust and the mantle responses not addressed by this simple model. However, we find lithosphere must be small enough (less than one order of magnitude) that, even with an extremely simplified view of crustal conditions and that stresses deforming the middle crust may also deform the dynamics, model results are in good agreement with observations uppermost crust and mantle lithosphere. In the case of western from real complexes. In particular, metamorphic core complexes in the North America, this condition is probably met by the thinness of the northern Rockies of the U.S. have consistent aspect ratios of 0.6–3.5, elastic uppermost crust and the presence of a high geothermal with much of that range attributable to uncertainty in the exact width gradient, hydration, or both in the mantle lithosphere. Finally, some and depth of the individual footwalls. This aspect ratio is consistent change in either the collision velocity or the effective viscosity of the with our numerical models where the cratonic thickness is approxi- middle crust must initiate core complex formation. Because our mately 80% of the total crustal thickness and where the change in targeted core complexes are often associated in time and space with Argand number is approximately 30–50. The latter could be the result plutonism, we prefer a causal decrease in effective viscosity of the of a (very reasonable) factor of 2 decrease in the effective viscosity of middle crust due to heating of the crustal welt. the middle crust at the orogenic welt, easily produced by radiogenic We model these particular dynamics numerically. The resulting heating or the introduction of small amounts of melt (bb1%) in the solutions differ substantially from other numerical models of core total crustal volume. The required craton thickness is consistent with complex evolution because the boundary conditions differ substan- crustal tomography for the western U.S. tially. Previous numerical solutions for viscous flows related to To summarize, a rigid, deformable fluid model for metamorphic metamorphic core complexes have mostly specified channel flows core complex formation allows for localized vertical displacements of with a priori boundary conditions, or generated emergent channel crustal rocks not easily accommodated by channel flow or thin viscous flows by imposing large viscosity contrasts across distinct boundaries sheet models. Models of this type predict observed characteristic within the lower crust (e.g. Teyssier et al., 2005; Rey et al., 2001; scaling of core complexes associated with continental sutures. Vanderhaeghe and Teyssier, 2001). Such channelized flows differ from Furthermore, the success of theses models implies that stiffness the solutions developed in this work in that velocities are primarily contrasts within the lithosphere in settings of continental collision are parallel to channel walls and that stresses are not transmitted from relatively small, producing stress continuity and therefore coupling of the viscous region to surrounding material, rather are supported by the continental crust and mantle. the much stiffer channel walls. Such models therefore assume strong mechanical layering of the crust, imply that displacements within a References weak crustal region velocity are mostly horizontal, and imply decoupling of material above and below a weak crustal region. Armstrong, R.L., 1968. Sevier orogenic belt in Nevada and Utah. Geological Society of – In contrast, under rigid, deformable boundary conditions, gravita- America Bulletin 79, 429 458. Armstrong, R.L., 1982. 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