Rheological stratification of the lithosphere

In most quantitative models of continental rifting, the lithosphere is assumed to consist of multiple layers that are characterized by different rheologies. (Section 2.10.4). This vertical stratification agrees well with the results from both geophysical investigations of continental lithosphere and with the results of laboratory experiments that reveal the different behaviors of crust and mantle rocks over a range of physical conditions. In the upper part of the lithosphere strain is accommodated by faulting when stress exceeds the frictional resistance to motion on fault planes. In the ductile layers, strain is described using temperature-dependent power law rheologies that relate stress and strain-rate during flow (Section 2.10.3). Using these relationships, experimentally derived friction and flow laws for crustal and mantle rocks can be incorporated into models of rifting. This approach has allowed investigators to study the effects of a rheological stratification of the lithosphere on strain localization and delocalization processes during extension, including the development of large-offset normal faults (Sections 7.3, 7.6.4). The sensitivity of strain patterns to the choice of crustal rheol-ogy for different initial conditions are illustrated below using three different physical models of continental rifting.

Behn et al. (2002) explored how the choice of crustal rheology affects the distribution of strain within the lithosphere during extension using a simple two-layer model composed of an upper crustal layer and a lower mantle layer (Fig. 7.28a). These authors incorporated a strain-rate softening rheology to model brittle behavior and the development of fault-like shear zones. Ductile deformation was modeled using temperature-dependent flow laws that describe dislocation creep in the crust and mantle. Variations in the strength (effective viscosity) of the crust at any given temperature and strain rate are defined by material parameters that are derived from rock physics experiments. The use of several flow laws for rocks with different mineralogies and water contents allowed the authors to classify the rheologies as either weak, intermediate, or strong. Variations in crustal thickness and thermal structure were added to a series of models to examine the interplay among these parameters and the different rheologies. The results show that when crustal thickness is small, so that no ductile layer develops in the lower crust, deformation occurs mostly in the mantle and the width of the rift is controlled primarily by the vertical geother-mal gradient (Fig. 7.28b,f). By contrast, when the crustal thickness is large the stress accumulation in the upper crust becomes much greater than the stress accumulation in the upper mantle (Fig. 7.28c,d). In these cases the deformation becomes crust-dominated and the width of the rift is a function of both crustal rheology and the vertical geothermal gradient (Fig. 7.28e,f).

Figure 7.28e illustrates the effects of the strong, intermediate and weak crustal rheologies on rift morphology (half-width). The models predict the same rift half-width for mantle-dominated deformation. However, the transition between mantle- and crust-dominated deformation begins at a slightly larger crustal thickness for the strong rheology than for the intermediate or weak rheologies. In addition, the strong crustal rheology results in a rift half-width for the crust-dominated regime that is ~1.5 times greater than the value predicted by the intermediate rheology and ~4 times greater than that predicted by the weak rheology. Figure 7.28f summarizes the combined effects of crustal thickness, crustal rheology, and a vertical geothermal gradient on rift half-width. These results illustrate that the evolution of strain patterns during lithospheric stretching is highly sensitive to the choice of crustal rheology, especially in situations where the crust is relatively thick.

A similar sensitivity to crustal rheology was observed by Wijns et al. (2005). These authors used a simple two-layer crustal model where a plastic yield law controlled brittle behavior below a certain temperature and the choice of temperature gradient controlled the transition from a brittle upper crust into a ductile lower crust.

This formulation and a 20-km-thick upper crust lying above a 40-km-thick lower crust allowed them to investigate how a mechanically stratified crust influenced fault spacing and the distribution of strain during extension. They found that the ratio of the integrated strength of the upper and lower crust governs the degree of strain localization on fault zones. When this ratio is small, such that the lower crust is relatively strong, extension results in widely distributed, densely spaced faults with a limited amount of slip on each fault. By contrast, a large strength ratio between the upper and lower crust, such that the lower crust is very weak, causes extension to localize onto relatively few faults that accommodate large displacements. In this latter case, the large-offset faults dissect the upper crust and exhume the lower crust, leading to the formation of metamorphic core complexes (Section 7.3). Wijns et al. (2005) also concluded that secondary factors, such as fault zone weakening and the relative thicknesses of the upper and lower crust (Section 7.6.5), determine the exact value of the critical ratio that controls the transition between localized and delocalized extension.

The results of Wijns et al. (2005), like those obtained by Behn et al. (2002), suggest that a weak lower crust promotes the localization of strain into narrow zones composed of relatively few faults. This localizing behavior reflects the ability of a weak lower crust to flow and transfer stress into the upper crust, which may control the number of fault zones that are allowed to develop. This interpretation is consistent with field studies of deformation and rheology contrasts in ancient lower crust exposed in metamorphic core complexes (e.g. Klepeis et al. 2007). It is also consistent with the results of Montesi & Zuber (2003), who showed that for a brittle layer with strain localizing properties overlying a viscous layer, the viscosity of the ductile layer controls fault spacing. In addition, a weak lower crust allows fault blocks in the upper crust to rotate, which can facilitate the dissection and dismemberment of the upper crust by faulting.

Lastly, a third numerical model of rifting illustrates how the interplay among strain-induced weakening, layer thickness, and rheological contrasts can influence deformation patterns in a four-layer model of the lithosphere. Nagel & Buck (2004) constructed a model that consisted of a 12-km-thick brittle upper crust, a relatively strong 10-km-thick lower crust, a thin (3 km) weak mid-crustal layer, and a 45-km-thick upper mantle (Fig. 7.29a). The model incorporates temperature-dependent power law rheologies that determine viscous behavior in the crust and mantle. The mantle and upper and

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Figure 7.28 (a) Model setup for numerical simulations of lithospheric stretching. The transition from mantle- to crust-dominated deformation is illustrated by (b), (c), and (d), which show the deformation grid after 1% total strain for a crustal thickness (TJ of 6,12 and 27 km, respectively. Grayscale indicates the magnitude of shear stress on left and normalized strain-rate on right. C and M mark the base of the crust and top of the mantle, respectively. (e) Effect of crustal thickness on predicted rift half-width. (f) Effect of vertical geothermal gradient on predicted rift half-width (images provided by M. Behn and modified from Behn et al., 2002, with permission from Elsevier). Each point in (e) and (f) represents an experiment. Black, strong;gray, intermediate; and white, weak rheology.

lower crust also follow the Mohr-Coulomb failure criterion and cohesion loss during faulting is included. The model also incorporates a predefined bell-shaped thermal perturbation at its center that serves to localize deformation at the beginning of extension. The horizontal thermal gradient created by this perturbation, and the predetermined vertical stratification, control the mechanical behavior of the lithosphere during rifting.

As extension begins, the upper mantle and lower crust undergo localized necking in the hot, weak center of the rift. Deformation in the upper crust begins as a single graben forms above the area ofnecking in the lower crust and mantle and subsequently evolves into an array of parallel inward dipping normal faults. The faults root down into the weak mid-crustal layer where distributed strain in the upper crust is transferred into the necking area in the strong lower parts of the model (Fig. 7.29b,c).

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Figure 7.29 Model of symmetric rifting (images provided by T. Nagel and modified from Nagel & Buck, 2004, with permission from the Geological Society of America). (a) Model setup. (b) Total strain and (c) distribution of upper, middle and lower crust and mantle after 25,47 and 78 km of extension. Solid black lines, active zones of deformation; dashed lines, inactive zones; thin black lines, brittle faults; thick black lines, ductile shear zones.

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Figure 7.29 Model of symmetric rifting (images provided by T. Nagel and modified from Nagel & Buck, 2004, with permission from the Geological Society of America). (a) Model setup. (b) Total strain and (c) distribution of upper, middle and lower crust and mantle after 25,47 and 78 km of extension. Solid black lines, active zones of deformation; dashed lines, inactive zones; thin black lines, brittle faults; thick black lines, ductile shear zones.

After ~25 km of extension, the lower crust pulls apart and displacements on the normal faults lead the collapse and dismemberment of the upper crust at the margins of the rift. Mantle material wells upward into the zone of thinning where the collapsing upper crust is placed in direct contact with mantle rocks. After 40 km of extension, the array of normal faults is abandoned and upper crustal deformation is concentrated in the center of the rift. Finally, after ~75 km, new ocean lithosphere is generated, leaving behind two tectoni-cally quiet passive margins. This, and the other physical models described in this section, show how combinations of competing processes that either weaken or strengthen the crust can be used to explain much of the variability in deformation patterns observed in rifts.

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