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188   CHAPTER 7



           (a)                                        (c)
             t = 370 Myr, Δx = 222 km
            0                                           t = 40 Myr, Δx = 120 km
                                                       0
           -20                                        -20
           -40                                        -40   550  C
                                                           o
                o
           -60   550  C                               -60
           -80                                        -80
                                                           o
           -100                                       -100   1000  C
           -120                                       -120
                                                           o
                                                          1200  C
             400       500      600       700       800  400     500      600       700      800
            (b)
             t = 12 Myr, Δx = 120 km                  (d)
            0                                           t = 40 Myr, Δx = 120 km
                                                       0
           -20                                        -20
                o
           -40   550  C                                    o
                                                      -40   550  C
           -60
                                                      -60
           -80                                        -80
                 o
               1000  C
                                                           o
           -100                                       -100   1000  C
                 o
           -120   1200  C                             -120
                                                           o
                                                          1200  C
             400       500      600       700       800  400     500      600       700      800 Km
           Figure 7.27  Models of extension involving frictional-plastic (brittle) strain softening at (a) low extensional velocities
                                                             −1
                      −1
           (V ext  = 0.6 mm a ) and (b) high extensional velocities (V ext  = 100 mm a ). Models also show rift sensitivity to (c) a weak
                                                   −1
           and (d) a strong middle and lower crust at V ext  = 3 mm a  (images provided by R. Huismans and modifi ed from
           Huismans & Beaumont, 2007, with permission from the Geological Society of London). t, time elapsed in millions of
           years; Δx amount of horizontal extension. Vertical and horizontal scales are in kilometers.

           apply these results to specific natural settings, it is   are characterized by different rheologies. (Section
           important to realize that the effects of strain-induced   2.10.4). This vertical stratification agrees well with the

           weakening can be suppressed by other mechanisms that   results from both geophysical investigations of conti-
           affect the rheology of the lithosphere. For example, a   nental lithosphere and with the results of laboratory
           comparison of two models, one incorporating a weak   experiments that reveal the different behaviors of crust
           lower crust (Fig. 7.27c) and the other a strong lower   and mantle rocks over a range of physical conditions.
           crust (Fig. 7.27d), illustrates how a weak crust can   In the upper part of the lithosphere strain is accom-
           diminish crustal asymmetry. This suppression occurs   modated by faulting when stress exceeds the frictional
           because conjugate frictional shears that develop during   resistance to motion on fault planes. In the ductile
           rifting sole out in the weak ductile lower crust where   layers, strain is described using temperature-dependent
           they propagate laterally beneath the rift fl anks.  As   power law rheologies that relate stress and strain-rate
           rifting progresses, viscous flow in a weak lower crust   during flow (Section 2.10.3). Using these relationships,


           results in a nearly symmetric ductile necking of the   experimentally derived friction and flow laws for crustal

           lower lithosphere. These examples show that the degree   and mantle rocks can be incorporated into models of
           of rift asymmetry depends not only on strain softening   rifting. This approach has allowed investigators to study

           mechanisms and rifting velocities, but also on the   the effects of a rheological stratification of the litho-
           strength of the lower crust.                 sphere on strain localization and delocalization pro-
                                                        cesses during extension, including the development of
                                                        large-offset normal faults (Sections 7.3, 7.6.4). The sen-
                                                        sitivity of strain patterns to the choice of crustal rheol-

           7.6.6 Rheological stratification              ogy for different initial conditions are illustrated below
                                                        using three different physical models of continental
           of the lithosphere                           rifting.
                                                          Behn et al. (2002) explored how the choice of crustal
           In most quantitative models of continental rifting, the   rheology affects the distribution of strain within the
           lithosphere is assumed to consist of multiple layers that   lithosphere during extension using a simple two-layer
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