Lithospheric strength profiles

In most quantitative treatments of deformation at large scales, the lithosphere is assumed to consist of multiple layers characterized by different rheologies (e.g. Section 7.6.6). The rheologic behavior of each layer depends on the level of the differential stress (Ao) and the lesser of the calculated brittle and ductile yield stresses (Section 2.10.1). The overall strength of the lithosphere and its constituent layers can be estimated by integrating yield stress with respect to depth. This integrated strength is highly sensitive to the geother-mal gradient as well as to the composition and thickness of each layer, and to the presence or absence of fluids.

The results of deformation experiments and evidence of compositional variations with depth (Section 2.4) have led investigators to propose that the lithosphere is characterized by a "jelly sandwich" type rheo-logical layering (Ranalli & Murphy, 1987), where strong layers separate one or more weak layers. For example, Brace & Kohlstedt (1980) investigated the limits of lithospheric strength based on measurements on quartz and olivine, which are primary constituents of the

The climb process

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Figure 2.24 (a) The diffusion of a vacancy (v) through a crystal; (b) the downward climb of an edge dislocation as adjacent atoms (crossed) exchange bonds leaving behind a vacancy that moves by diffusion (from Structural Geology by Robert J. Twiss and Eldridge M. Moores. © 1992 by W.H. Freeman and Company. Used with permission).

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Figure 2.25 Nabarro-Herring creep: (a) vacancies diffuse toward surfaces of high normal stress; (b) creation of a vacancy (v) at a surface of minimum compressive stress; (c) destruction of a vacancy at a surface of maximum compressive stress (from Structural Geology by Robert J. Twiss and Eldridge M. Moores. © 1992 by W.H. Freeman and Company. Used with permission). Solid lines in b and c mark crystal surface, solid circle marks the ion whose position changes during the creation of a vacancy.

continental crust and upper mantle, respectively. The results of these and other measurements (e.g. Ranalli & Murphy, 1987; Mackwell et al., 1998) suggest that within the oceanic lithosphere the upper brittle crust gives way to a region of high strength at a depth of 20-60 km, depending on the temperature gradient (Fig. 2.26a). Below this depth the strength gradually decreases and grades into that of the asthenosphere. Continental crust, however, is much thicker than oceanic crust, and at the temperatures of 400-700 °C experienced in its lower layers the minerals are much weaker than the olivine found at these depths in the oceanic lithosphere. Whereas the oceanic lithosphere behaves as a single rigid plate because of its high strength, the continental lithosphere does not (Sections 2.10.5, 8.5) and typically is characterized by one or more layers of weakness at deep levels (Fig. 2.26b,c).

Figure 2.26c,d shows two other experimentally determined strength curves for continental lithosphere that illustrate the potential effects of water on the strength of various layers. These curves were calculated using rheologies for diabase and other crustal and mantle rocks, a strain rate of (8e/St) = 10-15 s-1, a typical thermal gradient for continental crust with a surface heat flow of 60 mW m-2, and a crustal thickness of 40 km (Mackwell et al., 1998). The upper crust (0-15 km depth) is represented by wet quartz and Byerlee's (1978) frictional strength law (Section 2.10.2), and the middle crust (15-30 km depth) by wet quartz and power-law creep (Section 2.10.3). These and other postulated strength profiles commonly are used in thermomechan-ical models of continental deformation (Sections 7.6.6, 8.6.2, 10.2.5). However, it is important to keep in mind that the use of any one profile in a particular setting involves considerable uncertainty and is the subject of much debate (Jackson, J., 2002; Afonso & Ranalli, 2004; Handy & Brun, 2004). In settings where ambient conditions appear to change frequently, such as within orogens and magmatic arcs, several curves may be necessary to describe variations in rock strength with depth for different time periods.

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