Thermally induced brittle deformation in oceanic lithosphere and the spacing of fracture zones
Introduction
The length of the mid-ocean ridge segments varies substantially among spreading centers and is correlated with several tectonic factors, including a positive correlation with spreading rate. The first order segments, bounded by transform faults (first order discontinuities), have an average length of 600 ± 300 km along fast (> 6 cm/yr) spreading ridges and 400 ± 200 km for slow (< 6 cm/yr) spreading ridges (MacDonald et al., 1991). Sandwell (1986) suggested that the length of the first order segments varies linearly with spreading rates. Although valid at the first order scale, such linear correlations are not supported at every level of the hierarchy. For example, the magmatic segments of slow to intermediate spreading ridges were shown to be 52.5 km long on average, independent of spreading rates (Briais and Rabinowicz, 2002).
Segment lengths are also apparently associated with regional variations in crustal thickness, creep strength, and mantle temperature. For instance, the Reykjanes ridge above the Iceland hot spot is known to have a uniform and much thicker crust for its spreading rate (Bunch and Kennett, 1980, Murton and Parson, 1993, Smallwood and White, 1998). This hot spot-affected ridge has been shown to exhibit signatures of wet mantle source for basaltic melt (Nichols et al., 2002). The water in crustal and mantle minerals has a strong weakening effect on creep strength although the preferential partitioning of water into melt phases complicates this straightforward relation (e.g., Karato, 1986, Hirth and Kohlstedt, 1996). In contrast, the Australian-Antarctic Discordance (AAD) has a highly rugged seafloor indicating increased fracturing (Hayes and Conolly, 1972, Weissel and Hayes, 1974) as well as anomalously thinner crust in comparison with other parts of the Southeast Indian Ridge (SEIR) (Tolstoy et al., 1995, Okino et al., 2004). Such regional features were attributed to colder mantle beneath the AAD (Weissel and Hayes, 1974), a hypothesis that was later supported by the systematics of major elements of basalt along the SEIR (Klein et al., 1991). These two regions, the Reykjanes ridge and the AAD, respectively exhibit reduced and enhanced segmentations at both the 1st and 2nd order compared with the other parts of the respective ridge systems. The degree of fracturing in those regions is substantially different in the profiles of free-air gravity anomaly (Fig. 1). The profile for the Reykjanes ridge (A–A') is smooth over the segment closer to Iceland and becomes rugged towards the southern end. The profile B–B' along the SEIR shows strong high frequency changes in depth and free-air gravity associated with the fracture zones over the AAD and with abrupt transition to a smooth segment east of the AAD.
A magma supply model has been proposed to explain the fundamentally different characteristics between slow- and fast-spreading centers, as well as axial morphology of a single ridge segment. According to this model, the variable amount of available magma at spreading centers and its along-ridge transport are responsible for along-ridge variations in axial bathymetry and associated geophysical and geochemical observations (MacDonald et al., 1991, MacDonald, 1998). Relating mantle dynamics to the conceptual magma supply model, calculations of mantle flow beneath slow spreading centers exhibit 3-D patterns that are segmented along the axis (Parmentier and Phipps Morgan, 1990, Lin and Phipps Morgan, 1992, Barnouin-Jha et al., 1997, Madge and Sparks, 1997). A problem with such flow models is that the wavelengths of the segmented mantle upwelling are larger (150 km) than the observed average second order segment length (~ 50 km) (Barnouin-Jha et al., 1997). However, when the effect of melt extraction on the viscosity of the magma residual was taken into account, a much shorter wavelength of segmented flow (as short as 70 km) was achieved (Choblet and Parmentier, 2001). Related to the magma supply model, ridge migration with respect to a hot spot reference frame was suggested to cause asymmetric mantle upwelling and melt production (Carbotte et al., 2004). This model provides an explanation for the observation that the majority of “leading” segments (that is, those that step in the same direction as ridge migration direction) are magmatically more robust.
Although the magma supply model is consistent with a range of observations, the model has yet to be linked with the brittle manifestation of mid-ocean ridge segmentation. Thermal stress due to the cooling of oceanic lithosphere is one possible driving force responsible for brittle ridge segmentation among many others (cf. Kastens, 1987). Using an order of magnitude argument, Collette (1974) suggested that thermal stress associated with the cooling of oceanic lithosphere should exceed its strength. By computing the bending moment of a semi-infinite thin elastic plate experiencing top-down cooling, it was suggested that segment length should be determined such that a plate can release thermal stress by bending (Turcotte, 1974). Expanding on this theory, Sandwell (1986) showed that ridge-bounding first order discontinuities can release thermal stress effectively when their spacing is proportional to spreading rate. Decomposing thermal stress into contraction and bending components, Haxby and Parmentier (1988) speculated that thermal bending stress, not contraction, would govern the spacing of transform faults because the magnitude of thermal contraction stress was independent of the ridge segment length. These studies, however, provide only an upper bound or indirect estimate of the fracture zone spacing. Sandwell and Fialko (2004) focused on the optimal spacing between thermal cracks, which minimizes stored elastic energy in a bending plate. It is notable that the spacing is not given a priori but is determined by the principle of minimum elastic energy.
A theory of thermal cracks provides useful insight into the spacing of ridge discontinuities if we assume that ridge segmentation occurs due to thermal stress. The stress distribution as a function of distance from a two-dimensional crack has been analyzed by Lachenbruch (1962). In a thermally contracting elastic half space, stresses are assumed to be released on the wall of a vertical crack. At greater distances from the wall, stress will increase to an ambient level so that each crack has a finite zone of stress relief. Since the strength of the material is limited, another crack will form at a distance where the stress exceeds the strength. In this fashion, the spacing between cracks is related to material strength and the size of the stress relief zones, which is determined by the material's elastic properties. Although this model could successfully explain crack spacing in permafrost, it leads to an apparent paradox for mid-ocean ridge segmentation. The model predicts a shorter spacing of cracks when the ambient level of stress is higher or the depth extent of cracks is shallower (Lachenbruch, 1962). Consequently, for fast and hot spreading centers, the Lachenbruch model implies a smaller fracture zone spacing because the amount of thermal stress is larger and brittle layers thinner compared to slow cooler spreading centers. In fact, the opposite trend is observed.
In this study, we investigate the role of thermal stress on the formation of mid-ocean ridge segmentation in terms of brittle deformation in young oceanic lithosphere. We address the influence of crustal thickness and rheology, factors that reflect a ridge system's tectonic setting, on fracture zone formation. A numerical method is used in which brittle deformation is allowed within the framework of continuum mechanics. This is an exploratory attempt towards a better understanding of ridge segmentation processes: relatively simple numerical models are used to draw implications relevant to actual ridge systems.
Section snippets
Numerical method
We use SNAC, an explicit finite difference code, to solve for the equations of momentum and heat energy conservation (Choi et al., in preparation). Although the code is fully three-dimensional, because of computational requirements, we only solve for 2-D problems here. The conservation equations are solved by the energy-based finite difference method (Bathe, 1996), which makes SNAC equivalent to a finite element code with linear tetrahedral elements except for the lack of explicit references to
Model setup
A series of 2-D models are constructed to represent a vertical cross-section along a straight ridge segment (Fig. 2). A 500 km long and 50 km deep domain is discretized into 1 × 1 km quadrilateral elements. To avoid complexities involving ridge axial processes, the domain is assumed to be initially at a small distance from the spreading center such that the initial temperature field is 0.3 My old lithosphere given by a half-space cooling model. Temperature is fixed at 0 °C on the top surface and
Models with weak crust
The temporal evolution of topography, temperature, viscosity, and plastic strain for the model with weak and normal thickness (7 km) crust (model 1 in Table 1) is shown in Fig. 3. The viscosity field is almost entirely determined by temperature while the dependence on stress is minimal. Lower viscosities are consistently found in the lower crust. Although brittle deformation occurred in the high viscosity uppermost part of the crust and mantle, the amount of plastic strain was only about 1%.
Effects of crustal thickness and creep strength
The models show that creep strength and crustal thickness strongly influence brittle deformation by the release of thermal stresses. Through the centers of surface troughs (grabens) that are connected to the primary cracks at depth, we measure the average spacing between the primary cracks (Table 3; Fig. 8).
Crustal thickness determines whether primary cracks are created. If the crust is thicker than a global mean (6–7 km, Chen, 1992, White et al., 1992) and thus has a weak lower part, then the
Conclusions
We show that crustal thickness, crustal creep strength, and the rule for plastic flow can substantially influence the brittle deformation of oceanic lithosphere. Crustal thickness determines whether brittle deformation would evolve into primary cracks or stay at secondary cracks without associated topographic features. Primary cracks only emerge when a crust is thinner than a certain threshold. Lower crustal creep strength has a net effect of shifting this threshold: When the creep strength is
Acknowledgements
We thank Joann Stock, Laetitia Le Pourhiet, and Paul Asimow for fruitful discussions and Dietmar Müller for suggestions on the manuscript. We would like to thank Claude Jaupart, Louis Geli, and two other anonymous reviewers for their useful and constructive reviews. This is contribution number 9174 of the Division of Geological and Planetary Sciences and 72 of the Tectonics Observatory. Development of SNAC was partially supported by the NSF ITR program under EAR-0205653. All calculations
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