Subsections

Global Effective Elastic Thickness, Mechanical Anisotropy and the Supercontinent Cycle

Pascal Audet and Roland Bürgmann

Introduction

The Earth experienced several supercontinent cycles since 2.7 Ga, the last one ending with the breakup of Pangaea into the current plate configuration. The driving mechanism is associated with vertical motion of the convective mantle from both subduction of ocean basins during supercontinent assembly and warm mantle upwelling causing breakup and the creation of new ocean floor (Gurnis, 1988). Although the details of the dynamics are still debated, it is generally agreed that continental margins are repeatedly deformed within weak, diffuse zones, and that stronger cratonic lithosphere remains intact during this process. Most cratonic cores within continents show crustal ages greater than 2.0 Gyr, are depleted in basaltic constituents, and have conductively cooled through time, thus acquiring a thick, high-viscosity thermo-chemical root (Jordan, 1978). Continental margins, in contrast, are much younger ($<0.5$ Gyr), have been thermally rejuvenated and structurally reactivated, and are much thinner. Such large differences in structure imply comparably large gradients in rheological properties of the lithosphere. These factors, combined with numerical simulations of coupled mantle convection and continental plates, suggest that deformation during supercontinent cycles is controlled by pre-existing structure acquired from past tectonic events. There is little observational constraint, however, on the spatial variability of rheological properties of the lithosphere because it cannot be observed directly.

Method

A useful proxy for the the long-term strength of the lithosphere is given by the flexural rigidity, $D=ET_e/12(1-\nu^2)$, where $E$ is Young's modulus and $\nu$ is Poisson's ratio, which governs the resistance to flexure (Watts, 2001). The strong dependence of $D$ on $T_e$ implies that the magnitude and spatial variations of $T_e$ can have a significant influence on the degree and style of deformation due to long-term tectonic loads. In particular, it is expected that spatial variations and gradients in $T_e$ can prescribe where strain may localize and consequently determine the locus of deformation as manifested by brittle (e.g. seismicity, faulting) and thermal processes (e.g. volcanism, rifting). $T_e$ is estimated by comparing the spectral coherence between topography and Bouguer gravity anomalies with that predicted for an equivalent elastic plate bending under surface and internal loading. The plate response is modeled either as isotropic or anisotropic, and the coherence is inverted for a single parameter, $T_e$, or the three parameters of an orthotropic elastic plate (i.e. having different rigidities in two perpendicular directions), $T_{min}$, $T_{max}$, and $\phi_e$, the direction of weakest rigidity. Here we use the wavelet transform method to calculate the coherence and estimate $T_e$ and $T_e$ anisotropy (Audet and Mareschal, 2007) and apply the technique to all major continents, with the exception of Greenland and Antarctica where thick ice caps complicate the analysis and data coverage is incomplete. We account for possible bias in $T_e$ estimation by considering the effect of gravitational ``noise'' and masking regions where the model fails.

Results

Figure 2.2 shows the azimuthal variations of the weak direction of $T_e$ superposed on the pattern of $T_e$ variations. In general, the $T_e$ pattern correlates with age since the last thermo-tectonic event. $T_e$ is high ($>100$ km) in Early to Late Proterozoic and Archean cratonic provinces, with the largest values found in the North American, West African, and East European shields. Some cratons (e.g. South Africa, North China, South India) exhibit lower $T_e$ ($50<T_e<100$ km) where lithosphere has been thinned by plume-related magmatism or delamination. Low $T_e$ ($<40$ km) is found in young Phanerozoic orogens (e.g. American Cordillera, Alpide belt) and tectonically active provinces (e.g. western North America, Afar Triple Junction and most of central-eastern Asia). $T_e$ is also generally low in the hanging wall of past and present subduction zones and along most continental margins, possibly due to thermal and fluid-related weakening as a consequence of subduction and rifting processes. $T_e$ anisotropy varies over short spatial scales ($\sim200-500$ km) in both magnitude and direction (Figure 2.2), thus ruling out a deep, sub-lithospheric mantle-flow origin. Magnitude of $T_e$ anisotropy is inversely correlated with $T_e$ as young, low-$T_e$ provinces display larger magnitude than older, high-$T_e$ cratons. Directions of weak rigidity are oriented normal to most continental margins and tectonic boundaries. $T_e$ anisotropy reflects directional variations in the flexural compensation of the lithosphere and has been speculated to originate from either dynamical or structural effects.

Figure 2.2: Global effective elastic thickness over continents calculated from the coherence between Bouguer gravity and topography using a wavelet transform. $T_e$ anisotropy (sampled on a 3 $^{\circ}\times 3^{\circ}$ grid) is superposed on filtered (using a Gaussian function of width 900 km) and color-contoured $T_e$ over continents and continental shelves (depth shallower than 500 m below sea level). Shaded areas correspond to regions where $T_e$ estimation is biased by gravitational ``noise.'' The length of black bars is given by the magnitude of $T_e$ anisotropy from the ratio $(T_{max}-T_{min})/(T_{max}-T_{min})$.
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These results allow us to clarify the role of rheological heterogeneity and mechanical anisotropy in continental evolution and deformation. That $T_e$ varies according to age since the last thermo-tectonic event and is partitioned between continental cores and margins is consistent with the episodic thermal rejuvenation of continental margins and resetting of lithosphere strength during thermo-tectonic events. These episodes originate from large-scale vertical convective motion of the mantle during continental assembly and breakup and are accompanied by margin-wide faulting and fault reactivation (either from rifting or thrusting) that further weakens marginal lithosphere and induces significant mechanical anisotropy. A weak and faulted lithosphere may enhance deformation by concentrating strain at pre-existing structures. Over time, these factors isolate continental interiors from deformation due to plate boundary forces during continental assembly, thus creating positive feedback and allowing only a small fraction of continental lithosphere to be recycled. Only in rare cases do plumes or delamination events de-stabilize cratonic cores. This model is consistent with numerical models of continental evolution that simulate the stability of cratonic crust and longevity of deeper roots as a consequence of higher yield strength with respect to oceanic lithosphere, and the buffering effect of weak mobile belts and margins that absorb stresses during repeated supercontinent cycles. This, in turn, implies that the inherited weakness of marginal lithosphere is relatively long-lived, despite its tendency to get recycled into the mantle during orogeny, possibly due to continuous accretion of terranes and plateaus that further enhances mechanical weakness and anisotropy.

Acknowledgements

This work was funded by the Miller Institute for Basic Research in Science (UC Berkeley).

References

Audet, P., and J.-C. Mareschal, Wavelet analysis of the coherence between gravity and topography: Application to the elastic thickness anisotropy in the Canadian Shield, Geophys. J. Int., 168, 287-298, 2007.

Gurnis, M. Large-scale mantle convection and the aggregation and dispersal of supercontinents, Nature, 332, 695-699, 1988.

Jordan, T. H., Composition and development of the continental tectosphere, Nature, 274, 544-548, 1978.

Watts, A. B., Isostasy and Flexure of the lithosphere, Cambridge University Press, Cambridge, UK, 2001.

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