Lithospheric strength and stress revisited: Pruning the Christmas tree

Highlights • Stress in cratons is limited by tectonic force from distant plate boundaries. • Average stress in cratonic lithosphere decreases as competent thickness increases. • Craton lithosphere undergoes mostly elastic deformation. • Brittle yielding and seismicity are restricted to very shallow crustal levels. • Effective elastic thickness is large even though average differential stress is low. Whether lithospheric stress can reach the maximum level predicted by the Christmas-tree strength envelope is a fundamental question but with controversial answers. There is little controversy that a deforming lithosphere in high heat flow regions is likely critically stressed, i.e., at full yield at all depths, as described by the envelope. But different conceptual frameworks offer opposite views for very cold lithosphere, either at full yield or far below yield. Here, we use simple numerical models to investigate stresses in end-member cold cratonic lithosphere (e.g., Canadian Craton) in comparison with end-member warm plate-boundary lithosphere (e.g., Canadian Cordillera). The two key elements of our modelling are (1) that lithospheric stress builds up elastically with horizontal tectonic loading not only in the elastic–frictional brittle regime but also in the viscoelastic ductile regime, and (2) that the stress level is limited by the available tectonic force. In a cratonic lithosphere, the limiting tectonic force is sustained by competent rock material over a large depth range, represented by the competent thickness Tc that exceeds 90 km. The lithosphere undergoes mostly elastic deformation at a stress level of a few tens of MPa. While weakly stressed strong lithosphere can still produce limited earthquakes at shallow depths due to structural and stress heterogeneity, the lithospheric stress under horizontal tectonic loading is theoretically predicted to be orders of magnitude lower than predicted by the Christmas-tree envelope. Stresses in a real lithosphere may substantially deviate from this theoretical level because of spatiotemporal variations in rheology and structure. For example, the stress memory of past loading history in cold lithosphere may or may not be erased by more recent tectonic stresses. Because much of previous scientific debates on lithospheric stress levels and comparison with seismicity were focused on topographically induced flexural stress, we also investigate the effect of vertical loading. We show that the effective elastic thickness Te derived from the flexural response is a reasonable proxy for Tc derived from horizontal tectonic loading; a very large Te such as > 80 km is generally associated with very low tectonic stress far below yield. However, the flexure-induced bending stress is not directly comparable with seismicity because it may either enhance or suppress seismogenic stress in the crust