The equivalent elastic thickness ( Te), seismicity and the long-term rheology of continental lithosphere: Time to burn-out “crème brûlée”? : Insights from large-scale geodynamic modeling

Abstract

Depending on the conditions and time scale, the lithosphere exhibits elastic, brittle-plastic or viscous-ductile properties. As suggested by rock mechanics experiments, a large part of the long-term lithospheric strength is supported in the ductile regime. Unfortunately, these data, validated for strain rates ∼ 10 − 6 s − 1 , small scales (few cm) and simplified conditions, cannot be univocally interpolated to geological time and spatial scales (strain rates ∼ 10 − 17 –10 − 13 s − 1 , 100–1000 km spatial scales, complex conditions) without additional parameterization. An adequate parameterization has to be based on “real-time” observations of large-scale deformation. Indeed, for the oceanic lithosphere, the Goetze and Evan's brittle-elastic-ductile yield strength envelopes derived from data of experimental rock mechanics were successfully validated by a number of geodynamic scale observations such as the observations of plate flexure and the associated T e (equivalent elastic thickness) estimates. Yet, for continents, the uncertainties of flexural models and of the other data sources are much stronger due to the complex structure and history of continental plates. For example, in one continental rheology model, dubbed “jelly sandwich”, the strength mainly resides in the crust and mantle, while in another, dubbed “crème-brûlée”, the mantle is weak and the strength is limited to the upper crust. These models have arisen because of conflicting results from distributed earthquake, elastic thickness ( T e) and rheology data. We address these problems by examining the plausibility of each rheological model from general physical considerations. We review the elastic thickness ( T e) estimates and their relationship to the seismogenic layer thickness ( T s) to show that these two quantities have no direct physical relation. We also show that some of small T e must be artifacts of inconsistent formulation of the mechanical problem in some Free-Air anomaly admittance models. We point out that this does not necessarily detract from the admittance method itself but refers to its incorrect application in the continental domain. We then explore, by analytical and numerical thermo-mechanical modeling, the implications of a weak and strong mantle for tectonic structural styles. We conclude that rheological models such as crème-brûlée, which invoke a weak lithosphere mantle, are generally incompatible with observations. The jelly sandwich is in better agreement and we believe provides a useful first-order explanation for the long-term support of the Earth's main surface features.