Testing the Yield-Stress Envelope Method Against Finite Element Models of Flexure

Abstract:

The dynamic evolution of the earth is strongly controlled by the rheology of the lithosphere. The elastic plate model (EPM) may be used to constrain the rheology by inferring elastic thickness (Te) from observations of topography and gravity. The EPM is extended to include yielding by the relevant lithospheric deformation mechanisms in the yield-stress envelope (YSE) method. Both the EPM and YSE methods have been widely used in Geophysics, but these models are subject to the thin plate approximation and other assumptions. We formulate fully dynamic finite element (FE) viscoelastic loading models to test whether the simplified models are accurate.

First, we compute 2D FE models of a trapezoidal load (i.e., island chain) with complex viscoelastic rheology including frictional sliding, low-temperature plasticity and high-temperature creep derived in laboratory studies. The corresponding YSE is constructed using rheology, strain rate, and curvature consistent with FE models. Results show that the YSE is accurate for curvature and strain rate taken from the outer-rise region, but may significantly underestimate Te based on observations near the load. This is because the thin plate approximation is valid only for long-wavelength features (e.g., in the outer rise region). Second, we compute 2D FE models of subduction zone settings with complex rheology. Comparisons with the YSE method show that significant underestimation of Te (20-30%) occurs when the maximum curvature from the FE model is used. This has important implications for previous studies which use the YSE method to constrain rheology (Hunter and Watts, 2016). We suggest that contrary to previous conclusions, the rheology at subduction zones is much weaker than the rheology derived in laboratory studies, consistent with rheology at Hawaii (Bellas et al., 2020). Finally, we show that the hypothesis by Burov (2015) on the strength of a plate with multiple strong and weak layers (i.e., weak lower crust) is invalid. This result may have important implications for interpreting elastic thickness estimates of the Tibetan plateau and Venus.