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SUMMARY Recent modelling studies have shown that laboratory-derived rheology is too strong to reproduce observations of flexure at the Hawaiian Islands, while the same rheology appears consistent with outer rise—trench flexure at circum-Pacific subduction zones. Collectively, these results indicate that the rheology of an oceanic plate boundary is stronger than that of its interior, which, if correct, presents a challenge to understanding the formation of trenches and subduction initiation. To understand this dilemma, we first investigate laboratory-derived rheology using fully dynamic viscoelastic loading models and find that it is too strong to reproduce the observationally inferred elastic thickness, Te, at most plate interior settings. The Te can, however, be explained if the yield stress of low-temperature plasticity is significantly reduced, for example, by reducing the activation energy from 320 kJ mol−1, as in Mei et al., to 190 kJ mol−1 as was required by previous studies of the Hawaiian Islands, implying that the lithosphere beneath Hawaii is not anomalous. Second, we test the accuracy of the modelling methods used to constrain the rheology of subducting lithosphere, including the yield stress envelope (YSE) method, and the broken elastic plate model (BEPM). We show the YSE method accurately reproduces the model Te to within ∼10 per cent error with only modest sensitivity to the assumed strain rate and curvature. Finally, we show that the response of a continuous plate is significantly enhanced when a free edge is introduced at or near an edge load, as in the BEPM, and is sensitive to the degree of viscous coupling at the free edge. Since subducting lithosphere is continuous and generally mechanically coupled to a sinking slab, the BEPM may falsely introduce a weakness and hence overestimate Te at a trench because of trade-off. This could explain the results of recent modelling studies that suggest the rheology of subducting oceanic plate is stronger than that of its interior. However, further studies using more advanced thermal and mechanical models will be required in the future in order to quantify this. 

Abstract Previous studies of flexure in continental settings assert that the elastic thickness of a multilayer lithosphere is controlled by the mechanically competent layer thicknesses only, following a cubic rule. More specifically, the cubic rule statesT_e = (T_e1³+T_e2³+ … T_en³)^1/3, whereT_eis the total elastic thickness, andT_eiis the elastic thickness of each competent layer. However, it is not necessarily clear thatT_eshould be insensitive to the properties of intermediate weak layers (e.g., a weak lower crust) which may act to decouple the surface load from lower competent layers. To test this idea, we formulate 2D viscoelastic loading models with layered viscosity to compute the fully dynamic, time‐dependent response of a multilayer lithosphere with a weak lower crust. Results show that the flexural response of a multilayer lithosphere to a surface load is initially consistent with the cubic rule. However, this solution is transient because the stress associated with the load cannot be transmitted through the weak lower crust on long timescales. Stress in the mantle lithosphere relaxes with time and eventually does not support the load at all due to the decoupling effect of flow in the weak lower crust. The steady state flexure of a multilayer lithosphere is controlled solely by the mechanically competent upper crust such thatT_e = T_e1, and this new rule is the major finding of this study. Our new findings now explain small estimates ofT_ein continental settings with thick mantle lithosphere such as the Northern Tien Shan, which previously, were poorly explained by the cubic rule. 

Abstract The rheology of oceanic lithosphere is important to our understanding of mantle dynamics and to the emergence and manifestations of plate tectonics. Data from experimental rock mechanics suggest rheology is dominated by three different deformation mechanisms including frictional sliding, low‐temperature plasticity, and high‐temperature creep, from shallow depths at relatively cold temperatures to large depths at relatively high temperatures. However, low‐temperature plasticity is poorly understood. This study further constrains low‐temperature plasticity by comparing observations of flexure at the Hawaiian Islands to predictions from 3‐D viscoelastic loading models with a realistic lithospheric rheology of frictional sliding, low‐temperature plasticity, and high‐temperature creep. We find that previously untested flow laws significantly underpredict the amplitude and overpredict the wavelength of flexure at Hawaii. These flow laws can, however, reproduce observations if they are weakened by a modest reduction (25–40%) in the plastic activation energy. Lithospheric rheology is strongly temperature dependent, and so we explore uncertainties in the thermal structure with different conductive cooling models and convection simulations of plume‐lithosphere interactions. Convection simulations show that thermal erosion from a plume only perturbs the lithospheric temperature significantly at large depths so that when it is added to the thermal structure, it produces a small increase in deflection. In addition, defining the temperature profile by the cooling plate model produces only modest weakening relative to the cooling half‐space model. Therefore, variation of the thermal structure does not appear to be a viable means of bringing laboratory‐derived flow laws for low‐temperature plasticity into agreement with geophysical field observations and modeling.