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  1. Abstract

    This article presents a comprehensive benchmark study for the newly updated and publicly available finite element code CitcomSVE for modeling dynamic deformation of a viscoelastic and incompressible planetary mantle in response to surface and tidal loading. A complete description of CitcomSVE’s finite element formulation including calculations of the sea‐level change, polar wander, apparent center of mass motion, and removal of mantle net rotation is presented. The 3‐D displacements and displacement rates and the gravitational potential anomalies are solved with CitcomSVE for three benchmark problems using different spatial and temporal resolutions: (a) surface loading of single harmonics, (b) degree‐2 tidal loading, and (c) the ICE‐6G GIA model. The solutions are compared with semi‐analytical solutions for error analyses. The benchmark calculations demonstrate the accuracy and efficiency of CitcomSVE. For example, for a typical ICE‐6G GIA calculation with a 122‐ky glaciation‐deglaciation history, time increment of 100 years, and ∼50 km (or ∼0.5°) surface horizontal resolution, it takes ∼4.5 hr on 96 CPU cores to complete with about 1% and 5% errors for displacements and displacement rates, respectively. Error analyses shows that CitcomSVE achieves a second order accuracy, but the errors are insensitive to temporal resolution. CitcomSVE achieves the parallel computational efficiency >75% for using up to 6,144 CPU cores on a parallel supercomputer. With its accuracy, computational efficiency and its open‐source public availability, CitcomSVE provides a powerful tool for modeling viscoelastic deformation of a planetary mantle with 3‐D mantle viscous and elastic structures in response to surface and tidal loading problems.

     
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  2. Abstract

    Seismic observations indicate accumulation of subducted slabs in the mantle transition zone in many subduction zones. By systematically conducting 2‐D numerical experiments, we demonstrate that a weak layer or zone beneath the spinel‐to‐post‐spinel phase transition leads to horizontally deflected (stagnant) slab structures in the mantle transition zone, which is consistent with recent studies of 3‐D global mantle convection models. Trench retreat velocity, Clapeyron slope and the viscosity contrast between the lower mantle and mantle transition zone also affect horizontally deflected slab formation. By considering grain size dependent viscosity and grainsize evolution for slabs going through the phase change in the lower mantle, our models with a dynamically generated weak zone beneath the phase boundary indicate that the geometry and viscosity reduction of the weak zone is strongly affected by grain growth rate. A smaller grain growth rate results in a thicker and wider weak zone that promotes deflected slab formation.

     
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  3. 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 statesTe = (Te13+Te23+ … Ten3)1/3, whereTeis the total elastic thickness, andTeiis the elastic thickness of each competent layer. However, it is not necessarily clear thatTeshould 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 thatTe = Te1, and this new rule is the major finding of this study. Our new findings now explain small estimates ofTein continental settings with thick mantle lithosphere such as the Northern Tien Shan, which previously, were poorly explained by the cubic rule.

     
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  4. Abstract

    Flexure occurs on intermediate geologic timescales (∼1 Myr) due to volcanic‐island building at the Island of Hawaii, and the deformational response of the lithosphere is simultaneously elastic, plastic, and ductile. At shallow depths and low temperatures, elastic deformation transitions to frictional failure on faults where stresses exceed a threshold value, and this complex rheology controls the rate of deformation manifested by earthquakes. In this study, we estimate the seismic strain rate based on earthquakes recorded between 1960 and 2019 at Hawaii, and the estimated strain rate with 10−18–10−15s−1in magnitude exhibits a local minimum or neutral bending plane at 15 km depth within the lithosphere. In comparison, flexure and internal deformation of the lithosphere are modeled in 3D viscoelastic loading models where deformation at shallow depths is accommodated by frictional sliding on faults and limited by the frictional coefficient (μf), and at larger depths by low‐temperature plasticity and high‐temperature creep. Observations of flexure and the seismic strain rate are best‐reproduced by models withμf = 0.3 ± 0.1 and modified laboratory‐derived low‐temperature plasticity. Results also suggest strong lateral variations in the frictional strength of faults beneath Hawaii. Our models predict a radial pattern of compressive stress axes relative to central Hawaii consistent with observations of earthquake pressure (P) axes. We demonstrate that the dip angle of this radial axis is essential to discerning a change in the curvature of flexure, and therefore has implications for constraining lateral variations in lithospheric strength.

     
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  5. 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.

     
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  6. 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. 
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  7. This article provides a review on the studies of large temporal and spatial scale dynamics of the Earth’s mantle. The review focuses on relevant observations and their geodynamic interpretations and implications. These observations include present-day Earth’s plate tectonics, long- and intermediate-wavelength geoid and gravity anomalies, and mantle seismic structures, as well as important tectonism and magmatism that have happened in the last one billion years, associated with the formation and breakup of supercontinents Pangea and Rodinia. Much of the discussion is centered on how these observations have motivated geodynamic studies and modeling that seek to understand and interpret the observations. This review covers four topics. The first is on the primary characteristics of mantle seismic structure and their dynamic origin. The present-day Earth’s mantle is predominated by long-wavelength structures (i.e., degree-2 in the lower mantle and LLSVPs near the core-mantle boundary) and linear structures in subduction zones, both of which can be interpreted as a result of mantle convection modulated by surface plate motion history in the last 100 million years. The second is on the long- and intermediate-wavelength geoid and gravity anomalies and their dynamic interpretation. The geoid anomalies are explained by mantle flow that is driven by buoyancy associated with the mantle structure. Such studies indicate that the upper mantle is at least one magnitude weaker than the lower mantle and strongly suggest the existence of a weak asthenosphere. Third, the cyclic process of formation and breakup of supercontinents Pangea and Rodinia is surface manifestation of time-dependent mantle convection. During supercontinent formation and its early stage, mantle structure is predominately degree-1 with cold downwellings in one hemisphere and hot upwellings in the other hemisphere. However, the degree-1 structure starts to transition to degree-2 mantle structure with two major antipodal upwelling systems (e.g., the present-day Earth) in the late stage of a supercontinent, leading to supercontinent breakup. Abundant observational and dynamic evidence support the 1-2-1 model for supercontinent cycle and mantle structure evolution. The fourth is on the origin of plate tectonics and long-term thermal evolution of the Earth which is a fundamentally important but also controversial topic in the studies of earth science. 
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