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Abstract The determination of the temperature in and above the slab in subduction zones, using models where the top of the slab is precisely known, is important to test hypotheses regarding the causes of arc volcanism and intermediate-depth seismicity. While 2D and 3D models can predict the thermal structure with high precision for fixed slab geometries, a number of regions are characterized by relatively large geometrical changes over time. Examples include the flat slab segments in South America that evolved from more steeply dipping geometries to the present day flat slab geometry. We devise, implement, and test a numerical approach to model the thermal evolution of a subduction zone with prescribed changes in slab geometry over time. Our numerical model approximates the subduction zone geometry by employing time dependent deformation of a Bézier spline that is used as the slab interface in a finite element discretization of the Stokes and heat equations. We implement the numerical model using the FEniCS open source finite element suite and describe the means by which we compute approximations of the subduction zone velocity, temperature, and pressure fields. We compute and compare the 3D time evolving numerical model with its 2D analogy at cross-sections for slabs that evolve to the present-day structure of a flat segment of the subducting Nazca plate. 

The thermal structure of subduction zones is fundamental to our understanding of physical and chemical processes that occur at active convergent plate margins. These include magma generation and related arc volcanism, shallow and deep seismicity, and metamorphic reactions that can release fluids. Computational models can predict the thermal structure to great numerical precision when models are fully described but this does not guarantee accuracy or applicability. In a trio of companion papers, the construction of thermal subduction zone models, their use in subduction zone studies, and their link to geophysical and geochemical observations are explored. In part I, the motivation to understand the thermal structure is presented based on experimental and observational studies. This is followed by a description of a selection of thermal models for the Japanese subduction zones. 

Abstract The thermal structure of subduction zones is fundamental to our understanding of the physical and chemical processes that occur at active convergent plate margins. These include magma generation and related arc volcanism, shallow and deep seismicity, and metamorphic reactions that can release fluids. Computational models can predict the thermal structure to great numerical precision when models are fully described but this does not guarantee accuracy or applicability. In a trio of companion papers, the construction of thermal subduction zone models, their use in subduction zone studies, and their link to geophysical and geochemical observations are explored. In this part II, the finite element techniques that can be used to predict thermal structure are discussed in an introductory fashion along with their verification and validation. Steady-state thermal structure for the updated subduction zone benchmark. a) Temperature predicted by TF for case 1; b) temperature difference between TF and Sepran using the penalty function (PF) method for case 1 at f_m=1 where f_mrepresents the smallest element sizes in the finite element grids near the coupling point; c) slab top temperature comparison for case 1; and d)–f) as a)–c) but now for case 2. The star indicates the position or temperature conditions at the coupling point. 

Abstract The thermal structure of subduction zones is fundamental to our understanding of the physical and chemical processes that occur at active convergent plate margins. These include magma generation and related arc volcanism, shallow and deep seismicity, and metamorphic reactions that can release fluids. Computational models can predict the thermal structure to great numerical precision when models are fully described but this does not guarantee accuracy or applicability. In a trio of companion papers, the construction of thermal subduction zone models, their use in subduction zone studies, and their link to geophysical and geochemical observations are explored. In this last part, we discuss how independent finite element approaches predict the thermal structure of the global subduction system and investigate how well these predictions correspond to geophysical, geochemical, and petrological observations. 

Abstract The plate interface undergoes two transitions between seismogenic depths and subarc depths. A brittle-ductile transition at 20–50 km depth is followed by a transition to full viscous coupling to the overlying mantle wedge at ∼80 km depth. We review evidence for both transitions, focusing on heat-flow and seismic-attenuation constraints on the deeper transition. The intervening ductile shear zone likely weakens considerably as temperature increases, such that its rheology exerts a stronger control on subduction-zone thermal structure than does frictional shear heating. We evaluate its role through analytic approximations and two-dimensional finite-element models for both idealized subduction geometries and those resembling real subduction zones. We show that a temperature-buffering process exists in the shear zone that results in temperatures being tightly controlled by the rheological strength of that shear zone’s material for a wide range of shear-heating behaviors of the shallower brittle region. Higher temperatures result in weaker shear zones and hence less heat generation, so temperatures stop increasing and shear zones stop weakening. The net result for many rheologies are temperatures limited to ≤350–420 °C along the plate interface below the cold forearc of most subduction zones until the hot coupled mantle is approached. Very young incoming plates are the exception. This rheological buffering desensitizes subduction-zone thermal structure to many parameters and may help explain the global constancy of the 80 km coupling limit. We recalculate water fluxes to the forearc wedge and deep mantle and find that shear heating has little effect on global water circulation.