[1] A strong 50-35 Ma decrease in India-Asia convergence is generally ascribed to continent-continent collision. However, a convergence rate increase of similar magnitude occurred between ∼65-50 Ma. An earlier increase occurred at ∼90 Ma. Both episodes of accelerated convergence followed upon arrival of a mantle plume below and emplacement of a large igneous province (LIP) on the Indian plate. We here first confirm these convergence rate trends, reassessing the Indo-Atlantic plate circuits. Then, using two different numerical models, we assess whether plume head arrival and its lateral asthenospheric flow may explain the plate velocity increases and whether decreased plume flux and increasing continent-plume distance may explain deceleration, even without continental collision. The results show that plume head arrival can indeed lead to absolute Indian plate motion accelerations on the order of several cm/yr, followed by decelerations on timescales similar to the reconstructed fluctuations. The 90 Ma increase could potentially be explained as response to the Morondova mantle plume alone. The 65-50 Ma convergence rate increase, however, is larger than can be explained by plume head spreading alone. We concur with previous hypotheses that plume-induced weakening of the Indian continental lithosphere-asthenosphere coupling and an increased slab pull and ridge push efficiency are the most likely explanations for the large convergence rate increase. The post-50 Ma decrease is best explained by orogeny-related increased trench resistivity, decreased slab pull due to continental subduction, and possibly restrengthening of lithosphere-asthenosphere coupling upon plume demise.

Computations have helped elucidate the dynamics of Earth's mantle for several decades already. The numerical methods that underlie these simulations have greatly evolved within this time span, and today include dynamically changing and adaptively refined meshes, sophisticated and efficient solvers, and parallelization to large clusters of computers. At the same time, many of these methods -discussed in detail in a previous paper in this series [Kronbichler et al.(2012)] -were developed and tested primarily using model problems that lack many of the complexities that are common to the realistic models our community wants to solve today.With several years of experience solving complex and realistic models, we here revisit some of the algorithm designs of the earlier paper and discuss the incorporation of more complex physics. In particular, we re-consider time stepping and mesh refinement algorithms, evaluate approaches to incorporate compressibility, and discuss dealing with strongly varying material coefficients, latent heat, and how to track chemical compositions and heterogeneities. Taken together and implemented in a high-performance, massively parallel code, the techniques discussed in this paper then allow for high resolution, 3d, compressible, global mantle convection simulations with phase transitions, strongly temperature dependent viscosity and realistic material properties based on mineral physics data.

This paper provides an overview of the new features of the finite element library deal.II version 9.0.

Grain size plays a key role in controlling the mechanical properties of the Earth's mantle, affecting both long‐time‐scale flow patterns and anelasticity on the time scales of seismic wave propagation. However, dynamic models of Earth's convecting mantle usually implement flow laws with constant grain size, stress‐independent viscosity, and a limited treatment of changes in mineral assemblage. We study grain size evolution, its interplay with stress and strain rate in the convecting mantle, and its influence on seismic velocities and attenuation. Our geodynamic models include the simultaneous and competing effects of dynamic recrystallization resulting from dislocation creep, grain growth in multiphase assemblages, and recrystallization at phase transitions. They show that grain size evolution drastically affects the dynamics of mantle convection and the rheology of the mantle, leading to lateral viscosity variations of 6 orders of magnitude due to grain size alone, and controlling the shape of upwellings and downwellings. Using laboratory‐derived scaling relationships, we convert model output to seismologically observable parameters (velocity and attenuation) facilitating comparison to Earth structure. Reproducing the fundamental features of the Earth's attenuation profile requires reduced activation volume and relaxed shear moduli in the lower mantle compared to the upper mantle, in agreement with geodynamic constraints. Faster lower mantle grain growth yields best fit to seismic observations, consistent with our reexamination of high‐pressure grain growth parameters. We also show that ignoring grain size in interpretations of seismic anomalies may underestimate the Earth's true temperature variations.

This paper provides an overview of the new features of the finite element library deal.II, version 9.3.

Particle‐in‐cell (PIC) methods couple mesh‐based methods for the solution of continuum mechanics problems with the ability to advect and evolve properties on particles. PIC methods have a long history and numerous applications in geodynamic modeling. However, they are historically either implemented in sequential codes or in parallel codes with structured, statically partitioned meshes. Yet today's codes increasingly use adaptive mesh refinement (AMR) of unstructured coarse meshes, dynamic repartitioning, and scale to thousands of processors. Optimally balancing the work per processor for a PIC method in these environments is a difficult problem, and many existing implementations are not sufficient for this task. Thus, there is a need to revisit these algorithms for future applications. Here we describe challenges and solutions to implement PIC methods in the context of large‐scale parallel geodynamic modeling codes that use dynamically changing meshes. We also provide guidance for how to address bottlenecks that impede the efficient implementation of these algorithms and demonstrate with numerical tests that our algorithms can be implemented with optimal complexity and that they are suitable for large‐scale, practical applications. We provide a reference implementation in the Advanced Solver for Problems in Earth's ConvecTion (ASPECT), an open source code for geodynamic modeling built on the DEAL.II finite element library.

Hotspot tracks are thought to originate when mantle plumes impinge moving plates. However, many observed cases close to mid-ocean ridges do not form a single age-progressive line, but vary in width, are separated into several volcanic chains, or are distributed over different plates. Here we study plume-ridge interaction at the example of the Tristan plume, which features all of these complexities. Additionally, the South Atlantic formed close to where plume volcanism began, opening from the south and progressing northward with a notable decrease in magmatism across the Florianopolis Fracture Zone. We study the full evolution of the Tristan plume in a series of three-dimensional regional models created with the convection code ASPECT. We then compute crustal thickness maps and compare them to seismic profiles and the topography of the South Atlantic. We find that the separation of volcanism into the Tristan and Gough chain can be explained by the position of the plume relative to the ridge and the influence of the global flow field. Plume material below the off-ridge track can flow toward the ridge and regions of thinner lithosphere, where decompression melting leads to the development of a second volcanic chain resembling the Tristan and Gough hotspot tracks. Agreement with the observations is best for a small plume buoyancy flux of 500 kg/s or a low excess temperature of 150 K. The model explains the distribution of syn-rift magmatism by hot plume material that flows into the rift and increases melt generation.

Many open problems in the Earth sciences can only be understood by modelling the porous flow of melt through a viscously deforming solid rock matrix. However, the system of equations describing this process becomes mathematically degenerate in the limit of vanishing melt fraction. Numerical methods that do not consider this degeneracy or avoid it solely by regularising specific material properties generally become computationally expensive as soon as the melt fraction approaches zero in some part of the domain.Here, we present a new formulation of the equations for coupled magma/mantle dynamics that addresses this problem, and allows it to accurately compute large-scale 3-D magma/mantle dynamics simulations with extensive regions of zero melt fraction. We achieve this by rescaling one of the solution variables, the compaction pressure, which ensures that for vanishing melt fraction, the equation causing the degeneracy becomes an identity and the other two equations revert to the Stokes system. This allows us to split the domain into two parts: In mesh cells where melt is present, we solve the coupled system of magma/mantle dynamics. In cells without melt, we solve the Stokes system as it is done for mantle convection without melt transport and constrain the remaining degrees of freedom.We have implemented this formulation in the open source geodynamic modelling code arXiv:1810.10105v1 [physics.geo-ph] 23 Oct 2018 2 J. Dannberg, R. Gassmöller, R. Grove, T. Heister ASPECT and illustrate the improved performance compared to the previous three-field formulation, showing numerically that the new formulation is optimal in terms of problem size and only minimally sensitive to model parameters. Beyond that, we demonstrate the applicability to realistic problems by showing large-scale 2-D and 3-D models of midocean ridges with complex rheology. Hence, we believe that our new formulation and its implementation in ASPECT will prove a valuable tool for studying the interaction of melt segregating through and interacting with a solid host rock in the Earth and other planetary bodies using high-resolution, three-dimensional simulations.