ALBERT

Description: Earth’s surface shows many features, of which the genesis can be understood only through their connection with processes in Earth’s deep interior. Recent studies indicate that spatial geochemical patterns at oceanic islands correspond to structures in the lowermost mantle inferred from seismic tomographic models. This suggests that hot, buoyant upwellings can carry chemical heterogeneities from the deep lower mantle toward the surface, providing a window to the composition of the lowermost mantle. The exact nature of this link between surface and deep Earth remains debated and poorly understood. Using computational models, we show that subducted slabs interacting with dense thermochemical piles can trigger the ascent of hot plumes that inherit chemical gradients present in the lowermost mantle. We identify two key factors controlling this process: (i) If slabs induce strong lower-mantle flow toward the edges of these piles where plumes rise, the pile-facing side of the plume preferentially samples material originating from the pile, and bilaterally asymmetric chemical zoning develops. (ii) The composition of the melt produced reflects this bilateral zoning if the overlying plate moves roughly perpendicular to the chemical gradient in the plume conduit. Our results explain some of the observed geochemical trends of oceanic islands and provide insights into how these trends may originate.

Description: 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. ©2018. American Geophysical Union. All Rights Reserved.

Description: Modelling the porous flow of melt through a viscously deforming solid rock matrix is a useful tool for interpreting observations from the Earth’s surface, and advances our understanding of the dynamics of the Earth’s interior. 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 regularizing 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 Aspect and illustrate the improved performance compared to the previous three-field formulation, showing numerically that the new formulation is robust in terms of problem size and only slightly sensitive to model parameters. Beyond that, we demonstrate the applicability to realistic problems by showing large-scale 2-D and 3-D models of mid-ocean 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, 3-D simulations.

Description: 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. © 2017. American Geophysical Union. All Rights Reserved.

Description: SUMMARY Combining finite element methods for the incompressible Stokes equations with particle-in-cell methods is an important technique in computational geodynamics that has been widely applied in mantle convection, lithosphere dynamics and crustal-scale modelling. In these applications, particles are used to transport along properties of the medium such as the temperature, chemical compositions or other material properties; the particle methods are therefore used to reduce the advection equation to an ordinary differential equation for each particle, resulting in a problem that is simpler to solve than the original equation for which stabilization techniques are necessary to avoid oscillations. On the other hand, replacing field-based descriptions by quantities only defined at the locations of particles introduces numerical errors. These errors have previously been investigated, but a complete understanding from both the theoretical and practical sides was so far lacking. In addition, we are not aware of systematic guidance regarding the question of how many particles one needs to choose per mesh cell to achieve a certain accuracy. In this paper we modify two existing instantaneous benchmarks and present two new analytic benchmarks for time-dependent incompressible Stokes flow in order to compare the convergence rate and accuracy of various combinations of finite elements, particle advection and particle interpolation methods. Using these benchmarks, we find that in order to retain the optimal accuracy of the finite element formulation, one needs to use a sufficiently accurate particle interpolation algorithm. Additionally, we observe and explain that for our higher-order finite-element methods it is necessary to increase the number of particles per cell as the mesh resolution increases (i.e. as the grid cell size decreases) to avoid a reduction in convergence order. Our methods and results allow designing new particle-in-cell methods with specific convergence rates, and also provide guidance for the choice of common building blocks and parameters such as the number of particles per cell. In addition, our new time-dependent benchmark provides a simple test that can be used to compare different implementations, algorithms and for the assessment of new numerical methods for particle interpolation and advection. We provide a reference implementation of this benchmark in aspect (the ‘Advanced Solver for Problems in Earth’s ConvecTion’), an open source code for geodynamic modelling.

Description: 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. © 2016. American Geophysical Union. All Rights Reserved.

Description: The Réunion mantle plume has shaped a large area of the Earth's surface over the past 65 million years: from the Deccan Traps in India along the hotspot track comprising the island chains of the Laccadives, Maldives, and Chagos Bank on the Indian plate and the Mascarene Plateau on the African plate up to the currently active volcanism at La Réunion Island. This study addresses the question how the Réunion plume, especially in interaction with the Central Indian Ridge, created the complex crustal thickness pattern of the hotspot track. For this purpose, the mantle convection code ASPECT was used to design three-dimensional numerical models, which consider the specific location of the plume underneath moving plates and surrounded by large-scale mantle flow. The results show the crustal thickness pattern produced by the plume, which altogether agrees well with topographic maps. Especially two features are consistently reproduced by the models: the distinctive gap in the hotspot track between the Maldives and Chagos is created by the combination of the ridge geometry and plume-ridge interaction; and the Rodrigues Ridge, a narrow crustal structure which connects the hotspot track and the Central Indian Ridge, appears as the surface expression of a long-distance sublithospheric flow channel. This study therefore provides further insight how small-scale surface features are generated by the complex interplay between mantle and lithospheric processes. © 2017. American Geophysical Union. All Rights Reserved.

Description: Mantle convection and long-term lithosphere dynamics in the Earth and other planets can be treated as the slow deformation of a highly viscous fluid, and as such can be described using the compressible Navier–Stokes equations. Since on Earth-sized planets the influence of compressibility is not a dominant effect, density deviations from a reference profile are at most on the order of a few percent and using the full governing equations poses numerical challenges, most modelling studies have simplified the governing equations. Common approximations assume a temporally constant, but depth-dependent reference profile for the density (the anelastic liquid approximation), or drop compressibility altogether and use a constant reference density (the Boussinesq approximation). In most previous studies of mantle convection and crustal dynamics, one can assume that the error introduced by these approximations was small compared to the errors that resulted from poorly constrained material behaviour and limited numerical accuracy. However, as model parametrizations have become more realistic, and model resolution has improved, this may no longer be the case and the error due to using simplified conservation equations might no longer be negligible: while such approximations may be reasonable for models of mantle plumes or slabs traversing the whole mantle, they may be unsatisfactory for layered materials experiencing phase transitions or materials undergoing significant heating or cooling. For example, at boundary layers or close to dynamically changing density gradients, the error arising from the use of the aforementioned compressibility approximations can be the dominant error source, and common approximations may fail to capture the physical behaviour of interest. In this paper, we discuss new formulations of the continuity equation that include dynamic density variations due to temperature, pressure and composition without using a reference profile for the density. We quantify the improvement in accuracy relative to existing formulations in a number of benchmark models and evaluate for which practical applications these effects are important. Finally, we consider numerical aspects of the new formulations. We implement and test these formulations in the freely available community software aspect, and use this code for our numerical experiments.