Eh Tan

GeoFramework: Coupling multiple models of mantle convection within a computational framework

Solver coupling can extend the capability of existing modeling software and provide a new venue to address previously intractable problems. A software package has been developed to couple geophysical solvers, demonstrating a method to accurately and efficiently solve multiscale geophysical problems with reengineered software using a computational framework (Pyre). Pyre is a modeling framework capable of handling all aspects of the specification and launching of numerical investigations. We restructured and ported CitcomS, a finite element code for mantle convection, into the Pyre framework. Two CitcomS solvers are coupled to investigate the interaction of a plume at high resolution with global mantle flow at low resolution. A comparison of the coupled models with parameterized models demonstrates the accuracy and efficiency of the coupled models and illustrates the limitations and utility of parameterized models.

Slabs in the lower mantle and their modulation of plume formation

Numerical mantle convection models indicate that subducting slabs can reach the core-mantle boundary (CMB) for a wide range of assumed material properties and plate tectonic histories. An increase in lower mantle viscosity, a phase transition at 660 km depth, depth-dependent thermal expansivity, and depth-dependent thermal diffusivity do not preclude model slabs from reaching the CMB. We find that ancient slabs could be associated with lateral temperature anomalies ~500°C cooler than ambient mantle. Plausible increases of thermal conductivity with depth will not cause slabs to diffuse away. Regional spherical models with actual plate evolutionary models show that slabs are unlikely to be continuous from the upper mantle to the CMB, even for radially simple mantle structures. The observation from tomography showing only a few continuous slab-like features from the surface to the CMB may be a result of complex plate kinematics, not mantle layering. There are important consequences of deeply penetrating slabs. Our models show that plumes preferentially develop on the edge of slabs. In areas on the CMB free of slabs, plume formation and eruption are expected to be frequent while the basal thermal boundary layer would be thin. However, in areas beneath slabs, the basal thermal boundary layer would be thicker and plume formation infrequent. Beneath slabs, a substantial amount of hot mantle can be trapped over long periods of time, leading to “mega-plume” formation. We predict that patches of low seismic velocity may be found beneath large-scale high seismic velocity structures at the core-mantle boundary. We find that the location, buoyancy, and geochemistry of mega-plumes will differ from those plumes forming at the edge of slabs. Various geophysical and geochemical implications of this finding are discussed.

Metastable superplumes and mantle compressibility

Seismically, the African superplume is known to have a sharp lateral transition in V_S and an interface between seismic anomalies with high relief. Such a structure is usually unstable in conventional thermo-chemical convection models. Using a compressible thermo-chemical convection model in which each material has a distinct equation of state, we find an expanded regime of metastable superplumes. In the preferred model, superplume material has a bulk modulus 6% higher and density 2.25% higher than ambient mantle. The inferred physical properties of the superplume are consistent with subducted oceanic crust, simultaneously satisfying seismological, geodynamical, mineralogical and geochemical constraints.

Compressible thermochemical convection and application to lower mantle structures

A new finite element code for compressible thermochemical convection is developed to study the stability of a chemical layer at the base of the mantle. Using composition-dependent compressibility and a density difference between compositions at a reference pressure, a composition-dependent density profile is derived. Together with depth-dependent thermal expansion, this combination of parameters yields a wide range of dynamic evolutions for the chemical layer. The chemical structures are classified into five major categories (classical plumes, mushroom-shaped plume, domes, ridges, and continuous layers) and a few abnormal cases, such as hourglass-shaped plumes and columnar plumes. Several models have a chemical structure morphologically similar to the African low V_S structure in the lower mantle, at least at a single time. Guided by our models, several dynamic scenarios are proposed for the dynamic nature of the lower mantle low-velocity structures (a.k.a. superplumes), including plumes at an early stage, plume clusters, ridges, passive piles, sluggish domes, and high-bulk-modulus domes. We predict seismic velocity anomalies from these dynamic models. The thermoelastic parameters used in the conversion are additional constraints. We compare the density structure with normal mode inversion, the predicted seismic signature observations, and the required thermoelastic parameters with mineral physics data. Among the proposed scenarios, only the scenario of high-bulk-modulus domes satisfies all constraints simultaneously. The implication on the geochemistry and mineralogy of lower mantle chemical structures is discussed.

On the location of plumes and lateral movement of thermochemical structures with high bulk modulus in the 3-D compressible mantle

The two large low shear velocity provinces (LLSVPs) at the base of the lower mantle are prominent features in all shear wave tomography models. Various lines of evidence suggest that the LLSVPs are thermochemical and are stable on the order of hundreds of million years. Hot spots and large igneous province eruption sites tend to cluster around the edges of LLSVPs. With 3-D global spherical dynamic models, we investigate the location of plumes and lateral movement of chemical structures, which are composed of dense, high bulk modulus material. With reasonable values of bulk modulus and density anomalies, we find that the anomalous material forms dome-like structures with steep edges, which can survive for billions of years before being entrained. We find that more plumes occur near the edges, rather than on top, of the chemical domes. Moreover, plumes near the edges of domes have higher temperatures than those atop the domes. We find that the location of the downwelling region (subduction) controls the direction and speed of the lateral movement of domes. Domes tend to move away from subduction zones. The domes could remain relatively stationary when distant from subduction but would migrate rapidly when a new subduction zone initiates above. Generally, we find that a segment of a dome edge can be stationary for 200 million years, while other segments have rapid lateral movement. In the presence of time-dependent subduction, the computations suggest that maintaining the lateral fixity of the LLSVPs at the core-mantle boundary for longer than hundreds of million years is a challenge.

Seismological support for the metastable superplume model, sharp features, and phase changes within the lower mantle

Recently, a metastable thermal-chemical convection model was proposed to explain the African Superplume. Its bulk tabular shape remains relatively stable while its interior undergoes significant stirring with low-velocity conduits along its edges and down-welling near the middle. Here, we perform a mapping of chemistry and temperature into P and S velocity variations and replace a seismically derived structure with this hybrid model. Synthetic seismogram sections generated for this 2D model are then compared directly with corresponding seismic observations of P (P, PCP, and PKP) and S (S, SCS, and SKS) phases. These results explain the anticorrelation between the bulk velocity and shear velocity and the sharpness and level of SKS travel time delays. In addition, we present evidence for the existence of a D” triplication (a putative phase change) beneath the down-welling structure.

Mantle dynamics of continentwide Cenozoic subsidence and tilting of Australia

Australia is distinctive because it experienced first-order, broad-scale vertical motions during the Cenozoic. Here, we use plate-tectonic reconstructions and a model of mantle convection to quantitatively link the large-scale fl ooding history of the continent to mantle convection since 50 Ma. Subduction-driven geodynamic models show that Australia undergoes a 200 m northeast downward tilt as it approaches and overrides subducted slabs between Melanesia and the proto–Tonga-Kermadec subduction systems. However, the model only produces the observed continentwide subsidence, with 300 m of northeast downward tilt since the Eocene, if we assume that Australia has moved northward away from a relatively hot mantle anomaly. The models suggest that Australia’s paleoshoreline evolution can only be reproduced if the continent moved northward, away from a large buoyant anomaly. This results in continentwide subsidence of ~200 m. The additional progressive, continentwide tilting down to the northeast can be attributed to the horizontal motion of the continent toward subducted slabs sinking below Melanesia.

Hydration-reduced lattice thermal conductivity of olivine in Earth’s upper mantle

Significance Thermal conductivity of mantle minerals is critical for controlling the temperature profile and dynamics of the mantle and subducting slabs. However, the effect of hydration on lattice thermal conductivity remains poorly understood. We studied lattice thermal conductivity of olivine (Mg0.9Fe0.1)2SiO4 (Fo90) to 15 GPa using ultrafast optics. The thermal conductivity of hydrous Fo90 with ∼7,000 wt ppm water is 2 times smaller than its anhydrous counterpart at transition zone pressures. Modeling thermal structure of a subducting slab shows that the hydration-reduced thermal conductivity in the oceanic crust further decreases the temperature within the subducting slab, which substantially lowers the olivine−wadsleyite transformation rate and extends the metastable olivine to greater depths. Such an effect could enhance water transportation to the transition zone. Earth’s water cycle enables the incorporation of water (hydration) in mantle minerals that can influence the physical properties of the mantle. Lattice thermal conductivity of mantle minerals is critical for controlling the temperature profile and dynamics of the mantle and subducting slabs. However, the effect of hydration on lattice thermal conductivity remains poorly understood and has often been assumed to be negligible. Here we have precisely measured the lattice thermal conductivity of hydrous San Carlos olivine (Mg0.9Fe0.1)2SiO4 (Fo90) up to 15 gigapascals using an ultrafast optical pump−probe technique. The thermal conductivity of hydrous Fo90 with ∼7,000 wt ppm water is significantly suppressed at pressures above ∼5 gigapascals, and is approximately 2 times smaller than the nominally anhydrous Fo90 at mantle transition zone pressures, demonstrating the critical influence of hydration on the lattice thermal conductivity of olivine in this region. Modeling the thermal structure of a subducting slab with our results shows that the hydration-reduced thermal conductivity in hydrated oceanic crust further decreases the temperature at the cold, dry center of the subducting slab. Therefore, the olivine−wadsleyite transformation rate in the slab with hydrated oceanic crust is much slower than that with dry oceanic crust after the slab sinks into the transition zone, extending the metastable olivine to a greater depth. The hydration-reduced thermal conductivity could enable hydrous minerals to survive in deeper mantle and enhance water transportation to the transition zone.

Accelerating DynEarthSol3D on tightly coupled CPU-GPU heterogeneous processors

DynEarthSol3D (Dynamic Earth Solver in Three Dimensions) is a flexible, open-source finite element solver that models the momentum balance and the heat transfer of elasto-visco-plastic material in the Lagrangian form using unstructured meshes. It provides a platform for the study of the long-term deformation of earths lithosphere and various problems in civil and geotechnical engineering. However, the continuous computation and update of a very large mesh poses an intolerably high computational burden to developers and users in practice. For example, simulating a small input mesh containing around 3000 elements in 20 million time steps would take more than 10 days on a high-end desktop CPU. In this paper, we explore tightly coupled CPU-GPU heterogeneous processors to address the computing concern by leveraging their new features and developing hardware-architecture-aware optimizations. Our proposed key optimization techniques are three-fold: memory access pattern improvement, data transfer elimination and kernel launch overhead minimization. Experimental results show that our proposed implementation on a tightly coupled heterogeneous processor outperforms all other alternatives including traditional discrete GPU, quad-core CPU using OpenMP, and serial implementations by 67%, 50%, and 154% respectively even though the embedded GPU in the heterogeneous processor has significantly less number of cores than high-end discrete GPU. HighlightsWe accelerate Dynamic Earth Solution 3D program on CPU-GPU heterogeneous processors.We propose data transformation to improve GPU memory performance.We propose to merge kernels to minimize kernel launch overhead.We show performance gain over implementations on discrete GPU and multi-core CPU.

Development, verification, and maintenance ofcomputational software in geodynamics

Research on dynamical processes within the Earth and planets increasingly relies upon sophisticated, large-scale computational models. Improved understanding of fundamental physical processes such as mantle convection and the geodynamo, magma dynamics, crustal and lithospheric deformation, earthquake nucleation, and seismic wave propagation, are heavily dependent upon better numerical modeling. Surprisingly, the rate-limiting factor for progress in these areas is not just computing hardware, as was once the case. Rather, advances in software are not keeping pace with the recent improvements in hardware. Modeling tools in geophysics are usually developed and maintained by individual scientists, or by small groups. But it is difficult for any individual, or even a small group, to keep up with sweeping advances in computing hardware, parallel processing software, and numerical modeling methodology.