Implementation and application of adaptive mesh refinement for thermochemical mantle convection studies

Numerical modeling of mantle convection is challenging. Owing to the multiscale nature of mantle dynamics, high resolution is often required in localized regions, with coarser resolution being sufficient elsewhere. When investigating thermochemical mantle convection, high resolution is required to resolve sharp and often discontinuous boundaries between distinct chemical components. In this paper, we present a 2-D finite element code with adaptive mesh refinement techniques for simulating compressible thermochemical mantle convection. By comparing model predictions with a range of analytical and previously published benchmark solutions, we demonstrate the accuracy of our code. By refining and coarsening the mesh according to certain criteria and dynamically adjusting the number of particles in each element, our code can simulate such problems efficiently, dramatically reducing the computational requirements (in terms of memory and CPU time) when compared to a fixed, uniform mesh simulation. The resolving capabilities of the technique are further highlighted by examining plume‐induced entrainment in a thermochemical mantle convection simulation

Microanalytical study of some cosmic dust discovered in sea-floor sediments in China

The study of cosmic dust can provide useful data in the investigation of the origin of the Earth and the evolution of celestial bodies. Three types of cosmic dust (ferriginous, siliceous, and glassy) were discovered in the seafloor sediments near China. Their chemical composition and microstructure were examined by X-ray diffraction, fractography, and electron microscopy. The major mineral in an iron-containing cosmic dust is magnetite. The silicate spheres contain sundry metals and metal oxides. Glassy microtektites are similar in composition to tektites, and are found in all the major meteorite areas worldwide

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

Controls on trench topography from dynamic models of subducted slabs

A finite element method with constrained elements and Lagrange multipliers is used to study tectonic faults in a viscous medium. A fault, representing the interface between overriding and subducting plates, has been incorporated into a viscous flow model of a subduction zone in which both thermal buoyancy and the buoyancy associated with the phase change from olivine to spinel are included. The fault causes stress to concentrate in its vicinity, giving rise to a weak plate margin and a mobile plate if a power law rheology is used. Surface dynamic topography with either a Newtonian or a power law rheology and with typical subduction zone parameters is characterized by a narrow and deep trench and a broadly depressed back arc basin. This suggests that oceanic trenches and back arc basins over subduction zones are dynamically compensated by viscous flow. Our models show that trench depth increases with fault dip angle, slab dip angle, slab length, and age of oceanic lithosphere just prior to subduction. The influence of fault dip angle and age of lithosphere on trench depth is greater than the influence of slab dip angle and slab length. These relationships of trench depth versus subduction zone parameters explain well the statistics of observed trench depths. For those subduction zones with oceanic lithosphere on both sides of the trench, observed trench depths have been corrected for fault and slab dip angles, based on the relationships from the dynamic models. After correction to a common set of parameters, trench depth correlates linearly with age of lithosphere prior to subduction with a slope which is close to what models having high viscosities within the transition zone and lower mantle predict. Comparison between the trench depths, corrected for fault and slab dip angles, and model trench depths suggests that the resisting tangential stress on faults in subduction zones may range from 15 MPa to 30 MPa, depending on model details

Dynamic feedback between a continentlike raft and thermal convection

Seismic observations of the mantle, which include long-wavelength structure, a k^(−1) dependence of heterogeneity on harmonic k, and a heterogeneous upper boundary layer, and supercontinent kinematics may be explained by the dynamic interaction between a continent like raft and thermal convection. We have formulated finite element models of convection with rafts simulating continental plates in a cylindrical geometry. The azimuthal interconnectivity of this geometry is vital to resolve the two-way dynamics between rafts and convection. Computations show that (1) raft motion is periodic, (2) long-wavelength thermal structure is significant within both thermal boundary layers and the fluid interior, and (3) the large-scale thermal structure with a wavelength longer than the width of raft is responsible for raft motion. These three results, which are observed for a range of Rayleigh numbers, internal heating rates, and raft sizes, are a direct consequence of the dynamic interaction between the raft and convection. The physical processes for a model with a Rayleigh number of 10^5 are representative: when the raft is stationary, due to the less efficient heat transfer through the raft and instabilities from the bottom boundary layer, heat accumulates beneath the raft and results in long-wavelength thermal anomalies. The long-wavelength thermal anomalies enhance raft motion. Accompanying the enhanced raft movement, the long-wavelength thermal anomalies diminish and the raft velocity decreases or the raft comes to rest. Since convection models without rafts generate less long-wavelength heterogeneity compared to the models with rafts, or continental plates, we suspect that continental plates may play a crucial role in mantle dynamics. Interestingly, raft motion with a period of about 10 transit times is usually significant; 10 transit times is about 600 m.y. if scaled to the Earth. This is close to the observed 300–500 m.y. period of supercontinent aggregation and dispersal

Role of plates and temperature-dependent viscosity in phase change dynamics

The effects of plates and slabs on phase change dynamics have been investigated with convection models. Two complementary methods to simulate plates are used: material property and imposed surface velocity methods with temperature-dependent viscosity. For a wide range of model parameters, plates and slabs exert a significant control on phase change dynamics. As plate length (and hence plate age and convection cell aspect ratio) increases, both the propensity for slab penetration and the mass flux across an endothermic phase change increase. When cold downwellings are stiffened with a temperature-dependent rheology, slab penetration is enhanced, but total mass flux changes little. Plates organize large-scale flow and thermal structure and thereby affect phase change dynamics. As plates become larger, the resulting largerscale structures are influenced less by endothermic phase changes, thus reducing the degree of layering. A model showing completely layered convection for a plate of unit length becomes unlayered when the plate is 3 or 5 times longer. For a given Clapeyron slope, the proportion of time for slab penetration increases from zero for cases with small plates to more than 0.5 for cases with large plates. The degree of layering, plate velocity, and mass flux are controlled by large-scale structures, while slab penetration may be more related to small-scale features. Therefore, whether or not subducted slabs penetrate the phase change may not necessarily indicate that convection is entirely layered or entirely unlayered. The episodicity of convection induced by an endothermic phase change strongly depends on plate length, rheology, and Clapeyron slope. A large plate and a stiff slab both weaken the episodicity of convection. Only for a certain range of Clapeyron slopes can the phase change induce a strong episodic thermal convection

Viscous flow model of a subduction zone with a faulted lithosphere: Long and short wavelength topography, gravity and geoid

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95454/1/grl6341.pd

A benchmark study on mantle convection in a 3-D spherical shell using CitcomS

As high-performance computing facilities and sophisticated modeling software become available, modeling mantle convection in a three-dimensional (3-D) spherical shell geometry with realistic physical parameters and processes becomes increasingly feasible. However, there is still a lack of comprehensive benchmark studies for 3-D spherical mantle convection. Here we present benchmark and test calculations using a finite element code CitcomS for 3-D spherical convection. Two classes of model calculations are presented: the Stokes' flow and thermal and thermochemical convection. For Stokes' flow, response functions of characteristic flow velocity, topography, and geoid at the surface and core-mantle boundary (CMB) at different spherical harmonic degrees are computed using CitcomS and are compared with those from analytic solutions using a propagator matrix method. For thermal and thermochemical convection, 24 cases are computed with different model parameters including Rayleigh number (7 × 10^3 or 10^5) and viscosity contrast due to temperature dependence (1 to 10^7). For each case, time-averaged quantities at the steady state are computed, including surface and CMB Nussult numbers, RMS velocity, averaged temperature, and maximum and minimum flow velocity, and temperature at the midmantle depth and their standard deviations. For thermochemical convection cases, in addition to outputs for thermal convection, we also quantified entrainment of an initially dense component of the convection and the relative errors in conserving its volume. For nine thermal convection cases that have small viscosity variations and where previously published results were available, we find that the CitcomS results are mostly consistent with these previously published with less than 1% relative differences in globally averaged quantities including Nussult numbers and RMS velocities. For other 15 cases with either strongly temperature-dependent viscosity or thermochemical convection, no previous calculations are available for comparison, but these 15 test calculations from CitcomS are useful for future code developments and comparisons. We also presented results for parallel efficiency for CitcomS, showing that the code achieves 57% efficiency with 3072 cores on Texas Advanced Computing Center's parallel supercomputer Ranger

Free-surface formulation of mantle convection—II. Implication for subduction-zone observables

Viscous and viscoelastic models for a subduction zone with a faulted lithosphere and internal buoyancy can self-consistently and simultaneously predict long-wavelength geoid highs over slabs, short-wavelength gravity lows over trenches, trench-forebulge morphology, and explain the high apparent strength of oceanic lithosphere in trench environments. The models use two different free-surface formulations of buoyancy-driven flows (see, for example, Part I): Lagrangian viscoelastic and pseudo-free-surface viscous formulations. The lower mantle must be stronger than the upper in order to obtain geoid highs at long wavelengths. Trenches are a simple consequence of the negative buoyancy of slabs and a large thrust fault, decoupling the overriding from underthrusting plates. The lower oceanic lithosphere must have a viscosity of less than 10^(24) Pa s in order to be consistent with the flexural wavelength of forebulges. Forebulges are dynamically maintained by viscous flow in the lower lithosphere and mantle, and give rise to apparently stiffer oceanic lithosphere at trenches. With purely viscous models using a pseudo-free-surface formulation, we find that viscous relaxation of oceanic lithosphere, in the presence of rapid trench rollback, leads to wider and shallower back-arc basins when compared to cases without viscous relaxation. Moreover, in agreement with earlier studies, the stresses necessary to generate forebulges are small (~ 100 bars) compared to the unrealistically high stresses needed in classic thin elastic plate models