Volcanic rifted margins are typically associated with a thick magmatic layer of seaward dipping reflectors and anomalous regional uplift. This is conventionally interpreted as due to melting of an ...arriving mantle plume head at the onset of rifting. However, seaward dipping reflectors and uplift are sometimes asymmetrically distributed with respect to the subsequent plume track. Here we investigate if these asymmetries are induced by preexisting lateral variations in the thickness of continental lithosphere and/or lithospheric stretching rates, variations that promote lateral sublithospheric flow of plume material below only one arm of the extending rift. Using three-dimensional numerical experiments, we find that South Atlantic rifting is predicted to develop a strong southward asymmetry in its distribution of seaward dipping reflectors and associated anomalous relief with respect to the Tristan Plume that “drove” this volcanic rifted margin, and that the region where plume material drains into the rift should experience long-lived uplift during rifting—both as observed. We conclude that a mantle plume is still needed to source the anomalously hot sublithospheric material that generates a volcanic rifted margin, but lateral along-rift flow from this plume, not a broad starting plume head, is what controls when and where a volcanic rifted margin will form.
Full text
Available for:
BFBNIB, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK
We present a new technique, the “double Jacobian,” to solve problems in cylindrical or spherical geometries, for example, the Stokes flow problem for convection in Earth's mantle. Our approach ...combines the advantages of working simultaneously in Cartesian and polar or spherical coordinates. The governing matrix equations are kept in Cartesian coordinates, thereby preserving their Cartesian symmetry. However, the element geometry is described as a linear simplex in polar or spherical coordinates, thereby preserving appropriate cylindrical or spherical surfaces and internal interfaces. Isoparametric representations can still be used to define complex surface shapes. Using linear polar or spherical elements allows search routines for triangular or tetrahedral simplexes to rapidly find arbitrary points in terms of their polar or spherical coordinates. The double Jacobian approach becomes especially powerful when element sizes vary strongly within the mesh, while the exact cylindrical or spherical surfaces or internal interfaces have to be preserved, as happens in several geophysical applications.
The “double Jacobian” approach allows the user to more easily solve problems in geometries for which an analytical coordinate mapping is known, by combining the advantages of working simultaneously in Cartesian and polar, spherical, or another analytical coordinate system. Governing matrix equations can be kept in their often simplest and symmetric Cartesian form, while the resulting discretization can simultaneously preserve an exact match to cylindrical or spherical bounding or internal surfaces. The approach can greatly reduce the well‐known numerical artifact of “spurious hydrostatic flow” that arises in response to a numerically imprecise discretization of a spherical boundary during geophysical computation of flow in the presence of a central gravitational attraction. It also leads to analytical, faster to assemble finite element integration routines. This figure shows the amplitude of spurious hydrostatic Stokes flow for Earth's mantle that arises from spherical shell discretizations using Cartesian linear, quadratic isoparametric, and double jacobian P2P1 element formulations.
Full text
Available for:
BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
Several mechanisms have been suggested for the formation of flat slabs including buoyant features on the subducting plate, trenchward motion and thermal or cratonic structure of the overriding plate. ...Analysis of episodes of flat subduction indicate that not all flat slabs can be attributed to only one of these mechanisms and it is likely that multiple mechanisms work together to create the necessary conditions for flat slab subduction. In this study we examine the role of localized regions of cratonic lithosphere in the overriding plate in the formation and evolution of flat slabs. We explicitly build on previous models, by using time‐dependent simulations with three‐dimensional variation in overriding plate structure. We find that there are two modes of flat subduction: permanent underplating occurs when the slab is more buoyant (shorter or younger), while transient flattening occurs when there is more negative buoyancy (longer or older slabs). Our models show how regions of the slab adjacent to the subcratonic flat portion continue to pull the slab into the mantle leading to highly contorted slab shapes with apparent slab gaps beneath the craton. These results show how the interpretation of seismic images of subduction zones can be complicated by the occurrence of either permanent or transient flattening of the slab, and how the signature of a recent flat slab episode may persist as the slab resumes normal subduction. Our models suggest that permanent underplating of slabs may preferentially occur below thick and cold lithosphere providing a built‐in mechanism for regeneration of cratons.
Key Points:
Two modes of flat subduction: permanent underplating and transient flattening
Cratonic lithosphere in the overriding plate produces highly contorted slab shapes
Permanent underplating provides a built‐in mechanism for regeneration of cratons
Full text
Available for:
FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
We present 2-D, 3-D, and spherical mesh generators for triangular and tetrahedral elements. The mesh nodes are treated as if they were linked by virtual springs that obey Hooke’s law. Given the ...desired lengths for the springs, a finite element problem is solved for optimal (static equilibrium) nodal positions. A ‘guide-mesh’ approach allows the user to define embedded high-resolution sub-regions within a coarser mesh. The method converges rapidly. For example, the algorithm is able to refine within a few iterations a specific region embedded in an unstructured tetrahedral spherical shell so that the edge-length factor l0r∕l0c=1∕33 where l0r and l0c are the desired spring length for elements inside the refined and coarse regions respectively. The algorithm also includes routines to locally improve the quality of the mesh and to avoid ill-shaped ‘sliver-like’ tetrahedra. We include a geodynamic modelling example as a direct application of the mesh generator.
•Mesh generator for Cartesian 2-D/3-D and Earth-appropriate spherical coordinates.•Builds unstructured tetrahedral meshes with embedded high-resolution sub-regions.•Guide-mesh defines variable preferred element sizes in the mesh.•Tools for mesh quality improvement (removing tetrahedral slivers).•Algorithm suitable for adaptive mesh refinement.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Cover Image Morgan, Jason P.; Taramón, Jorge M.; Hasenclever, Jörg
International journal for numerical methods in fluids,
06/2020, Volume:
92, Issue:
6
Journal Article
Peer reviewed
The cover image is based on the Research Article
Shape‐preserving finite elements in cylindrical and spherical geometries: The double Jacobian approach
by Jason P. Morgan,
...https://doi.org/10.1002/fld.4799
.
image
Full text
Available for:
BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
The treatment of far-field boundary conditions (BCs) is one of the most poorly resolved issues for regional modelling of geodynamic processes. The mantle velocity field, along the side-walls and base ...of a modelling region, is typically much more poorly known than the geometry of past global motions of the surface plates, as constrained by global plate motion reconstructions. In this thesis, I have developed numerical tools that allow the study of 3-D spherical regional models with no fictitious internal boundaries using an embedded high resolution region within a global spherical coarse mesh. A key piece in any numerical simulation using the Finite Element Method (FEM) is the mesh. I have developed an algorithm to generate high-quality unstructured meshes with embedded high resolution regions within 2-D and 3-D Cartesian, 2-D cylindrical and 3-D spherical shell domains. The mesh nodes are treated as if they were linked by virtual springs and the FEM is used to solve iteratively for the optimal nodal positions for the static equilibrium of this spring system. A 'guide-mesh' is incorporated to easily define preferred element sizes throughout the mesh. A new technique, the 'Double Jacobian', is presented for more accurate solution in cylindrical or spherical geometries. This approach combines the advantages of working simultaneously in both Cartesian and polar or spherical coordinates. On the one hand, the governing matrix equations are kept in Cartesian coordinates, preserving their symmetry. On the other hand, the element geometry is described in 'straight-sided' polar or spherical coordinates, preserving the appropriate curved boundary surfaces and interfaces. These 'straight-sided' polar or spherical elements allow search routines to rapidly find arbitrary points in polar or spherical coordinates. The tools described above have been applied to study the influence of the Tristan da Cunha plume during the early rifting and break-up of the South Atlantic. Global plate motion BCs are applied through time using GPlates. Models show a migration of hotter and weaker plume material towards the rifting region before the break-up, influenced by the lateral thickness variations in the initial structure of the lithosphere. Once the plume material reaches the rifting region, it is found to preferentially migrate southwards. This migration appears to be due to the presence of thicker S\~ao Francisco and conjugate Congo cratonic roots in the North combined with a ridge 'suction' force due to stretching of non-cratonic lithosphere in the South. This mechanism could explain the observed preferential southward formation of early-rifting-related Seaward Dipping Reflectors (SDRs) along South Atlantic margins with respect to their Tristan Plume progenitor.
PDF
