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Computing

Different computation paradigms including sequential and parallel programming each with the corresponding discretised domain.

Different computation paradigms including sequential and parallel programming each with the corresponding discretised domain shown on the left. For sequential programming, the code performs two tasks A and B in a sequential manner, on a single thread which has access to all of the computer’s memory. When the same code is executed in parallel relying on OpenMP, each processor of the computer concurrently carries out a part of tasks A and B so that the compute wall clock time is shorter. If relying on MPI-based parallelisation, the domain is usually broken up so that each thread ‘knows’ only a part of the domain. Tasks A and B are also executed in parallel by all the CPUs, but now, there is a distributed architecture of processors and memory interlinked by a dedicated network. The Scientific colour map ‘batlow‘ is used to represent individual domain parts to all readers.

  • Creator: Fabio Crameri
  • This version: 11.11.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from van Zelst et al. (2021) is available via the open-access s-ink.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
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Numerical discretisation (space & time)

One-dimensional discretisation in space and time based on discrete temporal and spatial steps.

One-dimensional discretisation used in geodynamic numerical models in space (horizontal axis) and time (vertical axis) based on discrete steps in space (h) and time (Δt).

  • Creator: Fabio Crameri
  • This version: 11.11.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from van Zelst et al. (2021) is available via the open-access s-ink.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
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Sea-level change mechanisms (sketch)

Sketches outlining the solid-Earth induced sea-level change mechanisms over different time periods, covering elastic, viscous, and mantle convection time scales.

Sketches outlining the solid-Earth induced change of sea level over different time periods, covering elastic (instantaneous), viscous (thousand to hundred thousand years), and mantle convection (Million to Billion years) time scales. Shown are the solid Earth and oceans (filled areas) and their surfaces after an applied change to the system (lines).

On the shortest time scales, the solid Earth deforms elastically in response to an imposed load: an ice sheet uplifts the ground near areas of mass loss and depresses the ocean basins, which gain mass. The sea surface drops near the mass loss because the diminished ice sheet gravitationally attracts less seawater. Relative to the ground surface, sea-level drops near melting ice, but rises faster than average over the rest of the ocean.

Following glacial unloading, Earth deforms viscously on time scales of 1’000–100’000 years as the mantle flows back into the depressed region. This uplifts the region near the former ice sheet (locally causing relative sea-level drop) and depresses the surrounding peripheral forebulge. If the forebulge collapses beneath the sea surface, the added basin volume causes far-field (eustatic) sea-level drop.

On time scales of one Million years and longer, solid Earth processes associated with plate tectonics and mantle dynamics dominate sea-level change (Harrison, 1990; Miller et al., 2005). Shown here are the major processes that can elevate global average (eustatic) sea level (and depress it when acting oppositely). Global sea level rises when the “container” volume of the ocean basins decreases, which can have multiple reasons. Sea level also rises, if water exchange with the deep mantle becomes imbalanced.

  • Creator: Clint P. Conrad
  • This version: 27.10.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Clint Conrad based on Conrad (2013) is available via the open-access s-Ink repository.
  • Related reference: Conrad, C.P. (2013), The solid earth’s influence on sea level, Geological Society of America Bulletin, 125, 1027-1052, doi:10.1130/B30764.1.
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Global-scale mantle flow (sketch)

A sketch outlining the link between the viscous convection within the Earth’s mantle and tectonic surface plate motions.

A sketch outlining the link between the viscous convection within the Earth’s mantle and tectonic surface plate motions, deforming Earth’s surface across wide areas. Shown are the relative positions and motion of some of Earth’s continental (brown) and oceanic plates (blue) captured by the hypothetical cross-section through the middle of the planet. The dynamic link between surface and mantle motion is highlighted by arrows representing first-order material flow direction. This global-scale mantle flow is believed to also affect the shape, position and mobility of large low shear-velocity provinces (LLSVPs; red) at the base of the mantle (yellow) just above the Earth’s core (orange).

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Seismic wave travel paths

A schematic highlighting the travel paths of seismic waves through the Earth’s interior.

A schematic highlighting the travel paths of seismic waves through the Earth’s interior. Seismic waves travelling through the Earth follow a curving path due to changes in composition, pressure, and temperature within the layers of the Earth. They follow the same laws of refraction and reflection at interfaces as others waves. When they encounter boundaries between different media, the waves behave according to Snell’s law, with the resulting angle of refraction across the boundary depending on the velocity difference between the two media. Seismic wave arrivals, and the lack of arrivals of direct S- and P-waves, at distant seismic stations have taught us that there are multiple layers within the Earth.

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Subduction zone initiation types

Illustration of the three types of subduction zone initiation (SZI) events, namely Newly destructive, Episodic subduction, and Polarity reversal.

Illustration of the three types of subduction zone initiation (SZI) events. As outlined in Crameri et al. (2020), the SZI type is either Newly destructive (a subduction fault establishing from an intact-plate portion or some sort of non-subduction-related plate weakness), Episodic subduction (a subduction fault establishing at the same location following a previous, yet terminated subduction zone with the same polarity), or Polarity reversal (formation of a new subduction fault with opposite polarity to the fault of the pre-existing, terminating subduction zone).

  • Creator: Fabio Crameri
  • This version: 24.10.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from Crameri et al. (2020) is available via the open-access s-Ink repository.
  • Related reference: Crameri, F., V. Magni, M. Domeier, G.E. Shephard, K. Chotalia, G. Cooper, C. Eakin, A.G. Grima, D. Gürer, A. Király, E. Mulyukova, K. Peters, B. Robert, and M. Thielmann (2020), A transdisciplinary and community-driven database to unravel subduction zone initiation, Nature Communications, 11, 3750. doi:10.1038/s41467-020-17522-9
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Subduction initiation forcing

The illustration depicts two endmember states in subduction zone initiation: vertically-forced and horizontally-forced subduction initiation.

Illustration of the two endmember states forcing a new subduction zone. The two endmember forcing states characterising subduction zone initiation (SZI) can be described as either vertically-forced or horizontally-forced. As outlined in Crameri et al. (2020), the dominant forcing is either—but never exclusively—vertical (i.e., some combination of plate buoyancy force, the force from any surface load, and vertical mantle-flow force), or horizontal (i.e., some combination of tectonic force and horizontal mantle-flow force).

  • Creator: Fabio Crameri
  • This version: 24.10.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from Crameri et al. (2020) is available via the open-access s-Ink repository.
  • Related reference: Crameri, F., V. Magni, M. Domeier, G.E. Shephard, K. Chotalia, G. Cooper, C. Eakin, A.G. Grima, D. Gürer, A. Király, E. Mulyukova, K. Peters, B. Robert, and M. Thielmann (2020), A transdisciplinary and community-driven database to unravel subduction zone initiation, Nature Communications, 11, 3750. doi:10.1038/s41467-020-17522-9
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Earth interior model

Simplified model of the Earth’s interior and its global dynamics featuring a solid inner and a fluid outer core, a viscous partially molten but not fluid mantle, and characteristic surface topography.

Simplified model of the Earth interior and its global dynamics featuring a solid inner and a fluid outer core, a viscous partially molten but not fluid mantle, with hot material rising from the core-mantle boundary in form of active mantle plumes and cold material, including oceanic surface plates, sinking back into the mantle in a process called subduction. The dynamics in the Earth interior crucially shapes the rocky surface of the planet, creating mountain ranges and deep-sea trenches.

  • Creator: Fabio Crameri
  • This version: 06.10.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri adjusted from Crameri & Tackley (2016) is available via the open-access s-ink.org repository.
  • Related reference: Crameri, F., and P. J. Tackley (2016), Subduction initiation from a stagnant lid and global overturn: new insights from numerical models with a free surface, Progress in Earth and Planetary Science, 3(1), 1–19, doi:10.1186/s40645-016-0103-8
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Planetary interior

Comparison of suggested mantle convection in the Earth (mobile-lid mode) and Venus (inefficient short slab mode).

Comparison of suggested mantle convection in Earth and Venus. Mobile-lid mantle convection in the Earth involves most surface plates (dark brown), which are recycled by sinking back into the deep mantle, where large low shear-wave velocity provinces (LLSVPs) exist (whitish). The ongoing plate destruction causes a more heterogeneous mantle and a surface of variable age, with young and thin oceanic plates and old and thick continental plates that remain at the surface. Mantle plumes (light red) tend to occur far away from sinking plates. By contrast, the mode of mantle convection on Venus is suggested to consist of a nearly immobile, mostly stagnant lid, and only localised, short sinking plate portions that are formed by (and thus spatially coincide with) hot mantle upwelling (light red). The resulting surface deformation matches observations from coronae on Venus. The short sinking portions do not, in contrast to Earth, significantly move their tail ends at the surface, which explains the uniformly aged, relatively thick surface plate (dark brown).

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