New M@TE! model:

we have provided a summary of your model as a starting point for the README, feel free to edit

Section 1: Summary of your model

Model Submitter:

Bénédicte Cenki-Tok or Cenki (0000-0001-7649-4498)

Model Creator(s):

• Bénédicte Cenki-Tok or Cenki (0000-0001-7649-4498)
  
• Patrice Rey (0000-0002-1767-8593)
  
• Diane Arcay (0000-0001-6773-0807)
  
• Julian Giordani (0000-0003-4515-9296)
  

Model slug:

cenki-2022-uht-granulitic-terranes-1

(this will be the name of the model repository when created)

Model name:

Timing of partial melting and granulite formation during the genesis of high to ultra‐high temperature terranes: Insight from numerical experiments

License:

Creative Commons Attribution 4.0 International

Model Category:

• model published in study
  

Model Status:

• completed
  

Associated Publication title:

Timing of partial melting and granulite formation during the genesis of high to ultra‐high temperature terranes: Insight from numerical experiments

Short description:

Long-lived high to ultra-high temperature (HT-UHT) granulitic terranes formed throughout Earth's history. Yet, the detailed processes involved in their formation remain unresolved and notably the sequence of appearance and duration of migmatisation and granulites conditions in the orogenic cycle. These processes can be evaluated by analytical and numerical models. First, solving the steady-state heat equation allows underlining the interdependency of the parameters controlling the crustal geotherm at thermal equilibrium. Second, performing two-dimensional thermo-mechanical experiments of an orogenic cycle, from shortening to gravitational collapse, allows to consider non-steady-state geotherms and understand how deformation velocity may affect the relative timing of migmatite and granulite formation. These numerical experiments with elevated radiogenic heat production and slow shortening rates allow the formation of large volumes of prograde migmatites and granulites going through the sillimanite field as observed in many HT-UHT terranes. Finally, the interplay between these parameters can explain the difference in predicted pressure-temperature-time paths that can be compared with the natural rock archive.

Abstract:

Long‐lived high to ultra‐high temperature (HT‐UHT) granulitic terranes formed throughout Earth's history. Yet, the detailed processes involved in their formation remain unresolved and notably the sequence of appearance and duration of migmatisation and granulites conditions in the orogenic cycle. These processes can be evaluated by analytical and numerical models. First, solving the steady‐state heat equation allows underlining the interdependency of the parameters controlling the crustal geotherm at thermal equilibrium. Second, performing two‐dimensional thermo‐mechanical experiments of an orogenic cycle, from shortening to gravitational collapse, allows to consider non‐steady‐state geotherms and understand how deformation velocity may affect the relative timing of migmatite and granulite formation. These numerical experiments with elevated radiogenic heat production and slow shortening rates allow the formation of large volumes of prograde migmatites and granulites going through the sillimanite field as observed in many HT‐UHT terranes. Finally, the interplay between these parameters can explain the difference in predicted pressure‐temperature‐time paths that can be compared with the natural rock archive.

Funder(s):
- European Union's Horizon 2020 research and innovation program under grant agreement no 793978

Section 2: your model code, output data

No embargo on model contents requested

Include model code:

True

Model code existing URL/DOI:

https://github.com/underworld-community/cenki-et-al-UHT-granulitic-terranes

Include model output data:

True

Section 3: software framework and compute details

Software Framework DOI/URL:

Found software: Underworld 2

Name of primary software framework:

Underworld 2

Software framework authors:
- John Mansour (0000-0001-5865-1664)
- Julian Giordani (0000-0003-4515-9296)
- Louis Moresi (0000-0003-3685-174X)
- Romain Beucher (0000-0003-3891-5444)
- Owen Kaluza (0000-0001-6303-5671)
- Mirko Velic
- Rebecca Farrington (0000-0002-2594-6965)
- Steve Quenette (0000-0002-0368-7341)
- Adam Beall (0000-0002-7182-1864)

Software & algorithm keywords:

• Python
  
• Finite Element
  

Section 4: web material (for mate.science)

Landing page image:

Filename: Figure2_v9.pdf
Caption: Figure 2. A-B. Model geometry, initial conditions as well as geotherm, viscosity and density profiles. The circles pattern superimposed on the continental crust represents the finite strain ellipses. White squares represent the Lagrangian particles recording the PTt paths presented in Fig. 4. A. Initial conditions for models RHP2diff, mimicking a Proterozoic highly differentiated and highly radiogenic crust. B. Initial conditions for model RHP1unif, simulating a Phanerozoic uniform and less radiogenic crust. C-J. Orogenic modeling results showing two snapshots for each model: i) shortening-delamination and ii) collapse. Shortening velocity is either slow (0.24 cm.y-1, C-F) or fast (2.4 cm.y-1, G-J).

Animation:

Filename:

Graphic abstract:

Filename: Figure3_v6.pdf
Caption: Figure 3. Depth – time profiles indicating the onset of partial melting and granulite formation through the evolution of the models.

Model setup figure:

Filename:
Description: The numerical models are performed with Underworld, a well-tested open-source finite element code, to solve the equations of conservation of momentum, mass, and energy for an incompressible fluid on a Cartesian Eulerian mesh (Moresi et al., 2007; Beucher et al., 2019). The 2D thermo-mechanical experiments involve a geological model of dimensions 480 km x 160 km discretized over a computational grid made of 240 x 80 elements. The initial setup consists of a 35 km or 40 km thick crust with 20 km of air-like material above, and mantle below (Fig. 2A-B). Each model runs through three stages:

i) a shortening phase during which the crust thickens to ~ 60 km with either a slow total velocity of 0.24 cm/yr during 70 My or a fast total velocity of 2.4 cm/yr during ~ 7 My (delivering a strain rate averaged over the length of the model of $1.6 \times 10^{-16} s^{-1}$ and $1.6 \times 10^{-15} s^{-1}$ respectively); ii) a rapid increase in BHF (from $0.020 W/m^2$ to $0.030 W/m^2$) over 2.5 My while the velocities imposed on the vertical boundaries are set to zero (vx = vy = 0 cm/yr) mimicking the thermal impact of a mantle delamination phase; iii) a relaxation phase in which the crust returns to normal thickness under slow extensional boundary conditions (total velocity of 0.10 cm/yr) associated with a decrease in BHF from $0.030 W/m^2$ to $0.020 W/m^2$ in ~ 70 My. Details of modeling procedures, rheological and thermal parameters, as well as the input Python script, are available as supplementary data.

These experiments focus on two end-member crustal structures with average values of total RHP at ~ $1 \mu W/m^3$ and ~ $2 \mu W/m^3$ (Fig. 2). A value of ~ $1 \mu W/m^3$ is in line with RHP calculations predicted from the present-day composition of the bulk continental crust determined by Taylor and McLennan (1995). Models RHP1unif mimic a Phanerozoic orogenic cycle involving a continental crust with a uniform RHP ($1.0483 \mu W/m^3$) yielding an initial Moho temperature of 650°C at 40 km depth (Fig. 1A). However, Mareschal and Jaupart (2013), Artemieva et al. (2017), and Gard et al. (2019) showed that the crustal RHP may have been higher than ~ $1 \mu W/m^3$ during the Proterozoic, having varied between ~ $0.8 \mu W/m^3$ and ~ $4 \mu W/m^3$ between 0.5 Ga and 2.5 Ga with an average RHP close to ~ $2 \mu W/m^3$. In addition, recent studies reveal that, in tectonically stable regions, the upper crust’s RHP may be higher than in the lower crust (Goes et al., 2020; Alessio et al., 2020). The conditions for model RHP2diff include a total average RHP of ~ $2.0922 \mu W/m^3$ with high RHP in the upper crust (~ $5 \mu W/m^3$) that decreases exponentially with a length scale factor $hc$ of 20 km yielding an initial Moho temperature at 35 km depth of 650°C (Fig. 1D). Models RHP2diff aim at approaching thermal conditions of a differentiated crust prevailing during the Proterozoic.