Plate bending earthquakes and the strength distribution of the lithosphere

[dansand]

-> submitter ORCID (or name)

0000-0002-2207-6837

-> slug

sandifordcraig-2023-subduction

-> license

CC-BY-4.0

-> alternative license URL

No response

-> model category

model published in study, forward model

-> model status

None

-> associated publication DOI

https://doi.org/10.1093/gji/ggad230

-> model creators

No response

-> title

No response

-> description

Tectonic plates are recycled into the mantle through subduction, where they bend and deform in various ways, such as brittle failure. This process creates deep sea trenches and results in characteristic earthquake patterns and gravity anomalies. In this study, we used a numerical model to investigate plate bending dynamics, complementing simpler approaches like flexural yield strength envelopes. We focused on the competition between bending stress and sources of net in-plane stress, such as slab pull, which influences the plate's neutral plane depth. It is difficult to reconcile the 'apparent' neutral plane depth with a net slab pull force greater than about 2 TN/m. Deviatoric compression in subducting plates more easily explains reverse earthquakes at depths of 20-50 km in the bending plate.

-> abstract

No response

-> scientific keywords

Dynamics of lithosphere, Lithospheric flexure, Subduction, Earthquakes

-> funder

https://ror.org/05mmh0f86, DP150102887
https://ror.org/03wnrjx87, URF\R1\180088
https://ror.org/02b5d8509

-> model embargo?

No response

-> include model code ?

• yes

-> model code/inputs DOI

https://github.com/dansand/subduction_GJI2022

-> model code/inputs notes

Model setup is provided by an ASPECT input file and a WorldBuilder file (https://github.com/GeodynamicWorldBuilder/WorldBuilder). Minor modifications to the ASPECT source code were implemented and are discussed in the associated publication as well as the model_code_inputs/README.md directory.

-> include model output data?

• yes

-> data creators

No response

-> model output data DOI

No response

-> model output data notes

Computations were done using the ASPECT code version 2.4.0. ASPECT output data from 2 simulations are included with this model. The reference model is the same model setup/data described in Sandiford and Craig, (2023). An alternative model is included in which the over-riding plate is welded to the left sidewall at the start of the simulation (whereas the initial temperature field in the reference model has a ridge). Note that both simulations develop a short-wavelength instability in the free surface of the over-riding plate, which begins approximately 3 Ma after the start of the simulation. The top level directories contains typical ASPECT output files, including log.txt and restart files. The primary output data consists of:

• plain text files representing model topography (e.g. topography.00000)
• a range of "field" data, in .vtu format in the ./solution sub-directory (e.g. solution-00000.0000.vtu). At each output step, there are 48 vtu files written. These can be opened with Paraview using the solution.pvd file in the top level. Quantities generally have SI units. Velocities are output as meters/year.
• particle information stored as .vtu files (16 per timestep). Particles were used to track the 2-km-thick weak entrained layer that facilitates the plate interface decoupling zone.

-> model output data size

47 Gb

-> software framework DOI/URI

https://doi.org/10.5281/zenodo.6903424

-> software framework source repository

https://github.com/geodynamics/aspect

-> name of primary software framework (e.g. Underworld, ASPECT, Badlands, OpenFOAM)

No response

-> software framework authors

https://orcid.org/0000-0003-2311-9402
https://orcid.org/0000-0003-0357-7115
https://orcid.org/0000-0003-0035-7723
https://orcid.org/0000-0001-7098-8198
https://orcid.org/0000-0002-9481-1749
https://orcid.org/0000-0002-8137-3903
https://orcid.org/0000-0001-9489-5236
https://orcid.org/0000-0002-5697-7203

-> software & algorithm keywords

C++, finite-element, adaptive-mesh-refinement, particles

-> computer URI/DOI

https://dx.doi.org/10.25914/608bfd1838db2

-> add landing page image and caption

Downdip component of strain rate tensor and resolved stress difference from the numerical model, focusing on features within the plate/slab. The resolved stress difference is defined as ($\sigma_{s} - \sigma_{z}$), where $\hat{s}$, and $\hat{z}$ are unit vectors in the downdip and slab normal directions. The fields show, for example, shortening/extension in the downdip direction. Stress profiles at four locations are shown. The blue line ($x_0$) is the first zero crossing based on analysis of the flexural component of the topography. The black line is the location of maximum bending moment.

-> add an animation (if relevant)

https://github.com/ModelAtlasofTheEarth/model_submission/assets/10967872/f9e647c5-3341-400c-bac3-d5546f1d7226
Animation shows the model domain at 2x vertical exaggeration. The scalar field is the effective strain rate, i.e. $\dot\epsilon_{II} = \sqrt{J2} = \sqrt{0.5(\dot\epsilon_{i,j}: \epsilon_{i,j})}$. Upper panel shows the evolution of the model topography (a true free surface). The topographic profile reveals the long-wavelength isostatic thermal subsidence, as well as the flexural topography associated with the subduction zone. The model exhibits a very short-wavelength instability in the free surface of the over-riding plate, which begins approximately 3 Ma after the start of the simulation.

-> add a graphic abstract figure (if relevant)

The main panel shows the variation in terms that arise in a 2D "vertically integrated" form of the force balance (or stress equilibrium) equations. Assuming a traction-free surface, the force balance states that across a horizontal section of the lithosphere, the following terms must sum to zero: 1) integrated basal shear traction, 2) the difference in the vertically-integrated deviatoric stress and 3), the difference in the vertically-integrated vertical normal stress (often called the GPE). In the figure, the overbar symbols represent vertical integration across the lithosphere. Specifically, integration from a reference height, (taken here as the mean ridge height) down to a reference depth (taken here as 150 km beneath the reference height). In the main panel, the black line shows the horizontal variation in the vertically integrated deviatoric stress difference ($\tau_{xx} - \tau_{zz}$). Positive values indicate a state of deviatoric tension. The dashed blue line shows the horizontal variation in the vertically integrated vertical normal stress ($\sigma_{yy}$) (or the GPE). Strictly speaking, this quantity is only equal to the GPE when the vertical normal stress is lithostatic, but the term is retained in this study due to convention. The upper panel shows the subducting plate topography at 2 different scales.

-> add a model setup figure (if relevant)

The main panel shows the full model domain and initial temperature field. The texture is generated with a line integral convolution of the velocity field. Contours show evolution of the slab during the 10 Myr simulation. Velocity arrows show convergence rates at 5 Myr into the simulation. Inset panels show details of the adaptive mesh refinement during the simulation.

-> add a description of your model setup

The subduction model comprises a rectangular domain with a depth of 2900 km, and an aspect ratio of 4. The initial conditions comprise an adiabatic mantle with a potential temperature of 1350 C and two plates, whose age and thermal structure follows the cooling 1d cooling profile for a half-space (infinite in the depth direction). One of these plates is attached to a slab that extends to 660 km depth, and has an age of 100 Myr at the trench. The upper plate is modelled with a younger thermal age, 25 Myr at the trench. Imposing an initial slab that reaches the transition zone was found to be a more stable initial configuration in terms of instabilities of the free surface. 7 levels of mesh refinement were used, with the largest (Q2) elements having an edge length of 45 km, and the smallest elements have an edge length of ∼ 700 m. The interface is modelled through an entrained weak layer approach. A thin layer (here 2 km thick) represented by a separate composition is imposed on the top of the subducting plate, as well as between the subducting slab and upper plate. This composition has a low coefficient of friction, providing a shear stress that varies between between about 10 - 20 MPa throughout the plate interface domain. See the included model input file (.prm) for further details.

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Section 1: Summary of your model

Model Submitter:

Dan Sandiford (0000-0002-2207-6837)

Model Creator(s):

• Dan Sandiford (0000-0002-2207-6837)
• Timothy J Craig (0000-0003-2198-9172)

Model name:

sandifordcraig-2023-subduction

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

Model long name:

Plate bending earthquakes and the strength distribution of the lithosphere

License:

Creative Commons Attribution 4.0 International

Model Category:

• model published in study
• forward model

Model Status:

• None

Associated Publication title:

Plate bending earthquakes and the strength distribution of the lithosphere

Abstract:

This study investigates the dynamics and constitutive behaviour of the oceanic lithosphere as it bends and yields during subduction. Two main observational constraints are considered: the maximum bending moment that can be supported by the lithosphere, and the inferred neutral plane depth in bending. We particularly focus on regions of old lithosphere where the ‘apparent’ neutral plane depth is about 30 km. We use subduction modelling approaches to investigate these flexural characteristics. We reassess bending moment estimates from a range of previous studies, and show a significant convergence towards what we call the ‘intermediate’ range of lithosphere strength: weaker than some classical models predict, but stronger than recent inferences at seamounts. We consider the non-uniqueness that arises due to the trade-offs in strength as well background (tectonic) stress state. We outline this problem with several end-member models, which differ in regard to relative strength in the brittle and ductile regimes. We evaluate the consistency of these models in terms of a range of constraints, primarily the seismic expression of the outer rise. We show that a 30 km neutral plane depth implies that net slab pull is not greater than about 2 TN m−1. In contrast, models with low brittle strength imply that regions with a 30 km neutral plane depth are under moderate net axial compression. Under these conditions, reverse faulting is predicted beneath the neutral plane at depths >30 km. We show that moderate variations in background stress have a large impact on the predicted anelastic dissipation. We suggest brittle reverse faulting is a marginal phenomenon which may be inhibited by moderate changes in background stress.

Scientific Keywords:

• Dynamics of lithosphere
• Lithospheric flexure
• Subduction
• Earthquakes

Funder(s):

• Australian Research Council (https://ror.org/05mmh0f86)
• Royal Society (https://ror.org/03wnrjx87)
• Natural Environment Research Council (https://ror.org/02b5d8509)

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/dansand/subduction_GJI2022

Model code notes:

Model setup is provided by an ASPECT input file and a WorldBuilder file (https://github.com/GeodynamicWorldBuilder/WorldBuilder). Minor modifications to the ASPECT source code were implemented and are discussed in the associated publication as well as the model_code_inputs/README.md directory.

Include model output data:

True

Model output data notes:

Computations were done using the ASPECT code version 2.4.0. ASPECT output data from 2 simulations are included with this model. The reference model is the same model setup/data described in Sandiford and Craig, (2023). An alternative model is included in which the over-riding plate is welded to the left sidewall at the start of the simulation (whereas the initial temperature field in the reference model has a ridge). Note that both simulations develop a short-wavelength instability in the free surface of the over-riding plate, which begins approximately 3 Ma after the start of the simulation. The top level directories contains typical ASPECT output files, including log.txt and restart files. The primary output data consists of:

• plain text files representing model topography (e.g. topography.00000)
• a range of "field" data, in .vtu format in the ./solution sub-directory (e.g. solution-00000.0000.vtu). At each output step, there are 48 vtu files written. These can be opened with Paraview using the solution.pvd file in the top level. Quantities generally have SI units. Velocities are output as meters/year.
• particle information stored as .vtu files (16 per timestep). Particles were used to track the 2-km-thick weak entrained layer that facilitates the plate interface decoupling zone.

Section 3: software framework and compute details

Software Framework DOI/URL:

Found software: ASPECT v2.4.0

Software Repository:

https://github.com/geodynamics/aspect

Name of primary software framework:

ASPECT v2.4.0

Software & algorithm keywords:

• C++
• finite-element
• adaptive-mesh-refinement
• particles

Section 4: web material (for mate.science)

Landing page image:

Filename: res_fig_final_ann.png
Caption: Downdip component of strain rate tensor and resolved stress difference from the numerical model, focusing on features within the plate/slab. The resolved stress difference is defined as ($\sigma_{s} - \sigma_{z}$), where $\hat{s}$, and $\hat{z}$ are unit vectors in the downdip and slab normal directions. The fields show, for example, shortening/extension in the downdip direction. Stress profiles at four locations are shown. The blue line ($x_0$) is the first zero crossing based on analysis of the flexural component of the topography. The black line is the location of maximum bending moment.

Animation:

Filename: animation
Caption: Animation shows the model domain at 2x vertical exaggeration. The scalar field is the effective strain rate, i.e. $\dot\epsilon_{II} = \sqrt{J2} = \sqrt{0.5(\dot\epsilon_{i,j}: \epsilon_{i,j})}$. Upper panel shows the evolution of the model topography (a true free surface). The topographic profile reveals the long-wavelength isostatic thermal subsidence, as well as the flexural topography associated with the subduction zone. The model exhibits a very short-wavelength instability in the free surface of the over-riding plate, which begins approximately 3 Ma after the start of the simulation.

Graphic abstract:

Filename: gpe_fm26.png
Caption: The main panel shows the variation in terms that arise in a 2D "vertically integrated" form of the force balance (or stress equilibrium) equations. Assuming a traction-free surface, the force balance states that across a horizontal section of the lithosphere, the following terms must sum to zero: 1) integrated basal shear traction, 2) the difference in the vertically-integrated deviatoric stress and 3), the difference in the vertically-integrated vertical normal stress (often called the GPE). In the figure, the overbar symbols represent vertical integration across the lithosphere. Specifically, integration from a reference height, (taken here as the mean ridge height) down to a reference depth (taken here as 150 km beneath the reference height). In the main panel, the black line shows the horizontal variation in the vertically integrated deviatoric stress difference ($\tau_{xx} - \tau_{zz}$). Positive values indicate a state of deviatoric tension. The dashed blue line shows the horizontal variation in the vertically integrated vertical normal stress ($\sigma_{yy}$) (or the GPE). Strictly speaking, this quantity is only equal to the GPE when the vertical normal stress is lithostatic, but the term is retained in this study due to convention. The upper panel shows the subducting plate topography at 2 different scales.

Model setup figure:

Filename: s1a.png
Caption: The main panel shows the full model domain and initial temperature field. The texture is generated with a line integral convolution of the velocity field. Contours show evolution of the slab during the 10 Myr simulation. Velocity arrows show convergence rates at 5 Myr into the simulation. Inset panels show details of the adaptive mesh refinement during the simulation.
Description: The subduction model comprises a rectangular domain with a depth of 2900 km, and an aspect ratio of 4. The initial conditions comprise an adiabatic mantle with a potential temperature of 1350 C and two plates, whose age and thermal structure follows the cooling 1d cooling profile for a half-space (infinite in the depth direction). One of these plates is attached to a slab that extends to 660 km depth, and has an age of 100 Myr at the trench. The upper plate is modelled with a younger thermal age, 25 Myr at the trench. Imposing an initial slab that reaches the transition zone was found to be a more stable initial configuration in terms of instabilities of the free surface. 7 levels of mesh refinement were used, with the largest (Q2) elements having an edge length of 45 km, and the smallest elements have an edge length of ∼ 700 m. The interface is modelled through an entrained weak layer approach. A thin layer (here 2 km thick) represented by a separate composition is imposed on the top of the subducting plate, as well as between the subducting slab and upper plate. This composition has a low coefficient of friction, providing a shear stress that varies between between about 10 - 20 MPa throughout the plate interface domain. See the included model input file (.prm) for further details.

Errors and Warnings

Associated Publication
Error fetching metadata with application/ld+json from https://api.crossref.org/works/https://doi.org/10.1093/gji/ggad230: 406 Client Error: Not Acceptable for url: https://api.crossref.org/works/https://doi.org/10.1093/gji/ggad230
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Model Report

Thank you for submitting.

Using Github actions, we have regenerated a report summarising information about your model

• Please check the report below, including the Errors and Warnings section

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Parsed data

Section 1: Summary of your model

Model Submitter:

Dan Sandiford (0000-0002-2207-6837)

Model Creator(s):

• Dan Sandiford (0000-0002-2207-6837)
• Timothy J Craig (0000-0003-2198-9172)

Model name:

sandifordcraig-2023-subduction-1

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

Model long name:

Plate bending earthquakes and the strength distribution of the lithosphere

License:

Creative Commons Attribution 4.0 International

Model Category:

• model published in study
• forward model

Model Status:

• None

Associated Publication title:

Plate bending earthquakes and the strength distribution of the lithosphere

Abstract:

This study investigates the dynamics and constitutive behaviour of the oceanic lithosphere as it bends and yields during subduction. Two main observational constraints are considered: the maximum bending moment that can be supported by the lithosphere, and the inferred neutral plane depth in bending. We particularly focus on regions of old lithosphere where the ‘apparent’ neutral plane depth is about 30 km. We use subduction modelling approaches to investigate these flexural characteristics. We reassess bending moment estimates from a range of previous studies, and show a significant convergence towards what we call the ‘intermediate’ range of lithosphere strength: weaker than some classical models predict, but stronger than recent inferences at seamounts. We consider the non-uniqueness that arises due to the trade-offs in strength as well background (tectonic) stress state. We outline this problem with several end-member models, which differ in regard to relative strength in the brittle and ductile regimes. We evaluate the consistency of these models in terms of a range of constraints, primarily the seismic expression of the outer rise. We show that a 30 km neutral plane depth implies that net slab pull is not greater than about 2 TN m−1. In contrast, models with low brittle strength imply that regions with a 30 km neutral plane depth are under moderate net axial compression. Under these conditions, reverse faulting is predicted beneath the neutral plane at depths >30 km. We show that moderate variations in background stress have a large impact on the predicted anelastic dissipation. We suggest brittle reverse faulting is a marginal phenomenon which may be inhibited by moderate changes in background stress.

Scientific Keywords:

• Dynamics of lithosphere
• Lithospheric flexure
• Subduction
• Earthquakes

Funder(s):

• Australian Research Council (https://ror.org/05mmh0f86)
• Royal Society (https://ror.org/03wnrjx87)
• Natural Environment Research Council (https://ror.org/02b5d8509)

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/dansand/subduction_GJI2022

Model code notes:

Model setup is provided by an ASPECT input file and a WorldBuilder file (https://github.com/GeodynamicWorldBuilder/WorldBuilder). Minor modifications to the ASPECT source code were implemented and are discussed in the associated publication as well as the model_code_inputs/README.md directory.

Include model output data:

True

Model output data notes:

Computations were done using the ASPECT code version 2.4.0. ASPECT output data from 2 simulations are included with this model. The reference model is the same model setup/data described in Sandiford and Craig, (2023). An alternative model is included in which the over-riding plate is welded to the left sidewall at the start of the simulation (whereas the initial temperature field in the reference model has a ridge). Note that both simulations develop a short-wavelength instability in the free surface of the over-riding plate, which begins approximately 3 Ma after the start of the simulation. The top level directories contains typical ASPECT output files, including log.txt and restart files. The primary output data consists of:

• plain text files representing model topography (e.g. topography.00000)
• a range of "field" data, in .vtu format in the ./solution sub-directory (e.g. solution-00000.0000.vtu). At each output step, there are 48 vtu files written. These can be opened with Paraview using the solution.pvd file in the top level. Quantities generally have SI units. Velocities are output as meters/year.
• particle information stored as .vtu files (16 per timestep). Particles were used to track the 2-km-thick weak entrained layer that facilitates the plate interface decoupling zone.

Section 3: software framework and compute details

Software Framework DOI/URL:

Found software: ASPECT v2.4.0

Software Repository:

https://github.com/geodynamics/aspect

Name of primary software framework:

ASPECT v2.4.0

Software & algorithm keywords:

• C++
• finite-element
• adaptive-mesh-refinement
• particles

Section 4: web material (for mate.science)

Landing page image:

Filename: res_fig_final_ann.png
Caption: Downdip component of strain rate tensor and resolved stress difference from the numerical model, focusing on features within the plate/slab. The resolved stress difference is defined as ($\sigma_{s} - \sigma_{z}$), where $\hat{s}$, and $\hat{z}$ are unit vectors in the downdip and slab normal directions. The fields show, for example, shortening/extension in the downdip direction. Stress profiles at four locations are shown. The blue line ($x_0$) is the first zero crossing based on analysis of the flexural component of the topography. The black line is the location of maximum bending moment.

Animation:

Filename: animation
Caption: Animation shows the model domain at 2x vertical exaggeration. The scalar field is the effective strain rate, i.e. $\dot\epsilon_{II} = \sqrt{J2} = \sqrt{0.5(\dot\epsilon_{i,j}: \epsilon_{i,j})}$. Upper panel shows the evolution of the model topography (a true free surface). The topographic profile reveals the long-wavelength isostatic thermal subsidence, as well as the flexural topography associated with the subduction zone. The model exhibits a very short-wavelength instability in the free surface of the over-riding plate, which begins approximately 3 Ma after the start of the simulation.

Graphic abstract:

Filename: gpe_fm26.png
Caption: The main panel shows the variation in terms that arise in a 2D "vertically integrated" form of the force balance (or stress equilibrium) equations. Assuming a traction-free surface, the force balance states that across a horizontal section of the lithosphere, the following terms must sum to zero: 1) integrated basal shear traction, 2) the difference in the vertically-integrated deviatoric stress and 3), the difference in the vertically-integrated vertical normal stress (often called the GPE). In the figure, the overbar symbols represent vertical integration across the lithosphere. Specifically, integration from a reference height, (taken here as the mean ridge height) down to a reference depth (taken here as 150 km beneath the reference height). In the main panel, the black line shows the horizontal variation in the vertically integrated deviatoric stress difference ($\tau_{xx} - \tau_{zz}$). Positive values indicate a state of deviatoric tension. The dashed blue line shows the horizontal variation in the vertically integrated vertical normal stress ($\sigma_{yy}$) (or the GPE). Strictly speaking, this quantity is only equal to the GPE when the vertical normal stress is lithostatic, but the term is retained in this study due to convention. The upper panel shows the subducting plate topography at 2 different scales.

Model setup figure:

Filename: s1a.png
Caption: The main panel shows the full model domain and initial temperature field. The texture is generated with a line integral convolution of the velocity field. Contours show evolution of the slab during the 10 Myr simulation. Velocity arrows show convergence rates at 5 Myr into the simulation. Inset panels show details of the adaptive mesh refinement during the simulation.
Description: The subduction model comprises a rectangular domain with a depth of 2900 km, and an aspect ratio of 4. The initial conditions comprise an adiabatic mantle with a potential temperature of 1350 C and two plates, whose age and thermal structure follows the cooling 1d cooling profile for a half-space (infinite in the depth direction). One of these plates is attached to a slab that extends to 660 km depth, and has an age of 100 Myr at the trench. The upper plate is modelled with a younger thermal age, 25 Myr at the trench. Imposing an initial slab that reaches the transition zone was found to be a more stable initial configuration in terms of instabilities of the free surface. 7 levels of mesh refinement were used, with the largest (Q2) elements having an edge length of 45 km, and the smallest elements have an edge length of ∼ 700 m. The interface is modelled through an entrained weak layer approach. A thin layer (here 2 km thick) represented by a separate composition is imposed on the top of the subducting plate, as well as between the subducting slab and upper plate. This composition has a low coefficient of friction, providing a shear stress that varies between between about 10 - 20 MPa throughout the plate interface domain. See the included model input file (.prm) for further details.

Errors and Warnings

Associated Publication
Error fetching metadata with application/ld+json from https://api.crossref.org/works/https://doi.org/10.1093/gji/ggad230: 406 Client Error: Not Acceptable for url: https://api.crossref.org/works/https://doi.org/10.1093/gji/ggad230
Software Framework DOI/URI
doi.org metadata record succesfully extracted in json-ld format
Software framework authors
ORCID metadata record succesfully extracted in json-ld format
ORCID metadata record succesfully extracted in json-ld format
ORCID metadata record succesfully extracted in json-ld format
ORCID metadata record succesfully extracted in json-ld format
ORCID metadata record succesfully extracted in json-ld format
ORCID metadata record succesfully extracted in json-ld format
ORCID metadata record succesfully extracted in json-ld format
ORCID metadata record succesfully extracted in json-ld format
Submitter
ORCID metadata record succesfully extracted in json-ld format

Model Repository Slug
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Either propose a new slug or repo will be created with name sandifordcraig-2023-subduction-1.

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Model repository created at https://github.com/ModelAtlasofTheEarth/sandifordcraig-2023-subduction

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Model repository created at https://github.com/ModelAtlasofTheEarth/sandifordcraig-2023-subduction

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Model repository created at https://github.com/ModelAtlasofTheEarth/sandifordcraig-2023-subduction

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Model repository created at https://github.com/ModelAtlasofTheEarth/sandifordcraig-2023-subduction-1