We will explore a numerical model of horizontal extension. Horizontal extension occurs when the maximum compressive stess is vertical, producing normal faults and, in extreme cases, continental rifts.
Instead of modelling a portion of Earth's lithosphere, this model is set up to simulate a 20 cm sandbox. This particular setup is useful for testing numerical models, because physical sandbox experiments offer a sort of "ground truth" to evaluate how the model performs. Theoretically, models should be able to reproduce the outcomes of these physical sandbox experiments, but as we'll see, many complications usually prevent the models from doing so.
The exercise consists of three parts. First, we'll study the setup of the model, including the layers of materials and how extension is performed. You will be asked to sketch your prediction for how you think the model will evolve after a period of time. Next, we will walk through an actual run of the model. You will evaluate the outcome of the model to see if the result matches your predictions. You will also compare this run to similar experiments in several other geodynamic models. Finally, you'll be able to edit the code for the model and re-run it.
Click the link below to view an illustration of the model setup.
Study the setup, and sketch on top of it on Excalidraw.
Q1. Using Excalidraw (or any other program), sketch what you think will happen after extension of a few centimetres has occurred.
Sketch directly on top of the provided image.
Your sketch can include things like faults, folds, layer contacts, and topography.
To distinguish your prediction from the initial layer setup, use any color other than black.
Use the export button 
in the upper-left corner of Excalidraw to save an image of your sketch. Paste the image below.
(put your image here)
Q2. How is extension imposed in the model? Is this an initial condition or boundary condition?
Next we'll step through the sandbox extension model together, using a geodynamic modelling platform called Underworld. Follow along with the text and blocks of code that run the model. Feel free to ask questions. After we step through the code, answer the questions below.
Click here to launch an interactive notebook of the model:
Or use this link https://mybinder.org/v2/gh/mitchellmcm27/sandbox-extension-exercise/main?labpath=model-run-1.ipynb
(Make sure to leave this window or tab open as we continue the worksheet.)
Q3. Study the images showing the results of running this experiment on different modelling platforms. What are the main differences? Is there a model that more closely agrees with how you would expect a sandbox to behave (and could be considered "better" in that way)? Is there anything that all of the models get wrong (if so, what is it and why is it wrong)?
Q4. We assigned two distinct mechanisms to the "sand1" and "sand2" layers to control how they deform. What are the two mechanisms? How do they differ? Why is it beneficial to use such an approach in this experiment?
Q5. In the next section, you will edit the code to try to improve the model result. What is your goal here (what aspect of the result do you want to improve upon)? What will you change in the code to try to achieve this goal? (Your answer here can be general, specific, or somewhere in-between.)
Finally, we'll change some of the parameters of our model in a controlled way and investigate what happens.
Back in JupyterLab, open the model-run-2notebook and read the introduction.
Some of the explanations within the code have been removed from this notebook.
If you need to refer to them, look back at the model-run-1 notebook.
Depending on your goal, make changes to the code blocks. Focus on things that are relatively straightforward - changing a few numbers here or there. Feel free to ask classmates or instructors if you need feedback when deciding how to do this. (There's no right or wrong answer here, it's just interesting to poke around a bit.)
Run the code --- this will take some time. If you changed the code in a way that requires more computation, you may want to decrease the model run time (say, 0.5 hours instead of 1 hour).
Q6. What happened in terms of the model? Did it run to completion? How long did it take? Did you achieve your goal? What would you change in a hypothetical third run?
For an in-depth discussion of these types of models and a comparison to actual sandbox experiments, see the Buiter et al. (2006) paper.
Back in JupyterLab, you can open the mitchell folder and see the output from my model-run-2, where I increased the mesh resolution and decreased the number of particles per cell.