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Tutorial 9.3 Introduction to Topologies
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Introduction to Topologies

Authors: Samantha Ross1, Mark Turner2, Mike Gurnis2, Sabin Zahirovic1, Serena Yeung1 & James Egan1

Updated for GPlates 2.2 and the reconstruction of Müller et al. (2019) by Christopher Alfonso and Behnam Sadeghi

1EarthByte Research Group, School of Geosciences, The University of Sydney, Australia

2Division of Geological and Planetary Sciences, California Institute of Technology

Introduction to Topologies

Aim

Included files

Background

What is a topology? What is it used for?

How does GPlates form a dynamic geometry?

Exercise 1 – Creating a Topological Closed Plate Polygon

Exercise 2 – Editing an Existing Topology

Exercise 3 – Incorporating a new MOR into an existing plate polygon dataset

References

Appendix

Extending a new MOR to intersect with existing plate boundaries

Aim

This tutorial is designed to introduce the user to the concept of topologies, how to create them, how to edit them and how to manipulate mid-ocean ridge topologies.

Included files

Click here to download the data bundle for this tutorial.

The tutorial dataset includes the following files, from Müller et al. (2019):

Background

GPlates enables the user to create traditional geophysical features like hot spots, mid ocean ridges, and large igneous provinces, with static geometries such as points, lines, and polygons, respectively. GPlates also has the ability to create specialized topological features with dynamic geometries.

What is a topology? What is it used for?

A topology is a specialized feature type whose geometry is determined not by a static list of vertices, but rather from the composition of geometries from other, regular features. A topology does not contain any vertices itself, but instead contains a list of references to features. During the reconstruction process this boundary list is used to gather up the geometry of the boundary features, and form a complete closed polygon for the topology.

Using topology features, we have developed the concept of a "Continuously Closed Plate" (CCP), such that, as each margin moves independently, the plate polygon remains closed geometrically as a function of time. This methodology is a new improvement for combining kinematic plate models with geodynamic models.

Topologies are primarily used to model the large scale tectonic plates and deforming regions of the Earth’s crust.

Figure 1: Schematic of the generic features that are incorporated into the Continuously Closed Plate (CCP) algorithm. Red dots represent dynamically computed intersections between plate boundaries.

How does GPlates form a dynamic geometry?

The following diagrams show how GPlates creates a dynamic geometry for a simple hypothetical polygon, for two reconstruction times, 0 Ma, and 10 Ma.

A: 0 Ma

B: 10Ma

Figure 2: Hypothetical plate polygon from four intersecting lines at two times. Base features are drawn in blue. Plate polygon is outlined in grey, with grey dots showing polygon’s vertices. Red crosses have been added in the figures to highlight dynamically computed intersection points, relative to base features' vertices. First line on the boundary list is highlighted white (North Line); last line is highlighted in black (East Line)

A: Reconstruction at 0 Ma, the initial configuration of lines, intersection points, and resolved polygon vertices.

B: Reconstruction at 10 Ma, the lines have been reconstructed, new intersection points computed, and the polygon resolved. Some vertices from the North Line are no longer used as it has moved relative to the West Line.

In both reconstructions the East Line contributes none of its original vertices, and only the intersection points are used (no vertices exist on the East Line between the intersection points).

For more information about the Topology Tools in GPlates, see Tutorial 5.1, or the GPlates User Manual.

Exercise 1 – Creating a Topological Closed Plate Polygon

The Build Topology Tool is used to create new topology features from existing regular non-topological features. You will select a series of features, in an ordered fashion, moving around the intended boundary of the topology.

  1. Open GPlates and load the following files using File > Open Feature Collection:

  1. Go to Features > Manage Colouring and on the left hand panel of the Draw Style window, select FeatureType (Figure 3)

Figure 3: Draw Style Window, selecting colour by Feature Type

The four basic elements of the colour scheme are:

(see the GPlates manual for more info on the colour schemes available).

  1. Orient the globe to focus on the Somalia plate and zoom in a little (Figure 4).

Figure 4: Globe oriented to show the Somalia Plate, features coloured by Feature Type

  1. Change the reconstruction time to 5 Ma and play the animation to present day. See how the plate margins move

  1. Select the Topology Tool Figure 5 button.jpg, and then the Build New Boundary Topology Tool Figure 5 button.jpg. The topology tool is now activated and the new topology will initially have an empty list of sections (as you add sections to the topology, the Topology Sections Table will become populated with the features)

Now we will select features by clicking on them on the Globe. Please note that you do not have to switch to the Choose Feature Tool. The Build New Boundary Topology Tool Figure 5 button.jpg  is a specialized version of choosing features  and is located within the Topology submenu or can be selected by pressing ‘b’ on the keyboard.

  1. Select the southern margin of the Somalia plate: the SW Indian Ridge between Somalia and Antarctica

Notice that several features may now appear in the Clicked table below the globe. This table lists all the features found under the mouse click point. If more than one feature is under the click point, you can use the Clicked Table to further refine your selection to the proper feature.

  1. Once you have identified the desired feature, click the ‘Add’ button in the Section tab in the right panel (Figure 5).

The feature reference is transferred to the Topology Boundary Sections table in the bottom panel below the globe, and placed on the working list of boundary features for the new plate polygon.

At this point there is only one element on the boundary list, so the plate polygon will simply close using only that feature and its vertices (hence we see the black line from joining the ends of the green line).

Figure 5: Click ‘Add’ to add the first section of the Somalia plate (Step 7)

We will now continue creating the intended boundary of the new plate by selecting a feature to focus it, and then clicking Add to Boundary to insert it into the Topology Section Table.

We recommended creating a new topology by cycling around the boundary systematically (either a clockwise or counter-clockwise) and appending features to the end of the Topology Sections Table. In this example we will close Antarctica in the clockwise direction.

  1. Choose the southwestern margin of the plate (the southern portion of the East African Rift between Nubia and Somalia) and add it to the list (Figure 6).

Notice how now the south west corner of the plate is formed from the intersection of the two line data features, but it "wraps back upon itself"

With only two features on the list, the internal CCP algorithm chooses the shortest path to close the polygon and it results in a little wedge. This will be corrected as more features are added.

Figure 6: Build the Somalia Plate - Adding the second section results in a green and blue line being highlighted (the start and end of the topology so far); this will be corrected as more sections are added (Step 8)

  1. Continue clockwise along the west and north boundaries of the Somalia plate, selecting and adding the rest of the East African Rift, the Aden Ridge, and the Owen Fracture Zone (Figure 7).

Notice how the collection of vertices that form the work-in-progress plate polygon changes as GPlates calculates the topology on the fly.

Notice that the eastern boundary has not yet been defined, so GPlates simply closes the gap by connecting the two features.

Figure 7: Build the Somalia Plate - Adding these sections results in good intersections in the west and north, and an automatic closure in the east (Step 9).

  1. To complete the plate closure, add the final two sections of the boundary (the Central Indian Ocean Ridge; Figure 8).

Figure 8: Build the Somalia Plate - closing the plate boundary topology

Once you are satisfied with the entries in the Topology Sections Table, and the resulting geometry of the Closed Plate Polygon, we need to create our new topology.

  1. Select the ‘Create…’ button on the Topology Tab of the Topology Tools panel (on the right hand side of the screen).

  1. In the first step you will choose the Feature Type of the new Topology. Select: gpml:TopologicalClosedPlateBoundary.

The next step is to assign other basic property values to the Topology.

  1. The geometry type is "Boundary" (this value is automatically selected for you)

  1. Set the other basic feature properties - Plate ID, Begin Time, End Time, Name (Figure 9).

Figure 9: Build the Somalia Plate - Adding basic properties to the Plate Polygon Feature (Step 15).

  1. Select Next, Next, and then we have to save the feature to a feature collection.

  1. We will save this topology into a new feature collection.

You may notice that the outline of the Somalia plate is not very clearly visible on screen.

  1. Open the Layers Window (Window > Show Layers or Ctrl+L).

Notice that our new layer is pink, and is situated below the green layer that we created the topology from.

  1. Make the green layer invisible, and notice that our new topology is now clearly visible (Figure 10).

Figure 10: Somalia plate topology is now visible

Another way to make this visible with the reconstructed geometries, is to change the order of the layers in the Layers window. In GPlates, the layer that is at the top will appear on top of all other layers.

  1. Drag the pink layer so that it sits above the green layer in the Layers window and make both layers visible (Figure 11). Note that we can see our new topology as well as the spreading ridges and other reconstructed geometries.

Figure 11: Somalia plate topology on top of existing geometries

For more information about creating new topologies, see Tutorial 5.1, or the GPlates User Manual. 

Exercise 2 – Editing an Existing Topology

The Edit Topology Sections tool  is the tool used to edit existing topology features. Under this tool you will load an existing topology into the Topology Sections Table, and make edits to that ordered list of features.

We will edit the Somalia plate topology we created in Exercise 1 to exclude the Victoria block in the East African Rift.

  1. Use the Choose Feature Tool to select the existing Somalia plate topology we created in Exercise 1 (Figure 12). If you are having trouble selecting the plate boundary topology, try unchecking the “Show Topological Sections” option in the “View” → “Geometry Visibility” menu. This will hide features which have been used in topologies, such as the Somalia plate topology we created in Exercise 1.

Figure 12: The Somalia plate topology has been selected

  1. Click on the Edit Topology Sections button , under the “Topology” section (Figure 13).

Figure 13: Edit Topology Sections

Notice that the topology will be drawn with the highlighting described in Figure 6. The feature’s basic data is placed into the Topology tab of the Task Panel, and the Topology Sections Table will be filled with the list of boundary features (Figure 14).

a)b)

Figure 14: a) Topology Sections Table showing the boundaries that are currently making up the topology b) Button to expand table into a separate window - useful when the topology has many sections

  1. Zoom to the western boundary of the plate (Figure 15). This is the area where we want to edit the topology to incorporate more complexity by excluding the Victoria block.

Figure 15: Western boundary of the Somalia plate

  1. In the Topology Boundary Sections Table, select the southern portion of the East African Rift (“Somalia Africa boundary from PB03 GS”, plate ID 701) and move the insertion point for new topology sections to after this section by clicking on the downward-pointing arrow. This section of the boundary should now appear blue (Figure 16). This means that the new boundary sections that we add will be added after this section, and before the green boundary section.

Figure 16: Plate topologies ready to add more complexity after the southern East African Rift (blue) and before the northern section of the rift (green).

  1. Select the Victoria-Rovuma boundary feature (Figure 17) and add it to the boundary. You should now notice that it appears blue (this means that the next boundary section we add will come after this).

Figure 17: Editing the Somalia plate topology: the Victoria-Rovuma boundary feature has been added to the topology

  1. Select the Victoria - Somalia, EAR_Victoria, and EAR_Somalia UCCL features and add them to the boundary (Figure 18).

Figure 18: Editing the Somalia plate: the features listed in Step 6 have been added to the topology

Your final plate topology should now look like Figure 19.

Figure 19: The western boundary of the Somalia plate topology has been modified

  1. Now that we are happy with our modifications to the plate topology, click Apply… (on the Topology Tools section - right hand side of the screen).

The Somalia plate has now been modified to exclude the Victoria block (Figure 20).

Figure 20: The new Somalia plate topology

Don’t forget to save your new layer if you need to keep the changes you’ve made! (File → Manage Feature Collections…)

For more information about editing existing topologies, see Tutorial 5.1, or the GPlates User Manual. 

Exercise 3 – Incorporating a new MOR into an existing plate polygon dataset

We will now interactively construct a MOR feature with the intention of replacing an existing MOR. This requires the user to ensure the new MOR geometry intersects with pre-existing plate boundaries so that it can replace an old MOR. The user then has to delete the old MOR, and manually edit existing topologies to insert the new plate boundary. When deleting a MOR, the user must fix at least two polygons at any one time. That is because the old MOR formed the mutual boundary between two polygons.

Users must also take care to correct any other polygon artefacts they may have introduced by deleting the old redundant MOR. GPlates does not automatically detect polygon artefacts, so a careful interactive reconstruction in GPlates through time is required to ensure polygon closure without gaps, overlaps or “rubber-banding” artefacts.

For this example, we will create a new MOR in the Atlantic Ocean adjacent to the existing South America-Africa MOR, which exists between 60 and 20 Ma.

  1. If you are coming from Exercise 1 or 2, click File → Clear Session (if beginning at this Exercise, open GPlates and go to Step 2)

  1. File → Open Feature Collection… → Open the following files from the tutorial data bundle:

  1. Change the colour of the plate boundary topologies layer (coloured pink in the Layers window) to colour by single colour - black (Features → Manage Colouring; Figure 21)

  1. In the Layers window (Window → Show Layers…), hide the brown Resolved Topological Networks layer and drag the pink Resolved Topological Geometries layer to the top (Figure 22).

Figure 21: Changing the colouring for the plate boundary topologies.

Figure 22: Layers window showing that the pink Resolved Topological Geometries layer is at the top, and the brown Resolved Topological Networks layer has been hidden.

  1. Reconstruct to 60 Ma and focus on the black MOR forming the boundary between the South American (SAM) Plate and the African Plate (Figure 23).

Figure 23: The Atlantic Ocean, Africa and South America reconstructed at 60 Ma, centred on the South America-Africa MOR.

 

  1. Under the ‘Digitisation’ icon on the left, select ‘Digitise new polyline geometry’.

  1. Plot a series of points which span the length of the existing South America-Africa MOR (Figure 24). Note that your new MOR geometry must intersect the pre-existing plate boundaries of the two conjugate plates (SAM and Africa). Again if you plot an incorrect point, use the keyboard command Ctrl-Z to undo the action. The Appendix will detail how to extend a new MOR to intersect with existing boundaries if it doesn’t already.

Figure 24: Digitise the new MOR to intersect the plate boundaries of the SAM and African plates.

 

  1. Click ‘Create Feature’ to open up the Create Feature window. Select ‘gpml:MidOceanRidge’ as the feature type and specify the following properties (Figure 25):

 

Figure 25: Specify all the properties of the new MOR feature in the ‘Create Feature’ window.

 

  1. Select the plate boundaries dataset (Muller_etal_2019_PlateBoundaries_DeformingNetworks.gpmlz) to save your new MOR to, and click Create. You will then be taken back to the main GPlates window where you can reconstruct back to 20 Ma to check whether your MOR is reconstructing correctly.

Ideally, the endpoints of your MOR should continue to intersect the adjacent plate boundaries but in the situation in which they do not (Figure 26), refer to the Appendix before continuing.

Figure 26: In this example, the southern end of the new MOR feature reconstructed at 20 Ma does not intersect with the pre-existing plate boundaries, and therefore must be modified.

 

  1. Return to 60 Ma and select the first plate polygon to be edited (we will choose the South America plate), and then select ‘Edit Topology Sections’ under the ‘Topology’ icon (Figure 27).

Figure 27: Under the ‘Topology’ icon, select the SAM Plate using the ‘Choose Feature’ tool and then select the ‘Edit Topology Sections’ tool.

  1. Click the problematic boundary that needs to be replaced. In this example, there are three sections to be removed: “Ridge from iso A13…”, “South America-Africa”, and “Malvinas Ridge Jump”. When you click on a boundary section, it will be highlighted in the Topology Sections list at the bottom of the GPlates window. Click the “X” button next to each of these boundary sections to remove them.

At this stage, the boundary topology should look like Figure 28. Notice that a “rubber-banding” artefact will appear until you insert the new MOR boundary.

 

Figure 28: After removing the previous MOR boundary sections in the South Atlantic, the South America plate topology should look like this.

  1. In the Topology Boundary Sections window (Figure 29), click the downward-pointing arrow next to the NAM transform, to ensure that the new section will be inserted in the correct position.

Figure 29: The new sections will be inserted after the blue section (NAM transform) and before the green section (Ridge from iso from ANT at 67.7 Ma).

  1. Select the new MOR feature by clicking on it, and then click the ‘Add’ button on the right hand side of the main window (Figure 30).

Figure 30: The SAM plate topology after adding the new MOR feature.

 

In the next window, notice that the ‘Valid time’ for which the topology can exist for is limited from 60.1 to 58.1 (Figure 30). This is because the plate topology you are modifying will cease at 58.1 Ma (and transform into a ‘new’ one). The new MOR topology you have just incorporated into the polygon will similarly cease to exist at this point in time. If you select any feature, you will notice that the right-hand-side window will display the Valid time for which the feature will exist.

  1. Click Apply.

 

You have now successfully fixed one polygon.

  1. You must repeat this process on the other polygon (the Africa plate in this case) that shared the old MOR boundary.

Once you have done this you will want to make sure that you have not created any artefacts or discontinuities. The best way to see gaps, overlaps and rubber-banding artefacts is by turning off the lines and just displaying the resolved topologies.

  1. In the Layers list, disable all Reconstructed Geometries layers in the ‘Layers’ window (Figure 31).

Figure 31: The new South America and Africa plates, with all Reconstructed Geometries layers hidden.

You can avoid these problems by carefully extending the new MORs to intersect at the same place as the old boundary (see Appendix). However, there is likely to be a lot of manual work to introduce new MORs into existing plate polygon datasets.

For more information about editing MOR topologies, see Tutorial 5.2, or the GPlates User Manual. 

References

Müller, R. D., Zahirovic, S., Williams, S. E., Cannon, J., Seton, M., Bower, D. J., Tetley, M. G., Heine, C., Le Breton, E., Liu, S., Russell, S. H. J., Yang, T., Leonard, J., and Gurnis, M., 2019, A Global Plate Model Including Lithospheric Deformation Along Major Rifts and Orogens Since the Triassic: Tectonics, v. 38, no. 6, p. 1884-1907. doi: 10.1029/2018tc005462

Appendix

Extending a new MOR to intersect with existing plate boundaries

If intending to replace an existing MOR with a new MOR feature, it is crucial that the new MOR geometry intersects with pre-existing plate boundaries in order for the user to edit the new topology in. If the MOR fails to intersect these plate boundaries, which may be the case after reconstructing back through time, it is possible to interactively extend the MOR to intersect with the required plate boundaries.

Using the ‘Choose Feature’ tool, select the problematic MOR and click the ‘Insert Vertex’ tool (Figure 32).

Figure 32: Select the MOR feature and click the ‘Insert Vertex’ tool.

 

Add points to make the sure MOR intersects with neighbouring boundaries (Figure 33).

 

Figure 33: Plot points interactively to extend the MOR until it intersects with adjacent plate boundaries.

 

Once you are satisfied, select any other tool on the main interface (such as the ‘Choose Feature’ tool) to halt the process. You have now successfully extended your MOR feature!