Using GIMP to simulate tectonic plates movements

[Warlin]

Stage 0 : AIMS AND GOALS, REFERENCES, MATERIAL AND TOOLS.
First of all, thanks to all the many cartographers' guilders that have developped tutorials for tectonics :
- The world of tutoralia - tectonics plates, climate by Woekan,
- Using Gplates 1.4 to study plate movement by Pixie,
or have shown the way to other :
- [WIP] World of Aduhr by Charerg
- AERLAAN by PaGaN,
- Unexplored Lands by Kacey,
for the more recents' one (oct 2017).

This tutorial aims to help cartographers to modelize throught the ages some tectonic movements with a small script-fu applet developped early in the 2017 year.

For that you need some material :
- seven relative eulerian pole grids in png format,
- two script-fu documents which you have to implement to GIMP (don't forget to move the txt extension to scm) : https://docs.gimp.org/en/install-script-fu.html
a workplace like this :
- 1800x900 px image size,
- ocean layer (filled with grey), continent mass layer (transparent + green mass), limit lines layer (transparent + red, green and violet lines).
Capture du 2017-10-13 12-19-39.png
and to know (or learn) some gimp techniques :
- offset and flip tool : layer->transform->offset, wrap around edge behavior and flip button.
- Selection from alpha and selection tool : layer->transparency->alpĥa to selection, and the intersection mode of the magic wand and lasso.

Table of content :
stage 1 : Basics, Eulerian pole and plate rotation,
stage 2 : Basics, Relative movement and plate limits,
stage 3 : Hard stuff, Fixing plates velocity,
stage 4 : Hard stuff, Mastering the Wham! effect,
stage 5 : Cool stuff, Implementing water level and erosion factors.

See you soon !

[kacey]

Wow this looks really cool Warlin! and to think I almost missed it. Luckily I was searching for something else when this crossed my path... Can't wait to find out more. I may have to pull out the old copy of gimp and follow along... That's if I can remember how to use it it's been a while.

[Warlin]

Wow this looks really cool Warlin! and to think I almost missed it. Luckily I was searching for something else when this crossed my path... Can't wait to find out more. I may have to pull out the old copy of gimp and follow along... That's if I can remember how to use it it's been a while.

Hope it'll help you. Cheers !

[Warlin]

Stage 1 : BASICS, EULERIAN POLE AND PLATE ROTATION.
To begin this stage, one rule that you can't forget to have in mind :
RULE 1 : All plate movement on a globe is a rotation around an Eulerian Pole.
Imagine that you want to move a plate from one region to another on an equirectangular map.
To find out how this is possible, you need to locate the Eulerian Pole and the lower amount of rotation degree (For tectonics, it's simplier to choose the shorter way...). For that you can use one of the derivative grids. On those, the Eulerian Pole is the dot that don't move : the center of the closed curves. But... There is two of them, you may say, isn't it? You're right : on a sphere there is the upper and the under pole.
By convention, the upper is the one that allows you to make rotate your plate in the trigonometric (conter-clock) way (Alpha>0).
Other convention : latitude are positive for the north one and longitude for the east one.
Example : 50°N/120°E is latitude +50 and longitude +120, 45°S/75°O is latitude -45 and longitude -75.
You can choose other convention if you want... Wait a minute : NO YOU CAN'T ! If you do that, movement will be quickly incomprehensible.
Now, you can locate the Eulerian Pole by simply pointing it with your cursor and read the (x,y) coordinate. If you're working with the standart workspace (see stage 0) some little mathematics states that : latitude = (450 - y)*2/10 and longitude = (x - 900)*2/10.
The amount of degree rotation is the number of lines you crossed between the initial and final location multiply by 30°.
Now that you have got your Eulerian pole located and your Alpha evaluated, let's use the tectonics tools. Select your plate layer, make the alpha to selection task, select green for your foreground color, go to tectonique -> mouvement de plaque, enter the coordinate and the alpha (don't forget the convention) and APPLY.
The applet use your selection to generate a path whose points coordinates are modified with a rotation matrix, make a selection from the new path, generate a new layer and fill the selection with the foreground color on this layer.
Stage1fiche01.png
There isn't only one way to rotate your plate. Let's see a new general way. You can play with the grids by using offset (only x one) and flip tool (vertical one) to fit better to this new one. Redo all the tasks (location of the eulerian pole, evaluation of the Alpha, selection of the initial plate, mouvement de plaque).
The result is not the same that the previous one. Why ? Don't forget the first rule : it's not a translation, it's a rotation !
Stage1fiche02.png
Let's play a little more with it and you'll find out some limits of this little applet. Example 1 : the continent mass go out of the workspace by the left or the right, or example 2 : the continent mass come near the north or south pole. For this two kind of problem, you have to draw again the limits of the land mass. Example 3 : after the repetition of successive rotation, the limits of the land mass begin to be too smooth and lost details, same solution : draw again the land mass.

Hope you're still interested, and see you soon !

[Pixie]

I just noticed today that you had started this already. So far, I can follow it and I promise I'll try it out when I find the time.

So, just to be sure on what I understand so far... the grids are just there as an aid to locate the euler pole and estimate the amplitude of the rotation, is that right?

KEEP IT UP! I have the feeling this will turn out to be VERY useful!

[Warlin]

I just noticed today that you had started this already. So far, I can follow it and I promise I'll try it out when I find the time.

So, just to be sure on what I understand so far... the grids are just there as an aid to locate the euler pole and estimate the amplitude of the rotation, is that right?

KEEP IT UP! I have the feeling this will turn out to be VERY useful!

Thanks Pixie for your support !
The grid has got another utility : they allow us to draw the divergent boundary.
Cheers.

[Warlin]

Stage 2 : BASICS, RELATIVE MOVEMENT AND PLATE BOUNDARIES.

To begin this stage, another rule that you must have in mind :
RULE 2 : There is no absolute eulerian Pole, all plate movements are relative to each other.
And because it'll be very difficult to work with that one, another rule more usefull :
RULE 2 bis : You can choose one relative pole to be the absolute one, all other are relative to this one or to one linked to it.
I think it's a bit unclear for the moment, but i hope it becomes clearer soon.

For this tutorial, let's take two plates. One will be the reference (plate 1) and the other a breakable one (plate 2+3).

1. How to determine relative Eulerian Pole and to draw plate boundaries ?
First of all, we have to determine the position of the convergent boundary beetween the plate 1 and plate 2+3. Let us draw a violet line near the coast of the plate 1. With this line, we can choose a derive grid that fit the best : the circles have to join the continent mass to this line with a perpendicular way (less energy to subduct). Use grids with perpicacity and don't forget the movement you have learn in the first stage (offset and flip tool).
The grid give you the Eulerian Pole and the mean to draw the divergent boundary that will break the plate 2+3 :
Divergent boundaries are straight line from one transform boundary to the next, and those follow the circles lines around the Eulerian pole.
For the mean of example, I forced the line by giving a curious form to the divergent boundary. This makes it easy to recognize the passive margins of the continental masses.
We have to complete the limits of all the plates. A black line will suffice. It has no physical meaning at all, it's just a necessary limit for computer processing.

2. How to calculate absolute eulerian pole and movement velocity ?
List all the data in a reference table whose entries will be :
Name of the plate,
Relative Eulerian pole coordinates,
Relative movement (°/10Myear),
Absolute Eulerian pole coordinates,
Absolute movement (°/10Myear),
Notes (boundaries, creation).
See the attached table for our three plates.
coordonnéesplaques.png
For the first one, there is only the absolute eulerian pole and velocity because it's our reference plate. Its movement is considered absolute in the Hot Spots terrestrial referential. For plate 2+3, the relative pole and velocity will allow us to calculate absolute eulerian pole and velocity. For that i have choose speed movement close to that observed on earth.
Use the applet "Pole absolue". The first coordinates are those of the reference plate (absolute ones) and the second those of the relative plate (relative ones). The result are the absolute eulerian pole coordinates of the plate and its velocity. You can thus calculate the absolute coordinates of all the eulerian poles.

3. Let's move all the plates !
Once all the data have been established, we have to evaluate the appropriate time interval for the plate to move (see stage 4 for further informations). We choose there a 20 Myear interval.
Select all the plates of the simplified model (alpha to selection for the plate layer). Make the plate boundaries layer active. Select the plate 1 with the magic wand in intersection mode. Activate the "Mouvement de plaque" applet with the absolute eulerian pole and velocity of this plate. Let's move. Repeat the operation for the last two plates and merge the three new layer. We get the rough situation of our model after a 20 Myear evolution. You can name your new layer with a Plate_20My tag.

4. Let's update the plate boundaries !
For the divergents boundaries, calculate the absolute eulerian pole and speed velocity by combining the two absolute poles of the plates they separate, with half speed each (use the "Pole absolu" applet). For the convergent boundaries, they follow the plate they belong to.
Repeat the same operation you use for the plates, but using the lasso tool instead of the magic wand (intersection mode) to move the various kind of plate boundaries (don't forget to select the right color for your foreground). Merge all the new layer in one and delimit your plates with black, violet and red lines. Name your layer and you're ready for a new iteration of the process.
Stage2fiche01.png

5. Have fun...
Repeat the process for differents situations : plate shape, eulerian pole and velocity, time interval. Make several iteration of the process to have a time evolution of your plates. Once you get used to the algorithm go to the next stage, things will get complicated...

See you soon and feel free to leave your comments.

[Warlin]

Stage 3 : HARD STUFF, PLATE VELOCITY AND BOUNDARIES.
No rule to begin with, but some observations about our good old Earth planet.
For this stage, let's consider the plate boundaries map of the Earth.
Tectonic_plates_boundaries_detailed-fr.svg.png

1. The earth observatory.
As we are now familiar with the Eulerian Poles, we can consider those of the different terrestrial plates. Here is a table with the twelve major plates. Speed and eulerian poles are relative to the earth hot spots. One can find other datas relative to the pacific plate reference.
PlaquePrincipales.png
To find regularities in this datas, the first possibility is to cross surface area plate with its speed. There's no match : African plate is 20 times larger than Caraibean's one but its speed is almost the same. The second possibilty is to cross the relative importance of boundary type (divergence, subduction, convergence, transform fault) with speed. No match again : Australian plate has got a 5 times greater speed than South-American's one with the same size and similar boundaries.
No regularity then ? Or is there any false reasoning somewhere ? Yes you have found ! It is in relation to the second rule : there is no meaning for relative speed unless it relates to a boundary. For instance : in the pacific plate reference, speed of Antarctic plate or Australian plate means something for divergence and subduction plate boundaries respectively, but African plate speed means nothing as there is no common boundary.

2. Some relative generalizations.
To find the relative speed of two plates that have got a common boundary we can use the "Pole relatif" applet. You can use any one of relative eulerian pole datas for the two plates. Here is a table that compile some results.
PlateBoundaries.png
a. Continental-continental divergence.
In this category we find : African/South-American, Eurasian/North-American, Antartic/Australian or African/South-American plate boundaries. The relative speed is between 0,2 and 0,7°/My.
Divergence&rift.png
b. Continental-continental convergence.
In this category we find : African/Eurasian, Eurasian/Indian, Arabian/Eurasian plate boundaries. The relative speed is between 0,1 and 0,6°/My.
c. Oceanic-continental subduction.
In this category we find : Nazca/South-American, Eurasian/Pacific or Cocos/North-American plate boundaries. The relative speed is between 0,7 and 1,4°/My.
Subduction&rift.png
d. Oceanic-oceanic divergence.
In this category we find : Nazca/Pacific, Scotia/Sandwich plate boundaries. The relative speed is between 1,0 and 2,0°/My.

With this observation, we have our third rule.
Rule 3 : The subduction seems to be the major motor process of the plate movement. The greater the relative importance of the subduction boundaries are, the greater the relative speed between this plate is.
The values ​​quoted above can be used to set realistic relative speeds between our plates. Of course these speeds are valid in the context of a terrestrial planet in its current age of geological evolution. Some older planet will have lower speed and some younger one greater speed, I presume (specialists more able than I am can fix the variations or confirm this assumption).

See you soon for another stage !

[Warlin]

Allright good fellows, here is a small compilation sheet that summarizes the initial stage of this tutorial.
Thanks to Grey Stallion who allowed me to use his map. You can see his work here.
Stage3FicheBilan.png
Hope to come back soon to finish this tutorial thread (with work on Kacey map), but I have to take a little break from tectonics not to be bored with it .
Cheers.

[kacey]

Wow this tutorial has gotten very complicated what a great source of information, I wish gimp worked a little better on my computer, but I have to stick with photoshop because it's more touch friendly gimp doesn't work well on my surface tablet.

Sorry it took so long to get this to you but Here's a transparent png of just the landmass

for Warlin.png

And here's a jpeg full size incase shrinking the other one made it too fuzzy, it's not perfect but I won't be fully cleaning up the coast until the topography is done, so things may change down the road. This coast is not by any means finished but it should do for working out tectonics... I hope.

for Warlin.jpg

Any tectonics' that I planned previously over on my thread are still the same except one area which I'll upload in a little bit once I mark it up.

I appreciate you offering to do the tutorial with my map, can't wait to see what you come up with though I cringe a little because it probably means I'll have to change some of my planned topography... I hope these will be ok for you, let me know if you need better files.