Let's look at some animations: see this webpage.
Future North American boundary:
A subduction animation:
What happened to the plate (the Farallon Plate) that subducted ahead of the Pacific Plate?
It seems fantastical how the plate just disappears in the animations! What happened to it?
If you are a sketpical type you might wonder how you could find evidence of this massive plate.
Let's take a look at an animation from this website.
Here is a document that summarize the seismic tomography concept.
Here is a pdf file with the above image and more explanation of seismic tomography.
Let's not take a look at another case: imaging the Yellowstone Plume: Nelson and Grand 2018.
It turns out to be a big linear algebra problem - solving a large set of linear equations. Therefore we will learn some linear algebra concepts to see how this works on much smaller examples.
Some chemical reactions (autocayltic) show an oscillatory behavior between their reactants. This process can happen in the earth sciences during mineral growthm, for example. This process is mathematically describe by a set of coupled ordinary differential equations.