This repository is for the exploration and modelling of apparent polar wander paths, which are use to describe the past movement of a tectonic plates with respect to the spin axis of the Earth. These are useful descriptions of plates dynamics in paleomagnetism, where the goal is to reconstruct the past history of the Earth lithosphere based on the remanent magnetization of rocks that had formed millions of years ago.
Paleomagnetism was one of the scientific disciplines that provided strong evidence in favor or the theory of plate tectonic motion during the past century. The idea is simple: when rocks are formed, they are magnetized in the same direction than the local magnetic field. If a new rock is formed in the present day (for example, when magma solidifies) close to the equator, it will acquire a remanent magnetization that will be close to be parallel to the surface, but if it is located close to the poles the magnetization will be perpendicular to the surface. Assuming that the magnetic field of the Earth is a dipole, measuring the remanent magnetization of rocks allows estimation of the relative position of the magnetic pole, which is define as paleomagnetic pole. We can do this for rocks with different chronological dating and estimate the relative position of the magnetic north pole for each one of these. If well the locations of the magnetic pole migrate over time, in the time scale of continental drift the average magnetic pole coincides with the spin axis of the Earth\footnote{The characteristic scale of tectonic plates motion is of the order of millions of years. A tectonic plate, and consequently a paloemagnetic pole, can move a few degrees in one million years. On the other hand, secular variation of Earth magnetic field can be observed in the periods of years. However, in reality we observe that the paleomagnetic poles move away gradually over time as we look to older rocks. This is caused by the movement of the rock itself and tracking how the paleomagnetic poles move allows geologists to reconstruct the history of a tectonic plate. This apparent movement of the paleomagnetic poles as we move backwards in time is called apparent polar wander path and is the time series we are interested in exploring for this project.
The initial paleomagnetic pole, that is, the expected paleomagnetic pole in the present, coincides with one of the geographical poles (by convention, here we will assume that is located in the geographic South pole). From the modelling perspective, this means that we do not need to worry about the initial condition of the system. Another important point is the level of uncertainty in the actual position of paleomagnetic poles. One single paleomagnetic pole is the result of multiple noisy measurement performed in same site. The final aggregate of all these measurements is reported as a new paleomagnetic pole with standard deviations in the order of 10 to 20 degrees. A cleaner view of the apparent polar wander path emerges when we average paleomagnetic poles over big temporal windows.
Finally, the movement of plate tectonics can be described (to certain level of approximation) as a series of stable Euler rotations that persist during certain periods of time. This is the case of a single tectonic plate moving with the same angular velocity around a certain Euler pole (different than the rotation axis of the Earth) for certain interval of time until some other dynamical process takes action, such as the collision of two plates, which results in a modification of the original trajectory of the first plate that can be described as a rotation but around a different axis and probably at different speed. We will formalize these notions in the following section.
The dataset we will use for this project was originally recollected from a series of previous papers in Torsvik2012. The same provides a series of 594 paleomagnetic poles for different continents. A total of 194 of these poles belong to sites dated with less than 130 million years for the present. In this project, we are going to focus just in this subset. The reason for doing this is that we just have accurate reconstructions of the relative tectonic plates movement for this period of time, in which we can have information coming from the oceanic platforms (for example, the opening of the Atlantic oceanic platform tell us about how Africa and South America and getting apart from each other). However, this information is not enough to reconstruct the total past history of the plates: we know about the existence of the super-continent Pangea, but we are not certain about where was located with respect to the mantle. However, for the last 130 million years we can inverse the movement of each plate to a common reference system, which is usually Africa since it was in the middle of Pangea.
The information provided in the dataset correspond to the latitude and longitude of each pole and the 95 percent confidence interval around this value, reported as the standard deviation in degrees from the mean position of the pole.
We are using the same virtual environment that in YoungCeed 2021.