We present a class of “ellipsoidal rotation matrices” which can be used to characterize tectonic plate motion; where geocentric Cartesian coordinates travel along paths tangential to the ellipsoid. We contrast them with conventional Euler pole plate motion models which are more closely aligned with spherical coordinate systems and inherently induce a change in geodetic ellipsoidal height. We demonstrate the use of each in the Indo-Australian tectonic plate setting, which is known to move approximately 7 cm/year in a north-northeast direction. Geocentric Datum of Australia 2020 (GDA2020) coordinates are “plate-fixed” static coordinates obtained using a conventional Euler pole plate motion model to align time dependent coordinates with the 2014 realization of the International Terrestrial Reference Frame at the epoch 2020.0. We show that this Euler pole plate motion model can introduce ellipsoidal height velocities of up to −0.2 mm/year. This is small but systematic, so pertinent for consideration with high accuracy vertical land motion studies using GDA2020 coordinates and velocities. We further investigate the comparative statistical accuracy of conventional Euler pole and the ellipsoidal models with respect to characterizing plate motion captured in high quality Global Navigation Satellite System data.
Plain Language Summary:
We introduce a new way to study the movement of Earth's tectonic plates, using something called “ellipsoidal rotation matrices.” These matrices help us understand how plates move along a path that agrees with the Earth's ellipsoidal shape. This is different to the traditional way of studying plate motion, which usually assumes the Earth is a perfect sphere. We tested both methods by looking at the Indo-Australian tectonic plate, which is moving north-northeast at about 7 cm per year. Our findings show that the traditional, spherical method could result in slightly misrepresenting how the land is moving vertically, by up to −0.2 mm per year, since the vertical motion signal cannot be separated from the tectonic plate motion adequately. While this might not seem like much, it could matter in studies that require very accurate measurements of land height changes over time. We verify how well each method is in capturing the real movement of the Indo-Australian tectonic plate and demonstrate that the ellipsoidal method is more accurate.
Citation: McCubbine, J. C., Riddell, A. R., & Brown, N. (2024). An ellipsoidal plate motion model of the Indo-Australian tectonic plate. Journal of Geophysical Research: Solid Earth, 129, e2023JB027765.
https://doi.org/10.1029/2023JB027765
