True Polar Wander on Dynamic Planets: Approximative Methods Versus Full Solution

Abstract

Internal and external planetary processes such as mantle convection, deglaciation, or large meteorite impacts cause bodies to move as a whole relative to their rotation axis. The rotation poles of planets and moons thus wander on their surfaces, as shown by paleomagnetic, astrometric, and geodetic measurements (e.g., Mitrovica & Wahr, 2011). Such reorientation in space is commonly referred to as true polar wander (TPW).The TPW mechanism can be described as follows. Let us assume that a rotating planet in hydrostatic equilibrium is subject to a sudden loading with a positive geoid anomaly, shifting the principal directions of the planet's inertia tensor in effect (the principal direction that has the largest associated moment of inertia is hereafter referred to as the main inertia axis, MIA). When viewed by an observer on the surface of the planet, the rotation axis will start a circular motion, known as free oscillations, around the new MIA. As soon as free oscillations dampen out (Nakada & Karato, 2012), the resulting position of the rotation pole will be closer to the principal axis of the load than in the initial state. Such motion of the rotation axis misaligns it with the hydrostatic rotational bulge, which effectively prevents the rotation axis from moving further toward the load axis (see figure 1 in Matsuyama et al., 2014). Gold (1955) argued that the stabilization is only transient, because the rotational bulge will eventually adjust to the new direction of rotation. The planet is then free to reorient further, and the process gradually