Long-term polar motion on a quasi-fluid planetary body with an elastic lithosphere: Semi-analytic solutions of the time-dependent equation

In order to understand long-term polar motion (so-called true polar wander), I present a large-scale and time-dependent solution of the Liouville equation based on the quasi-fluid approximation. The formulation includes the stabilizing effect of an oblate fossil shape memorized in an elastic lithosphere. Reorientation is assumed to be driven by a surface mass excess that is axi-symmetric and grows linearly with time. Without a fossil bulge, the time scale of true polar wander (specifically the time scale to settle to an equilibrium state) depends mainly on the time to build the load and its final magnitude. A fossil bulge works against reorientation such that the initial latitude of load emplacement now also influences the time scale. I conclude that it is necessary to consider where a load is emplaced in order to reconstruct paleo-poles on a planetary body with a remnant rotational bulge.