A Full‐Maxwell Approach for Large‐Angle Polar Wander of Viscoelastic Bodies

Abstract

For large‐angle long‐term true polar wander (TPW) there are currently two types of nonlinear methods which give approximated solutions: those assuming that the rotational axis coincides with the axis of maximum moment of inertia (MoI), which simplifies the Liouville equation, and those based on the quasi‐fluid approximation, which approximates the Love number. Recent studies show that both can have a significant bias for certain models. Therefore, we still lack an (semi)analytical method which can give exact solutions for large‐angle TPW for a model based on Maxwell rheology. This paper provides a method which analytically solves the MoI equation and adopts an extended iterative procedure introduced in Hu et al. (2017) to obtain a time‐dependent solution. The new method can be used to simulate the effect of a remnant bulge or models in different hydrostatic states. We show the effect of the viscosity of the lithosphere on long‐term, large‐angle TPW. We also simulate models without hydrostatic equilibrium and show that the choice of the initial stress‐free shape for the elastic (or highly viscous) lithosphere of a given model is as important as its thickness for obtaining a correct TPW behavior. The initial shape of the lithosphere can be an alternative explanation to mantle convection for the difference between the observed and model predicted flattening. Finally, it is concluded that based on the quasi‐fluid approximation, TPW speed on Earth and Mars is underestimated, while the speed of the rotational axis approaching the end position on Venus is overestimated.

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

“…I compare the full LE solution with the ω‖MIA approximation and with the solution obtained via Eq. 23 in Hu et al (2017b), labeled as PWL2 (see the green symbols in Figure 6).…”

“…For slowly rotating bodies, Equation 10 is inappropriate and Hu et al (2017b) derive a different approximation in their Eq. 23.…”

“…In Section 5, where the slowly rotating Venus is investigated, Equation 10 is replaced by Eq. 23 from Hu et al (2017b) (labeled as "PWL2").…”

“…Such an approximation is commonly referred to as the "quasi-fluid" approach (Lefftz et al, 1991;Ricard et al, 1993). Recently, Hu et al (2017bHu et al ( , 2019 analyzed the quasi-fluid approximation, and by comparing the traditional solutions to their full-Maxwell approach they showed that the prediction of the TPW speed on Earth and Mars were underestimated in previous literature.…”

“…Hu et al (2017aHu et al ( , 2017b develop a new approach, in which they iteratively solve the linearized LE to obtain a large angle TPW. Hu et al (2017b) argue that the validity of the ω‖MIA approximation "was discussed in detail in Cambiotti et al (2011) who showed that even for the Earth this assumption is not always appropriate". However, such a statement may be misleading, because Cambiotti et al (2011) actually employ the ω‖MIA approximation, see their Equation 7.…”