Theoretical constraints on true polar wander

Abstract

[1] For the present geologic epoch, true polar wander (TPW) is relatively small, but simple theoretical considerations suggest that it could have been larger in other epochs. In this work, we use scaling arguments to assess the qualitative behavior of TPW and a simple Maxwell model to analytically describe how changes in mass anomalies translate into TPW. Unlike previous work, we derive simple analytical estimates of TPW based on the characteristic amplitudes and timescales for changes in the moment of inertia. We find estimates for both the amplitude and speed of TPW as a function of Earth properties. The following four main factors influence how large the maximum TPW can be: the (geological) timescale over which the desired TPW occurs t TPW , the viscosity structure of the mantle which yields a weighted average viscosity h, the characteristic amplitude of the nonhydrostatic changes in the moment of inertia dC, and the added moment of inertia due to the equatorial bulge (C À A). For the nominal values h = 3 Â 10 22 Pa s and dC/(C À A) = 0.003, the maximum TPW is 61°over 100 Myr and 8°over 10 Myr. The maximum TPW speed is only sensitive to h, dC, and (C À A), and is 2.4°Myr -1 for the nominal values. TPW is shown to act as a low-pass filter; rapid changes in moment of inertia produce smaller and delayed TPW. A consequence of this is that inertial interchange TPW does not have a different character than TPW. TPW can have an important contribution to plate motions over relatively long timescales but not over shorter timescales. Our simple approach allows us to assess whether multiple TPW events are possible but the major uncertainty continues to be the mantle viscosity structure.

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

“…Although the diagonal terms in B ij ðtÞ are negligibly small and excluded from this equation, those in A ij ðtÞ are included for comparison with the equation of Tsai and Stevenson (2007). As mentioned later, those in A ij ðtÞ are also negligible in the case of the Earth.…”

“…The typical example is Tsai and Stevenson (2007). Their work is an example of approaches based on the quasi-fluid approximation with no fossil effect.…”

“…Instead of the linear approximation, the present formulation is mainly grounded on the quasi-fluid approximation (Spada et al, 1992a(Spada et al, , 1996aRicard et al, 1993;Richards et al, 1997Richards et al, , 1999Greff-Lefftz, 2004;Tsai and Stevenson, 2007;Rouby et al, 2008). I extend this theory in the absence of a fossil shape to apply to a planetary body with an elastic lithosphere that retains a fossil shape.…”

“…Concerning the deformation model, their work is different from the other previous works cited. Most of these studies like Ricard et al (1993) employ visco-elastic deformation theory for a multi-layered sphere whereas Tsai and Stevenson (2007) employ only viscous deformation theory for a uniform sphere, or the socalled Darwin model (e.g., Spada and Alfonsi, 1998), for the sake of simplification. This is the only difference, and the physical aspect of the rotation model is fundamentally the same (see also Appendix A.3).…”

Continental velocity through Precambrian times: The link to magmatism, crustal accretion and episodes of global cooling

“…Such rapid oscillatory APW movements have been attributed to Inertial Interchange True Polar Wander (IITPW) which could in principle, occur if interchange of the Earth's inertial axes occurs when the maximum principal inertia axis (I max ) falls below the intermediate axis (I int ) to cause the silicate outer shell to move over the liquid outer core and align the new I max with the spin axis (Goldreich and Toomre, 1969). However, it appears that the high rates of motion postulated from the Palaeozoic evidence are unlikely to be sustained by mantle structure (Tsai and Stevenson, 2007) and the short term operation of an equatorial geomagnetic field is a possible alternative explanation (Abrajevitch and Van der Voo, 2010). The polar loops that characterise Proterozoic times after w2.2 Ga (Fig.…”