Theoretical constraints on true polar wander

[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 tau(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 delta C, and the added moment of inertia due to the equatorial bulge (C - A). For the nominal values eta = 3 x 10(22) Pa s and delta C/(C - A) = 0.003, the maximum TPW is 61 degrees over 100 Myr and 8 degrees over 10 Myr. The maximum TPW speed is only sensitive to eta, delta C, and (C - A), and is 2.4 degrees 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.