Long-term rotational effects on the shape of the Earth and its oceans

The centrifugal potential associated with the Earth's rotation influences the shape of both the solid Earth and the oceans. Changes in rotation thus deform both the ocean and solid surfaces.; The equilibrium form of the rotating Earth is generally computed using hydrostatic theory that treats the planet as an inviscid body. I have found that a thin elastic shell acts to reduce the flattening of the equilibrium form relative to the value obtained from the traditional hydrostatic calculation. Furthermore, this perturbation is large enough that the excess non-hydrostatic flattening of the Earth, defined as the difference between the observed and hydrostatic forms, may be a significant underestimate of the departure of the observed form from its equilibrium state.; The ocean surface and the Earth's solid surface deform by different amounts in response to an applied potential load and thus a relative sea-level change is produced. Due to the presence of the elastic lithosphere and slowly decaying modes of viscous relaxation within the mantle, even geologically long potential forcings can produce a non-negligible sea-level signal. Using the geologically constrained history of rotational variations over the past 130 million years (the Cretaceous-Tertiary) I have found that the sea-level signal induced by true polar wander may be as large as the sea-level change that has been observationally inferred for that time. True polar wander produces a long wavelength global pattern of sea-level trends that may be mistaken for a uniform signal. The well-documented, and presumed global, Cretaceous-Tertiary sea-level cycle should therefore be reinterpreted as a combination of a globally uniform and a spatially varying true polar wander signal. Furthermore, the distinct pattern of the induced sea-level variations enables the use of regional sea-level records as a test of, often contentious, true polar wander events proposed on the basis of paleomagnetic data. A preliminary sea-level test of a proposed Early Cambrian inertial interchange true polar wander event found good general agreement between predicted and observed sea-level trends. Observational sea-level constraints were not found to provide consistent support for a rapid true polar wander event proposed for the Late Cretaceous.