Effects of non‐hydrostatic core‐mantle boundary topography and core dynamics on Earth rotation

VLBI estimates for the retrograde annual nutation have shown that there is a 2 mas discrepancy with model results that assume a hydrostatically pre-stressed earth. This discrepancy has been used to infer that the non-hydrostatic Y02 component of core-mantle-boundary (CMB) topography is roughly 0.5 km in amplitude. However, the possible effects of other topographic components have not been fully examined. Based on an earth model with a rigid mantle, a homogeneous and incompressible fluid core, and a slightly non-hydrostatic core-mantle boundary, we investigate effects of the core and of non-hydrostatic CMB topography on the Earth's nutations, Chandler wobble and tidal changes of the length of day (LOD). A convergent numerical technique is developed to solve the differential and boundary equations for both the free and forced motions. In our solution, the fluid pressure is represented by a truncated sum of spherical harmonic functions in a special set of coordinates. We retain second-order CMB topographic factors with the equatorial core rotation in our nutation calculations. Using the degree variances of a recent seismically inferred CMB model (with non-hydrostatic CMB topography of about 3.5 km rms), the rms contribution of the randomly generated non-Y02 topographic components to the retrograde annual nutation is about 0.55 mas. However, the effects of CMB topography depend on the reference earth model. A simple analysis shows that nutational effects for a realistic earth, with a non-rigid mantle and realistically stratified core, can be inferred by dividing our results by a factor of 2.61. The transformation then gives an rms effect of about 0.2 mas on the retrograde annual nutation. The effects depend on some CMB components more than they do on others. For example, results as large as 0.77 mas in the retrograde annual amplitude are possible for a realistic earth due to certain individual non-Y02 CMB topographic components with mean-to-peak amplitudes of 4–5 km. The effects grow quadratically with topography, so that a 2 mas nutation amplitude would require those components to be 6–7 km in amplitude. The CMB topography is poorly known at present, but components of such magnitude may be unlikely. For the Chandler wobble and the tidal variations of LOD, the effects of CMB topography are likely to be small.

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