The subseismic approximation in core dynamics

Abstract

SUMMARY Scaling arguments have been used to justify the subseismic approximation (SSA) for analysing long-period oscillations of the Earth's liquid core. This approximation neglects the contribution of flow pressure to elastic compression relative to that of transport along the equilibrium pressure gradient. Here we present numerical tests of the SSA for a suite of 90 core undertones (gravity modes) in non-rotating Earth models with uniformly stable liquid cores. These tests confirm that the error incurred by invoking the SSA in the interior of the liquid core is at most 0(1 per cent), for an oscillation of ~6 hr period, and decreases with increasing period. On the other hand, the SSA is grossly violated at the core boundaries, and its adoption at the boundaries is likely to lead to serious errors in computations of the surface gravity signal associated with the oscillations. This failure of the SSA also prevents the construction of a variational principle for the subseismic wave equation in a non-neutral core with elastic boundaries.