Direct contribution of the surface layers to the Earth's dynamical flattening

The global dynamic flattening (H) is an important quantity in research of rotating Earth. Precession observations give H_obs = 0.0032737 ≈ 1/305.5. We recalculate the geometrical flattening profile of the Earth interior from potential theory in hydrostatic equilibrium. Results coincide with that of Denis (1989). We derive expression for H to the third-order accuracy and obtain H_PREM = 1/308.5. This matches similar studies, in which there is a difference about 1% between this and the observed value. In order to understand where this difference comes from, we replace the homogenous outermost crust and oceanic layers in PREM with some real surface layers data, such as oceanic layer (ECCO), topography data (GTOPO30), crust data (CRUST2.0) and mixed data (ETOPO5). Our results deviate from the observed value more than H_PREM. These results verify the isostasy theory indirectly and may imply that the "positive" effects from such as mantle circulation associated with the density anomalies maybe larger than thought before.