Internal loading of an inhomogeneous compressible earth with phase boundaries

We use an approach described by Dehant & Wahr (1991) to estimate the geoid and boundary topography caused by mass loads inside the Earth. We show how the estimates are affected by compressibility and a radially varying density distribution, and by the presence of phase boundaries with density discontinuities. We compare results for earth models that have a chemical boundary at 670 km depth with those that have a phase boundary at that depth. We find that the 670 km topographies predicted for models with a chemical boundary are several times larger than for models with a phase boundary, depending principally on the value of the Clapeyron slope in the phase case. The geoid predicted in the chemical boundary case is about 30-40 per cent smaller than that predicted in the phase case. The effects of compressibility and radially varying density are likely to be small. We estimate the laterally varying structure inside the fluid core by computing the topography on constant-potential surfaces within the core. We conclude that this structure is not likely to be a complicating factor when using nutation and Earth tide observations to estimate the flattening of the core-mantle boundary. Finally, we compute the inner core-outer core (icb) topography for loading inside the mantle and for loading inside the inner core. We show that in the first case, the icb topography is small and dominated by long wavelengths; in the second case, we conclude that, if the density heterogeneities inside the inner core are two orders of magnitude smaller than in the mantle, the icb topography can be about 100 m peak-to-peak.