Dynamical effects from equation of state on topographies and geoid anomalies due to internal loading

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Abstract
The effects of mantle compressibility on geoid and topographic signatures caused by internal loading in the mantle are studied. For a Cartesian compressible model the Green's functions of these geophysical signatures are determined by solving a two‐point boundary value problem with depth for each horizontal wave number associated with the density anomaly. Various types of equations of state have been considered, which include both constant and depth‐dependent thermodynamic parameters. Surface topographies are not changed too much by the effects of mantle compressibility, even for long wavelengths. The deformation of bottom boundary is not seriously influenced by mantle compressibility, except for long wavelengths and large viscosity contrasts between the upper and lower mantles. Geoid signals with horizontal wavelengths, exceeding 10,000 km, can be greatly influenced by mantle compressibility. For large viscosity contrasts, differences of up to 100% between incompressible and compressible geoid responses can be found. The admittance function also shows great sensitivity to mantle compressibility at long wavelengths. There are significant differences in the geophysical signatures from the ways in parameterizing the viscosity stratification in the mantle. An exponentially dependent viscosity model produces smaller geoid and surface topographical signals than for a single step function viscosity model.