Geoid anomalies in a dynamic Earth

In order to obtain a dynamically consistent relationship between the geoid and the earth's response to internal buoyancy forces, we have calculated potential and surface deformation Love numbers for internal loading. These quantities depend on the depth and harmonic degree of loading. They can be integrated as Green functions to obtain the dynamic response due to an arbitrary distribution of internal density contrasts. Spherically symmetric, self‐gravitating flow models are constructed for a variety of radial Newtonian viscosity variations and flow configurations including both whole mantle and layered convection. We demonstrate that boundary deformation due to internal loading reaches its equilibrium value on the same time scale as postglacial rebound, much less than the time scale for significant change in the convective flow pattern, by calculating relaxation times for a series of spherically symmetric viscous earth models. For uniform mantle viscosity the geoid signature due to boundary deformations is larger than that due to internal loads, resulting in net negative geoid anomalies for positive density contrasts. Geoid anomalies from intermediate‐wavelength density contrasts are amplified by up to an order of magnitude. Geoid anomalies are primarily the result of density contrasts in the interior of convecting layers; density contrasts near layer boundaries are almost completely compensated. Layered mantle convection results in smaller geoid anomalies than mantle‐wide flow for a given density contrast. Viscosity stratification leads to more complicated spectral signatures. Because of the sensitivity of the dynamic response functions to model parameters, forward models for the geoid can be used to combine several sources of geophysical data (e.g., subducted slab locations, seismic velocity anomalies, surface topography) to constrain better the structure and viscosity of the mantle.