Inference of mantle viscosity from gravity data: a genetic algorithm inversion method

Relative radial variations in the viscosity of the mantle can in principle be determined from surface gravity measurements: an analytical theory of mantle flow provides geoid kernels relating density maps and viscosity profiles to the Earth's gravity field. A scaled global tomographic map of seismic wave speeds can be used as an estimate of the Earth's density distribution. A linear inverse problem can then be set up, with gravity observations as data, and the viscosity profile as the unknown. This method has the limit of constraining only the ratios between viscosity values at the different depths, rather than the viscosity values themselves. Additionally, the solution to this inverse problem is strongly non-unique. Last, seismic velocities in the mantle are known only approximately, and establishing an appropriate velocity-to-density scaling for the mantle is, likewise, not trivial. We attempt to account for non-uniqueness in the inverse problem by exploring the solution space, formed of all possible radial profiles of Earth viscosity, by means of a non-deterministic global optimization method: the genetic algorithm. For each sampled point of the solution space, a forward calculation is conducted to determine a map of gravity anomalies, and its similarity to GRACE is then measured; the procedure is iterated to convergence, according to genetic algorithm criteria.