Radial models of mantle viscosity: results from a genetic algorithm

SUMMARY The long‐wavelength component of the geoid has been used to constrain radial variations in mantle viscosity using 3‐D velocity anomaly models determined from seismic tomography as the buoyancy forces driving viscous flow. Using a Genetic Algorithm (GA), the robustness of mantle viscosity models obtained by calculus‐based optimization methods is investigated. GAS are a relatively new class of optimization techniques, which are generating a growing interest in the geophysics community. These methods can be particularly useful for solving highly non‐linear optimization problems. Unlike traditional techniques, GAS do not require derivative information to form a Jacobian matrix or sensitivity kernels. Models are constructed from pieces of successful models following a simple set of rules. These simple rules are driven by stochastic, rather than deterministic, means. Because of the efficiency of the GA for the mantle viscosity problem, it is possible to explore a greater range of potential solutions than with a traditional optimization method. It is found that, while both calculus‐based and GA optimization methods find viscosity models with a low‐viscosity transition zone, the GA finds another class of models, with a high viscosity in the transition zone, that also satisfies the geoid data. The geoid alone is unable to resolve low‐viscosity transition‐zone models from high‐viscosity transition‐zone models. The effect of the scaling between seismic velocity and density on the preferred viscosity model is also explored. While a velocity‐to‐density scaling with a pronounced increase in the transition zone provides the best fit to the geoid, the preferred vertical viscosity profile is insensitive to the velocity‐to‐density scaling.