*Earth Planets Space,* Vol. 50 (Nos. 11, 12), pp. 1055-1065, 1998

## Synthetic tests of geoid-viscosity inversion: A layered viscosity case

Motoyuki Kido^{1} and Satoru Honda^{2}

^{1}Ocean Research Institute,University of Tokyo, 164-8639, Japan

^{2}Department of Earth and Planetary System Science, University of Hiroshima, 739-8526, Japan

(Received April 2, 1998; Revised November 2, 1998; Accepted November 5, 1998)

**Abstract: **
We revisited the resolving power of viscosity inversion in terms of geoid misfit in a 2-D Cartesian geometry under the assumption that the mantle viscosity is laterally stratified. Firstly, we considered a simple case of two viscosity layers only, which is described by two parameters of the amount and the depth of the viscosity jump. The uniqueness of the inversion was examined by evaluating misfits between the reference geoid for a reference viscosity and that for a viscosity described by the changing two parameters. The misfits are mapped into 2-D model space as a function of the two parameters. Three types of density distribution are tested; they are vertically constant (1), taken from a tomographic model (2), and the same but includes artificial noise (3). We found that, at least for this simple case, the viscosity solution keeps unique in the entire 2-D model space using whole degree band (1-8) of geoid. This holds even if the artificial noise is rather large (70%), though the solution is slightly different from the reference viscosity. However, we also observed non-uniqueness, such as trade-off between the two parameters, when individual degree components of geoid are concerned. In the next, we employed a more realistic viscosity structure, having seven iso-viscous layers. It is no longer possible to describe 6-D model space easily. Therefore we tried to reconstruct a reference viscosity from the reference geoid using genetic algorithm search. According to this analysis, nearly the same solution with the reference viscosity can be reconstructed, while solutions apart from the reference viscosity with increase of noise in the density distribution.

Corresponding author E-mail: kido@ori.u-tokyo.ac.jp

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