**Synthetic tests of geoid-viscosity inversion: a layered viscosity case**

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

_{1}

Ocean Research Institute, University of Tokyo

1-15-1, Minami-dai, Nakano-ku, Tokyo 164-8639, Japan

_{2}

Department of Earth and Planetary System Science, University of Hiroshima

Higashi-Hiroshima 739-8526, Japan

**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.

*Earth Planets Space*, **50 No.11--17**, 1055-1065, 1998.

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