Accurate models of the distribution of elastic heterogeneity in the Earth's mantle are important in many areas of geophysics. The purposes of this paper is to charaterize and compare quantitatively a set of recent three-dimensional models of the elastic structure of the Earth, to assess their similarities and differences, and to analyze their fit to one class of data in order to highlight fruitful directions for future research. The aspherical models considered are the followingL M84C (Woodhouse and Dziewonski, 1984), LO2.56 (Dziewonski, 1984), MDLSH (Tanimoto, 1990), SH.10c.17 (Masters et al., 1992), and S12-WM13 (Su et al., 1994). Through much of the discussion, M84C and L02.56 are combined into single whole mantle model, M84C+L02.56. The fit of each model to previously tabulated even degree normal mode structure coefficients taken from Smith and Masters (1989a) and Ritzwoller et al. (1988) for multiplets along the normal model fundamental and first, second, and fifth overtone branches is also presented. Rather than concentrating on detailed comparisons of specific features of the models, analyses of these models are general and statistical in nature. In particular, we focus on a comparison of the amplitude and the radial and geographical distrbition of heterogeneity in each model and how variations in each affect the fit to the normal mode observations.

In general, the results of the comparisons between the models are encouraging, especially with respect to the geopgraphical distribution of heterogenetiy and in the fit to the normal mode data sensitive to the upper mantle and lower-most lower mantle. There remain, hower, significant discrepancies in amplitude and in the radial distribution of heterogeneity, especially near the top of the upper mantle and near the top of the lower mantle. The confident use of these models to constrain compostional and dynamical information about the mantle will await the resolution of these discrepancies. The factors that may be responsible for the differences in the models and/or for the misfit between the observed and predicted normal mode data are divided into two types: intrinsic (or procedural) and extrinsic (or structural). We discuss only three extrinsic factors at length here, including errors in the reference crustal models, unmodled topography on discontinuities in the interior of the mantle, and errors in the assumed relationships between shear (&ngr;s) and compressional (&ngr;p) heterogeneity. ¿ American Geophysical Union 1995