Seismic tomography (Tanimoto 1990, Su & Dziewonski 1991 and Masters et al. 1992) has provided detailed three-dimensional map of the shear wave velocity in the Earth's mantle. These tomographic results when characterized by the radial correlation function (Jordan et al. 1993) shows no signature of the mantle transition zone. The radial correlation function and associated radial correlation length are subsets of the entire two-point correlation and therefore here we propose an optimal characterization of the two-point correlation in terms of its eigenfunctions. It is shown that the eigenrepresentation of the tomographic data converges rapidly and that the most energetic eigenfunctions reveal the signature of the mantle transition zone. ¿ American Geophysical Union 1995