An important research direction has been to develop ways in which the numerical results can be compared to observations, particularly those arising from global seismic tomographic models. Most convection models make no attempt to simulate the exact configuration of convection or density anomalies within in the current Earth; thus, such comparisons are made by extracting various diagnostics from the tomographic models and convection models.
One such diagnostic is the character of lateral heterogeneity at different depths, which has two components: the horizontally-averaged root mean square amplitude [ Peltier and Solheim, 1992; Tackley et al., 1993], and the shape of the spectrum, i.e., amplitude as a function of spherical harmonic degree [ Tackley et al., 1994]. The shape of the spectrum as a function of depth shows strong similarities between global tomographic models and the 3-D spherical models of Tackley et al. [1993, 1994]. In particular, there is a change in the slope of the spectrum at 660 km depth, from a red spectrum in the upper mantle, to a much broader 'pink' spectrum in the mid mantle. However, there are significant differences in the radial profile of total (rms.) amplitude, and in particular, there is little evidence in the seismic models for the strong peak in heterogeneity at 660 km depth observed in the convection models, although such peaks can be observed in local regions [ Woodward et al., 1994].
Some studies have focused on the radial correlation function [ Jordan et al., 1993; Puster and Jordan, 1994], which is simply the cross-correlation between different radial shells. For convection models with complete layering [ Glatzmaier and Schubert, 1993] or with phase transitions [ Tackley et al., 1993, 1994], there is a strong decorrelation of features across the 660 km discontinuity, which is not observed in most of the current global seismic tomographic models, leading these authors to favor predominantly whole mantle convection.
When comparing convection models with seismic tomography, however, a problem arises because the dynamically important features are at very small wavelengths ( 100 km) whereas global seismic tomography can only resolve very long wavelengths (>Å4000 km). In addition, the tomographic process applies a complex and uneven filtering to the pattern of heterogeneity in the Earth. These problems have been investigated by Johnson et al. [1993], who passed rays through convective datasets generated by Tackley et al. [1993], and performed synthetic seismic inversions. They found that globally averaged diagnostics are quite sensitive to the inversion parameters, although the overall broad-scale structure remained fairly robust.
Another class of diagnostic is based on the flow field, rather than thermal or seismic velocity fields, and in particular, the radial mass flux as a function of radius. The inhibitive effect of the 660 km phase transition is indicated by a minimum in the radial mass flux at this depth [ Peltier and Solheim, 1992]. However, numerical simulations of Tackley et al. [1994] show that the inhibitive effect of the phase transition on the flow is strongly dependent on wavelength, such that long wavelengths pass though the phase transition uninhibited, but short wavelengths of flow are inhibited from crossing the phase transition. Thus, it is possible for whole-mantle flow to be exhibited at long wavelengths, but for short wavelength features, such as slabs, to be deflected by the phase transition. Phipps Morgan and Shearer [1993] calculated the long-wavelength (up to spherical harmonic degree 10) flow field of the mantle, deduced from seismic tomography combined with mass anomalies calculated from global mapping of the 660 km discontinuity topography [ Shearer and Masters, 1992; Shearer, 1993], and find that at these long wavelengths, whole mantle convection is present, compatible with the numerical results.
The geoid is another important geophysical observable. Zhang and Christensen [1993] use a semi-dynamical spherical-shell model including the 660 km phase transition to compute geoid anomalies arising from the past 65 million years of subduction, finding that the geoid fit is much better when the Clapeyron slope is weak enough for slabs to penetrate into the lower mantle. Tackley et al. [1994] compare geoid spectra for theoretical simulations with and without phase transitions, and show that the partial layering induced by the endothermic phase transition does not have a large effect on the geoid amplitude, because the contribution of increased heterogeneity in the transitions zone is offset by an opposite and nearly equal contribution from deflection of the phase boundary. If the deflection of the 660 km discontinuity were large enough to enforce completely layered convection at long wavelengths, the resulting geoid signal would be too large (J. Phipps Morgan, and P.M. Shearer, Seismic and geoid constraints on mantle flow: Evidence for whole mantle convection, submitted to J. Geophys. Res., 1994).
Another approach to comparing numerical results to seismic Earth models is to combine seismic velocity anomalies with mineral physics results to estimate the magnitude of temperature anomalies in the deep mantle, to compare with results from numerical simulations. Cadek et al. [1994] and Yuen et al. [1993] performed such a calculation and found very cold anomalies (-1500 K) in the deep mantle, which are more compatible with rapidly emplaced cold material arising from avalanche events than with a quasi steady-state scenario of downwelling slabs.