The spectrum of tomographic earth models

The properties of mantle convection are expected to generate characteristic signatures in the spectrum of mantle heterogeneities and in its dependence on depth. The investigation of present tomographic models and the associated spectra of seismic velocity perturbations can provide insight into this problem. The characterization of heterogeneities in the mantle at all scales involves combining and comparing tomographic models at both global and regional scales. The former are expanded into the spherical harmonics domain while the latter are expanded into the Fourier domain. The comparison of both types of expansions is possible if we consider power spectral density per unit surface. Such a comparison should be carried out with great care and the scaling factors are derived to make it meaningful. The method is applied to recent global and regional tomographic models. It is shown that, contrary to previous assertions, there is an overall agreement between both kinds of models.