Using probabilistic seismic tomography to test mantle velocity–density relationships

We use a neighborhood algorithm to explore the fit to long period seismic data of a wide variety of long wavelength mantle models. This approach to the global tomographic inverse problem yields probability distributions for seismic velocities, density, and related properties as functions of depth. Such distributions can be robust even when individual models are not, and allow us to test several assumptions about the Earth that have long been enforced a priori in inversions. In particular, we are able to test the paradigm ofdeep mantle heterogeneity that is dominantly thermal in origin, producing velocity and density perturbations that are well correlated and have relative amplitudes given by Nlnb/Nlnvs 6 0.5. Our distributions show that such relationships are unlikely, and even though the results are consistent with recent best fitting models from damped seismic inversions, they demonstrate that many specific properties ofsuch models are not robust. The data clearly f density perturbations that are poorly or negatively correlated with velocity heterogeneity and have amplitudes several times larger (yielding Nlnb/Nlnvs s 1.0) than damped inversions allow. These characteristics are most pronounced in the upper mantle transition zone and the base ofthe lower mantle, suggesting layered convection. The negative density^velocity correlations f at these depths imply dominantly chemical heterogeneity, while the likelihood ofrelatively high amplitude density variations suggests that variable iron content is an important component ofthis heterogeneity. These results, which we show to be consistent with independent gravity constraints, represent a profound change in the interpretation of seismic constraints. In addition, the distributions show that even though best fitting density models from recent inversions or our sampling are consistent with the data, most specific properties of such models are not robust. This implies that it is more appropriate to use seismic model distributions, rather than individual models, to make geodynamic and geochemical inferences.