Most of our knowledge about the physical structure and the chemical composition of the Earth's deep interior is inferred from seismic data. The interpretation of seismic waves generally follows the assumption that the Earth's physical structure is grossly layered and that fluctuations of the physical parameters within individual layers are smooth in structure and small in magnitude. While this view greatly facilitates the analytic and interpretative procedure, it is clearly at odds with evidence from outcrops and boreholes, which indicates that compositional, structural and petrophysical...