Erratum to: Seismic waves in 3-D: from mantle asymmetries to reliable seismic hazard assessment

Acknowledgments This paper is strongly relying upon the work of many colleagues and collaborators to whom we are greatly thankful, in particular: Carlo Doglioni, Gillian Foulger, Vahid Gholami, Hossein Hamzehloo, Volodya Kossobokov, Cristina La Mura, Anatoly Levshin, Andrea Magrin, Antonella Peresan, Federica Riguzzi, Franco Vaccari, Peter Varga, Tatiana Yanovskaya. Financial support from PRIN 2010-2011 and RITMARE projects, funded by Italian Ministry of University and Research, is gratefully acknowledged. In addition, Fig. 3 should be updated by new one as below