A Complutense International Seminar on "Earth Sciences and Mathematics" was organised and held in Madrid at the Facultad de Ciencias Matemáticas of the Universidad Complutense de Madrid in September 2006. Scientists from both fields, Mathematics and Earth Sciences, took part in this International Seminar, addressing scientific problems related to our planet from clearly complementary approaches, seeking to gain and learn from this dual approach and proposing a closer collaboration in the near future. This volume is the second one of a Topical Issue on "Earth Sciences and Mathematics" and contains papers addressing different topics as analysis of InSAR time series, fuzzy classification for remote sensing, modelling gravitational instabilities, geodynamical evolution of the Alboran Sea, statistical warning systems for volcanic hazards, analysis of solutions for the hydrological cycle, study of the ice flow, magma intrusion in elastic layered media, river channel formation, Hartley transform filters for continuous GPS, and deformation modeling.

Introduction to Earth Sciences and Mathematics, Volume II (A. G. Camacho, J. I. Díaz, J. Fernández).- On the mathematical analysis of an elastic-gravitational layered Earth model for magmatic intrusion: The stationary case (A. Arjona, J.I. Díaz, J. Fernández, and J.B. Rundle).- Modelling gravitational instabilities: slab break-off and Rayleigh-Taylor diapirism (S. Zlotnik, M. Fernández and P. Díez).- On the coupling between channel level and surface ground water flows (S. N. Antonsev, and J.I. Díez).- Time evolution od deformation using time series of differential interferograms: Application to La Palma Island (Canary Islands) (P.A. Perlock, P.J. González, K.F. Tiampo, G. Rodríguez-Velasco, S. Samsonov, and J. Fernández).- Improvements to remote sensing using fuzzy classification, graphs and accuracy statistics (D. Gómez, J. Montero, and G. Biging).- Postseismic deformation following the 1994 Northridge earthquake identified using the localized Hartley transform filter (K. F. Tiampo, D. Assefa, J. Fernández, L. Mansinha, and H. Rasmussen).- A mathematical study of the ice flow behaviour in a neighbourhood of the grounding line (M. A. Fontelos, and A. I. Muñoz).- A warning system for Stromboli volcano based on statistical analysis (G. Nunnari, G. Puglisi, A. Spata).- Potential symmetry properties of a family of equations occurring in ice sheet dynamics Potential. (J. I. Díaz and R. Wiltshire).- Mathematical analysis of a model of river channel formation (J. I. Díaz, A. C. Fowler, A. I. Muñoz, E. Schiavi).- Asymmetric delamination and convective removal numerical modelling: comparison with evolutionary models for the Alboran sea region (J.L. Valera, A.M. Negredo, A. Villaseñor).