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It has recently been realized that supernova neutrino signals may be affectedby shock propagation over a time interval of a few seconds after bounce. In thestandard three-neutrino oscillation scenario, such effects crucially depend onthe neutrino level crossing probability P_H in the 1-3 sector. By using asimplified parametrization of the time-dependent supernova radial densityprofile, we explicitly show that simple analytical expressions for P_Haccurately reproduce the phase-averaged results of numerical calculations inthe relevant parameter space. Such expressions are then used to study thestructure of P_H as a function of energy and time, with particular attention tocases involving multiple crossing along the shock profile. Illustrativeapplications are given in terms of positron spectra generated by supernovaelectron antineutrinos through inverse beta decay.Comment: Major changes both in the text and in the figures in order to include  the effect of a step-like shock front density profile; final version to  appear in Physical Review

Analysis of energy and time dependence of supernova shock effects on neutrino crossing probabilities