a) Probability distributions for shocks in front of ICMEs (to be superposed, they are drawn with curves rather than with a histogram as in Fig. 4). The blue curve, which is mostly hidden here but better shown in Fig. 11a, is the observed distribution. The other curves are four examples of adding statistical noise to the observed distribution (see Sect. 4.2). b) Corresponding deduced shock shapes from Eqs. (15) and (16) with the apex distance, ρ_max, normalized to 1 and ϕ_max = 35° (see Fig. 7 for the parameter definition).