A Mixture Density Network (MDN), as introduced by Bishop (1995). The output of an MDN approximates a parametric distribution p(t|x) for the target t, conditioned on the input x. The parameters describing this distribution are given by the output z of a neural network, such as the MLP shown in Fig. 1. In this study, the input consists of traveltime data d, while the target represents the parameters of interest m′, which form a subspace of the l-dimensional radial P-wave velocity earth model m (eqs 1 and 2).