Average arrival time of wave pulses through continuous random media

It is pointed out that a continuous random medium can cause an average advance of the arrival time of a pulse. This advance will occur for unsaturated and partially saturated propagation, but not in full saturation (which corresponds to the discrete scatterer case). The effect, which is associated with Fermat's principle of least time, can be observed by measuring the difference between intensity-weighted and unweighted average arrival times.