Starting from Newton, the main equations of physics are differential equations -- which implicitly implies that all the corresponding processes are differentiable -- and thus, continuous. However, in practice, we often encounter processes or objects that change abruptly in time or in space. In physics, we have phase transitions when the properties change abruptly. In geosciences, we have sharp boundaries between different layers and discontinuing representing faults. In many such situations, it is important to detect these discontinuities. In some cases, we know the equations, but in many other cases, we do not know the equations, we only know that the corresponding process is discontinuous. In this paper, we show that by applying the soft computing techniques to translate this imprecise knowledge into a precise strategy, we can get an efficient algorithm for detecting discontinuities; its efficiency is shown on the example of detecting a fault based on the seismic signals.