The Institute of Air Transportation Systems in Hamburg, Germany, researches methodologies for optimized supersonic flight routing that prevents the (primary) sonic boom from reaching the ground. The sonic boom shall either be cut off vertically or laterally. In initial trials, lateral cutoff positions of the sonic boom carpet were searched geometrically by ray tracing. Thereby, it was found that smooth interpolation of atmospheric data is necessary for geometrical convergence of different ray tracing methods, and that determining the marginal ray was oftentimes virtually impossible leeward. (These findings will be elaborated in more detail.) For those reasons, acoustic propagation has been introduced based on the Augmented Burgers equation, and implementing the Tricomi equation for covering flight maneuvers is planned in the short term. Our main research goal is finding numerical methods for determining the acoustic sonic boom cutoff that are first and foremost practical, i.e., fast, accurate, and robust. In this respect, we will discuss different termination conditions in signature propagation for the purpose of sonic boom carpet computation.