Efficient approach to computing travel time with the parabolic equation model

An efficient method for computing the travel time of an acoustic wave using the parabolic equation model is presented. The frequency derivative of the acoustic phase is the differential travel time associated with a propagation in range. By taking this difference across closely spaced frequencies this method computes the acoustic travel time. This method requires the computation of the field at two frequencies rather than over the full band. The method compares well with other travel time methods for four different cases, including deep water, upslope and shallow water, and a three-dimensional propagation environment.