Numerical implementation of an adaptive fast-field program for sound propagation in layered media using the chirp z transform

Using the chirp z transform, a numerically efficient adaptive integration algorithm for fast-field programs has been developed. The fast-field program (FFP) is a numerically efficient algorithm for computation of the sound pressure due to a time harmonic point source above a general boundary in a layered medium. The new algorithm allows the user to specify the precise location of the range sample points, or “detectors,” independent of the horizontal wave-number sampling grid. This feature makes the algorithm particularly attractive for use in applications where sampling on a predetermined spatial grid is required. An example of such an application is the computation of the acoustic frequency response as a function of range. In this case the complex sound pressure must be computed at many frequencies while maintaining a constant range sampling interval. In addition, the algorithm can be used to recompute the sound pressure field with different range resolutions without recomputing the horizontal wavenumber spectrum samples. It is also shown that the algorithm can be used to adaptively increase the number of integration points required to evaluate the Sommerfeld integral that results from the FFP type of formulation.