Current understanding of the acoustic processes occurring in the seafloor is used to develop a detailed ray approach for simulating the received time series of a broadband acoustical signal interacting once with the seafloor. The environment is assumed to be horizontally stratified, and the seafloor is described in terms of a geoacoustic profile. The frequency response is constructed from the superposition of the individual responses of each of the eigenrays. The ray approach includes the effects of reflection from the water–sediment interface, penetration into the sediment, refraction due to a constant compressional sound‐speed gradient in the sediment, absorption within the sediment, phase shifts due to caustics, and multipaths. The one‐bounce time series is constructed from the inverse Fourier transform of the product of the source spectrum and the eigenray frequency response. As an example application, the one‐bounce time series for an explosive source in a deep water environment is calculated and analyzed in terms of acoustical processes. Excellent agreement with measured time series is demonstrated.