Pseudoresonances and virtual modes in underwater sound propagation

Abstract

An underwater sound field can be expressed as a sum over a set of continuous normal modes (or a suitable branch line integral, BLI) plus a sum of discrete normal modes. It is known that the significant contributions of the continuous modes come from resonances in the integrand of the BLI—strong, sharp, symmetric peaks which can be located and approximated. Each strong resonance gives rise to a virtual mode, resembling a discrete mode except as to range dependence. We show that there may also be a pseudoresonance—strong, sharp, but asymmetric—which contributes a virtual mode of still different range dependence. A pseudoresonance occurs whenever the highest discrete mode is very near or at cutoff, or when physical parameters almost allow one more discrete mode. Sometimes a pseudoresonance may be the major or the only contributor from the BLI. Equations to fit a pseudoresonance are defined in a special case, and calculation of each consequent virtual mode is carried out. The special case, a homogeneous water layer overlying a bottom half space, was chosen to allow analytical calculations throughout, but pseudoresonances and consequent virtual modes are not peculiar to this case.