Numerically efficient spectral representations for guided ocean acoustics

Abstract

Spectral representations play an important role in the mathematical modeling of ocean acoustic propagation. Such representations, usually employed for range-independent oceans, can take the form of spectral integrals, of normal mode expansions with or (approximately) without continuous spectra, and of generalized ray expansions or their asymptotic high-frequency approximations (ART). None of these representations individually provides a satisfactory computational option at high frequencies and over broad range intervals extending from near the source to long distances. Here, one may employ hybrid representations that combine self-consistently a more desirable mix of ray fields and normal mode fields, with any integrals that remain taken over contours whereon the integrands decay and are only weakly oscillatory. Hybrid formulations can also repair deficiencies in complicated transitional domains of ART, and they can overcome the proliferation of ray species, due to ray splitting at boundaries and interfaces, when the model incorporates elastic layers. For weakly range-dependent models, spectral integrals can be devised that track the sound field uniformly through cutoff regions of local modes. Examples are shown to illustrate these concepts and their numerical implementation for time-harmonic and time-dependent propagation in various model environments.