Refraction of Sound in a Horizontally Inhomogeneous, Time-Dependent Ocean

Measurements of the three-dimensional (3-D) structure of a sound-speed field in the ocean with the spatial and temporal resolution required for prediction of acoustic fields are extremely demanding in terms of experimental assets, and they are rarely available in practice. In this study, a simple analytic technique is developed within the ray approximation to quantify the uncertainty in acoustic travel time and propagation direction that results from an incomplete knowledge or purely statistical characterization of sound-speed variability in the horizontal plane. Variation of frequency of an acoustic wave emitted by a narrowband source due to a temporal variation of environmental parameters is considered for deterministic and random media. In a random medium with locally statistically homogeneous, time-dependent 3-D fluctuations of the sound speed, calculation of the signal frequency and bearing angle variances as well as the travel-time bias due to horizontal refraction is approximately reduced to integration of respective statistical parameters of the environmental fluctuations along a ray in a background, range-dependent, deterministic medium. The technique is applied to acoustic transmissions in a coastal ocean, where tidally generated nonlinear internal waves are the prevailing source of sound-speed fluctuations, and in a deep ocean, where the fluctuations are primarily due to spatially diffuse internal waves with the Garrett-Munk spectrum. The significance of 3-D and four-dimensional (4-D) acoustic effects in deep and shallow water is discussed