The Propagation of Underwater Sound at Low Frequencies as a Function of the Acoustic Properties of the Bottom

Abstract

The correlation and theoretical analysis of a large number of transmission measurements made in the Potomac River and Chesapeake Bay areas warrants the conclusions which follow. Given a source of audiofrequency sound in water, the sound pressure level which may be measured at appreciable distances will be influenced in a complicated way by the boundaries, especially by the bottom. The sea bottom may be classified by its behavior for sound as “soft,” “hard,” or intermediate in character. Specifically, the velocity of sound and the density of the bottom may be estimated from acoustic measurements (hydrophone soundings and range runs), by sampling, and from hydrographic data. The effect of the boundaries on sound propagation from a ship-mounted source may be determined from an analysis of the normal modes of vibration of the acoustic system of the sea between surface and bottom. The analysis is particularly effective for frequencies at which the wave-lengths are comparable to the physical dimensions of the system. For low frequencies and given bottom conditions, the most important factor governing the propagation is the ratio of the depth of the water to the free wave-length of the sound. A detailed interpretation of the observed transmission phenomena may be given in terms of the initial stimulation, the relative attenuation, and the phase velocities of the modes. Damping and phase constants may be determined for each mode by means of special charts which give the propagation and distribution constants in terms of the acoustic properties of the system. The over-all transmission is given as the sum of the effects produced by the individual modes. “Damped” transmission, which occurs over “soft” bottom, is always accompanied by considerable attenuation, the amount ranging in practice from about 12 db/1000 ft. as a lower limit to about 40 db/1000 ft. under conditions of strong bottom absorption. “Soft” bottoms are frequently encountered in land-locked basins such as fiords, estuaries, and river channels. “Guided” transmission which occurs over “hard” bottom at all frequencies higher than a minimum critical frequency, is characterized by negligible damping due to bottom absorption and by an attenuation with distance caused primarily by cylindrical spreading from the source. The latter amounts to 3 db per distance double. “Hybrid” transmission, which occurs over hard bottom at frequencies below the lowest critical frequency, is associated with large and erratic damping from bottom absorption. The critical frequency depends upon the hardness of the bottom, and is slightly higher than the frequency for which the water depth is equal to a quarter wave-length. The acoustic system of the sea between the surface and a hard bottom thus acts as if it were a high pass filter, analogous to an electromagnetic “wave guide.” This type of sound transmission is very commonly encountered, since hard bottom predominates along the sea coasts of all the continents.

A High-Efficiency Spectral Method for Two-Dimensional Ocean Acoustic Propagation Calculations

“…where the matrix K is a diagonal matrix with dimensions of (N + 1) × (N + 1) and the diagonal element value is determined by c k in Equation (8).…”

“…Currently, many simplified models of the Helmholtz equation have been developed, such as the parabolic equation model, normal mode model, and ray model. Each simplified model has its own applicable conditions; for instance, the parabolic equation model is suitable only for situations in which the physical parameters change slowly with the horizontal distance [ 7 ], while the normal mode model is appropriate only for cases in which the physical parameters are constant [ 8 ], and the ray model needs to be applied under high-frequency situations [ 9 ]. However, actual sound fields are relatively complex; hence, relatively few sound fields meet the constrained requirements of various models, making it difficult to calculate the ocean acoustic propagation through a simplified model.…”

30 CPS Sound Propagation in Shallow Water

“…1 , 2 The practical importance of this subject, for example in the prob- With the particular amplifier available, it was necessary to read the signals from the two hydrophones alternately and it is possible that some fine details of the sound pressure amplitude vs range curves were lost as a consequence. At Station II the currents and wind were weak enough so that it was possible to move a workboat along a desired radial path by pulling it with a line from the lighter.…”