Numerous shallow water acoustic transmission experiments over sandy-silty bottoms demonstrate that the frequency dependence of intrinsic sediment attenuation at frequencies less than 1 kHz is nonlinear. Computational analyses including modeled geoacoustic profiles have shown that good agreement with experimental data can be obtained for frequencies between 50 Hz and 1 kHz. Upper sediment attenuation values for 1 kHz are in ranges specified by Hamilton [J. Acoust. Soc. Am. 68, 1313–1340 (1980)], and a nonlinear frequency dependent attenuation with power-law of about 1.8 is necessary. In this presentation, the relationship between the power-law exponent and modal attenuation coefficients is quantified for several nearly range-independent experiments in different locations. These include the Gulf of Mexico (1972), the Strait of Korea (ACT III, 1995), the New Jersey Shelf (1995), and Nantucket Sound (2005). The intrinsic sediment attenuation behavior with frequency and depth implies that modal attenuation coefficients may be obtained using parameters from the models of experimental environments. The behavior of range averaged transmission loss and the modal attenuations of contributing modes is examined. The former is shown to be less sensitive than the latter to parameter changes in the usual situation where the upper sediment layer is the primary source of attenuation. [Work partially supported by ONR.]

Relatively simple approximations for transmission loss in shallow water based on ray theory were presented by Marsh and Schulkin (1962), Weston (1971), Smith (1974), and Rogers (1981). Formulas for averaged transmission loss versus range in stratified shallow water waveguides over sandy-silty sediments are derived entirely from mode theory. Results are contrasted with other mode based expressions obtained by Brekhovskikh (1960) and Grachev (1983). Convenient expressions for loss in Pekeris waveguides are developed by approximating the mode number dependence of the attenuation coefficients as quadratic, which is valid in Westons’s mode stripping region. Similar loss expressions for environments with downward refracting linear sound speed profiles are constructed using modal attenuation coefficient approximations for the “limiting mode” of Denham (1969). This quantity illustrates how changes in environmental parameters, particularly thermocline strength and depth, produce corresponding changes in averaged transmission loss. The loss formulas have several terms, each having a natural physical interpretation, and each is compared with the well known results of Rogers from ray theory. The corresponding expressions have the same parameter dependence, thereby providing a modal foundation for Rogers’s formulas. [Work partially supported by the ONR.]

Sound speed profiles in shallow water waveguides are small deviations from isospeed and often decrease monotonically with depth. Approximation formulas for the propagating modes are found using a modified form of the classical WKBJ method. The ocean bottom is taken as homogeneous. The approach is accurate for modes with phase speeds greater than, and even slightly less than, the maximum water sound speed. The validity and accuracy of the approximations over frequency and mode number are illustrated using benchmark numerical calculations. Comparisons with approximations from other methods, including previous WKBJ approaches, are described. The formulas here are typically more compact and convenient. The results demonstrate how changes in parameters, such as frequency, bottom sound speed, and water sound speed profile quantitatively affect the mode functions. Applications for representative waveguide profiles are provided. [Work supported by the Office of Naval Research.]

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