Peer Reviewed Publication
University of Washington Applied Physics Laboratory
This report reviews the Marsh-Schulkin (M-S), or Colossus, model of acoustic transmission loss in shallow water in light of new information and techniques that have emerged since its introduction in 1962. The M-S model, a semiempirical model based on extensive measurements taken off the Atlantic Coast, uses several concepts; (1) refractive cycle, or skip distance; (2) deflection of energy into the bottom at high angles by scattering from the sea surface; and (3) a simplified Rayleigh two-fluid model of the bottom for sand or mud sediments. With a few free parameters, including water depth, about 100,000 measurements from 100 Hz to 10 kHz were fitted within stated error bounds. The chief criticisms of the model have been that it could not be adjusted for arbitrary negative sound-speed gradients, and that it uses empirical bottom loss values. The M-S model yields good predictions when applied properly; it is not to be used for all environments. The M-S model is compared with Rogers’ semiempirical model based on numerical calculations of the normal-mode solutions to the wave equation for propagation in shallow water. The M-S model is also extended to treat arbitrary negative and bilinear sound-speed gradients by using new general expressions for skip distance, near-field anomaly, and reflection coefficients. The reflection coefficients are calculated from the Morse-Mackenzie relations for loss per bounce.
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