The effects of variations in sound speed on coupling coefficients between acoustic normal modes in shallow water over a sloping bottom

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Abstract
The conventional method for determining the coupling coefficient between acoustic normal modes in shallow water over a hard sloping bottom gives an incorrect result because it assumes the derivative normal to the bottom to be equal to the depth derivative. This problem can be circumvented by measuring depth normal to the bottom. The coupling coefficients determined in this manner are found to be at least three times smaller or larger than the corresponding conventional results (the exact ratio depends on the mode numbers). For well‐trapped modes in isospeed water over a sloping bottom with a finite sound speed, the coupling coefficient is approximately the same as would occur if there were a virtual pressure release surface at a fixed distance beneath the actual seafloor. This distance is typically about 30% greater than the cutoff water depth for the frequency under consideration. If the water column is not isospeed, then the depth functions of the modes can be expressed as perturbation series of the sinusoidal functions that correspond to the isospeed case. A negative sound‐speed gradient increases the coupling coefficients and, providing the sound speed does not exceed the phase velocity of the unperturbed modes, the increase is proportional to the relative variability of the sound‐speed profile.

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