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Prediction of attenuation of acoustic fields in weakly absorbing media often uses the substitution of (omega/c)--&gt;(omega/c)+ialpha(pw) into the idealized equations for constant frequency, with alpha(pw) representing the local plane wave attenuation coefficient. This assumption is flawed whenever the local absorption of sound is proportional to the square of the gradient of the acoustic pressure, as is the case when the absorption is caused by fluid velocity relaxation. A realistic analysis yields an improved weighting function over depth for determination of guided mode attenuation coefficients.

Relation of sound absorption and shallow water modal attenuation to plane wave attenuation