Experimental verification of models for determining dispersion from attenuation.

A modified broadband, through-transmission technique is used to compare the accuracy of three models: a nearly local model, a time-causal model, and a discrete minimum phase model, in determining the dispersion from the measured attenuation. By directly measuring the dispersion without first measuring the absolute phase velocity at different frequencies, the new technique eliminates the needs for measuring the speed of sound in the water and the trigger delays in data sampling, and minimizes the uncertainty in determining the phase spectra. Three specimens are used in the study: a block of Plexiglas that has a linear attenuation, a layer of a special rubber compound with an attenuation proportional to f(1.38) and a phantom made of castor oil that has an attenuation proportional to f(1.67). For linear attenuation all three models accurately predict the dispersion. For nonlinear attenuation, the time causal model is shown to be the most accurate model in predicting the dispersion. The nearly local model slightly overpredicts the dispersion in the case of the rubber compound and significantly overpredicts the dispersion in the case of the castor oil. The dispersion determined by the discrete minimum phase model seems to converge to the dispersion determined by the time causal model when the limit of integration is high enough.