Ultrasonic wave dispersion and attenuation in a periodically two-layered medium [cancellous bone modeling]

In this work, we use numerical method to simulate wavefield propagation through a stratified cancellous bone model. A broadband Berlage pulse with a dominant frequency of 0.9 MHz was used to simulate an ultrasonic signal traveling through the model. Based on our preliminary work of elastic cases, the simulated signal displayed strong reverberation after the main transmitted arrival, demonstrating strong scattering within the stratification. The frequency spectrum shows "periodic" passing and stopping-bands. Within the primary passing band, the phase velocity decreases with frequency and the attenuation increases mildly with frequency. Within the stopping bands, the medium supports a constant phase velocity, with maximum attenuation but wave transmission is prohibited. The first cutoff frequency increases apparently with the decrease of the thickness of the two-layered period. It is interesting that these results could be quite accurately predicted using the approximation theory, which does not consider any multiple scattering within the stratification.