Negative dispersion of quantitative ultrasound is uncommon in biological tissues. This thesis aims to explore the underlying physical mechanism, which causes the negative dispersion phenomenon in cancellous bone using a stratified model. We develop a full wave method, which considers all scattering paths within the model and anelasticity. We also employ an approximation method to compute dispersion and attenuation analytically.

Based on our numerical results, the simulated signal displays strong scattering. Negative dispersion is obvious. Undoubtedly, multiple scattering is a dominant physical process and m ight be a potential indicator to discriminate normal and abnormal bones. For the periodic case, the frequency spectrum shows "periodic" passing and stopping-bands. With in the primary passing band, the phase velocity decreases with frequency. With in the stopping band, the frequency components have no contribution to the time response. Comparisons between the two methods agree well, especially in the primary band.