2A-2 Evidence that the Negative Dispersion in Bone Results from Interference Between Fast and Slow Modes Each with Positive Dispersion

Measurements from many laboratories indicate that on average the phase velocity of ultrasonic waves propagating in bone decreases with increasing frequency. This negative dispersion in bone is inconsistent with the nearly local approximation to the Kramers-Kronig relations with one subtraction that relates attenuation to dispersion. We hypothesized that observed negative dispersion in bone might result from the interference between the fast and the slow compressional waves. Supporting evidence is offered by carrying out simulations in which bone was modeled with two independent approaches: one based on the Biot-Johnson model and one independent of that model. Results of both simulations are mutually consistent and show that for cases in which the interference between the fast and slow waves has occurred, a phase spectroscopy algorithm frequently yielded an apparent negative dispersion, even though each mode separately was characterized with positive dispersion