A Model Quantifying Pulse Propagation Through Layered Attenuative Media

The influence of attenuation on pulsed ultrasonic signals has been under intense investigation especially in biomedical applications where it is most noticeable. Because attenuation depends on frequency, signals will be dissipated and dispersed as they travel through the medium. For many materials attenuation can be measured in vivo using a transmit and receive system where a pressure signal goes through a layered medium of fixed dimensions. The amount of attenuation, loosely defined as signal loss, is often found to be linearly or nearly linearly dependent on frequency. From this fact and the notion of causality it is possible to predict the phase angle of the spectrum as a function of frequency. Because this phase is nonlinearly dependent on frequency, the signal will be dispersed. This implies that transient responses experience distortion and the measured velocity of the pulse will be shifted with respect to the sound velocity expected from a lossless medium. In his paper on power law attenuation [1], Szabo has proven the amount of dispersion is maximum when the attenuation is linearly dependent on frequency and correspondingly minimum with a frequency square dependency