Acoustic pulse transmission in half‐spaces and finite‐length cylindrical rods

Abstract

A combination of both dynamic finite‐element modeling (DFEM) and analytical techniques is used to evaluate the geometric attenuation of acoustic pulses propagated in elastic half‐spaces and finite‐length elastic cylindrical rods. Solutions for the half‐space are presented in a scale‐independent form and are relevant to the study of pulse propagation in large rock masses. For example, it is shown that if a surface‐mounted source has most of its spectral output below approximately 20 kHz, then the transmitted acoustic pulse within 1 m of the source exhibits a pulse‐shape distortion due to geometric attenuation that may dominate the distortion due to material attenuation. The results for the cylindrical rod are relevant to the study of pulse propagation in rock cores, and for this case the geometric effect yields a large increase in pulse‐shape distortion as a function of the distance from the source. For an aluminum cylindrical rod 1.0 m long, 0.05 m in diameter, and having a P‐wave velocity of 6 175 m/s, the geometric attenuation of acoustic pulses having rise times of approximately five microseconds is over 20 times larger than the material attenuation obtained for silica dolomite. In all studies, good agreement was found between the DFEM solution and the appropriate analytical solution. Furthermore, good agreement was also found between a DFEM solution and experimental results for acoustic pulse propagation along the cylindrical aluminum bar.